doc/specification/srp.ps

   1 %!PS-Adobe-2.0
   2 %%Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software
   3 %%Title: srp3.dvi
   4 %%Pages: 17
   5 %%PageOrder: Ascend
   6 %%BoundingBox: 0 0 612 792
   7 %%DocumentPaperSizes: Letter
   8 %%EndComments
   9 %DVIPSCommandLine: dvips -o srp3.ps srp3.dvi
  10 %DVIPSParameters: dpi=600, comments removed
  11 %DVIPSSource:  TeX output 1997.11.11:0522
  12 %%BeginProcSet: tex.pro
  13 /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N
  14 /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72
  15 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1}
  16 ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale
  17 isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div
  18 hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul
  19 TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if}
  20 forall round exch round exch]setmatrix}N /@landscape{/isls true N}B
  21 /@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B
  22 /FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{
  23 /nn 8 dict N nn begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N
  24 string /base X array /BitMaps X /BuildChar{CharBuilder}N /Encoding IE N
  25 end dup{/foo setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /df{
  26 /sf 1 N /fntrx FMat N df-tail}B /dfs{div /sf X /fntrx[sf 0 0 sf neg 0 0]
  27 N df-tail}B /E{pop nn dup definefont setfont}B /ch-width{ch-data dup
  28 length 5 sub get}B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{
  29 128 ch-data dup length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub
  30 get 127 sub}B /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data
  31 dup type /stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N
  32 /rc 0 N /gp 0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup
  33 /base get 2 index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx
  34 0 ch-xoff ch-yoff ch-height sub ch-xoff ch-width add ch-yoff
  35 setcachedevice ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff
  36 .1 sub]{ch-image}imagemask restore}B /D{/cc X dup type /stringtype ne{]}
  37 if nn /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup
  38 length 1 sub dup 2 index S get sf div put}if put /ctr ctr 1 add N}B /I{
  39 cc 1 add D}B /bop{userdict /bop-hook known{bop-hook}if /SI save N @rigin
  40 0 0 moveto /V matrix currentmatrix dup 1 get dup mul exch 0 get dup mul
  41 add .99 lt{/QV}{/RV}ifelse load def pop pop}N /eop{SI restore userdict
  42 /eop-hook known{eop-hook}if showpage}N /@start{userdict /start-hook
  43 known{start-hook}if pop /VResolution X /Resolution X 1000 div /DVImag X
  44 /IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for
  45 65781.76 div /vsize X 65781.76 div /hsize X}N /p{show}N /RMat[1 0 0 -1 0
  46 0]N /BDot 260 string N /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V
  47 {}B /RV statusdict begin /product where{pop product dup length 7 ge{0 7
  48 getinterval dup(Display)eq exch 0 4 getinterval(NeXT)eq or}{pop false}
  49 ifelse}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale rulex ruley false
  50 RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR rulex ruley scale 1 1
  51 false RMat{BDot}imagemask grestore}}ifelse B /QV{gsave newpath transform
  52 round exch round exch itransform moveto rulex 0 rlineto 0 ruley neg
  53 rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta 0 N /tail
  54 {dup /delta X 0 rmoveto}B /M{S p delta add tail}B /b{S p tail}B /c{-4 M}
  55 B /d{-3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{3 M}B /k{
  56 4 M}B /w{0 rmoveto}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p -1 w}B /q{
  57 p 1 w}B /r{p 2 w}B /s{p 3 w}B /t{p 4 w}B /x{0 S rmoveto}B /y{3 2 roll p
  58 a}B /bos{/SS save N}B /eos{SS restore}B end
  59 %%EndProcSet
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4251 0000001E00000003C00000000000000E00000003800000005D3F7FBD60>119
4252 D E end
4253 %%EndProlog
4254 %%BeginSetup
4255 %%Feature: *Resolution 600dpi
4256 TeXDict begin
4257 %%PaperSize: Letter
4258
4259 %%EndSetup
4260 %%Page: 1 1
4261 1 0 bop 831 739 a Ft(The)43 b(Secure)i(Remote)e(P)l(assw)l(ord)f(Proto)
4262 t(col)3069 687 y Fs(\003)1690 980 y Fr(Thomas)32 b(W)-8
4263 b(u)1294 1096 y(Computer)32 b(Science)i(Departmen)m(t)1532
4264 1212 y(Stanford)f(Univ)m(ersit)m(y)1463 1328 y Fq(tjw@cs.Stanford.EDU)
4265 1544 1524 y Fr(No)m(v)m(em)m(b)s(er)g(11,)f(1997)1767
4266 1914 y Fp(Abstract)332 2049 y Fo(This)i(pap)r(er)f(presen)n(ts)f(a)i
4267 (new)f(passw)n(ord)f(authen)n(tication)h(and)g(k)n(ey-exc)n(hange)e
4268 (proto)r(col)i(suitable)g(for)208 2148 y(authen)n(ticating)d(users)g
4269 (and)g(exc)n(hanging)f(k)n(eys)h(o)n(v)n(er)f(an)i(un)n(trusted)f(net)n
4270 (w)n(ork.)45 b(The)31 b(new)g(proto)r(col)e(resists)208
4271 2248 y(dictionary)e(attac)n(ks)g(moun)n(ted)i(b)n(y)f(either)g(passiv)n
4272 (e)f(or)h(activ)n(e)g(net)n(w)n(ork)f(in)n(truders,)h(allo)n(wing,)f
4273 (in)i(principle,)208 2347 y(ev)n(en)j(w)n(eak)h(passphrases)e(to)i(b)r
4274 (e)h(used)f(safely)-7 b(.)54 b(It)34 b(also)e(o\013ers)g(p)r(erfect)i
4275 Fn(forwar)l(d)j(se)l(cr)l(e)l(cy)p Fo(,)e(whic)n(h)e(protects)208
4276 2447 y(past)f(sessions)e(and)j(passw)n(ords)d(against)h(future)h
4277 (compromises.)50 b(Finally)-7 b(,)33 b(user)f(passw)n(ords)e(are)h
4278 (stored)g(in)208 2547 y(a)i(form)h(that)g(is)g(not)f
4279 Fn(plaintext-e)l(quivalent)i Fo(to)e(the)i(passw)n(ord)d(itself,)k(so)d
4280 (an)g(attac)n(k)n(er)f(who)i(captures)f(the)208 2646
4281 y(passw)n(ord)c(database)g(cannot)i(use)g(it)g(directly)g(to)g
4282 (compromise)e(securit)n(y)i(and)f(gain)h(immediate)g(access)f(to)208
4283 2746 y(the)39 b(host.)72 b(This)39 b(new)g(proto)r(col)f(com)n(bines)h
4284 (tec)n(hniques)g(of)g(zero-kno)n(wledge)d(pro)r(ofs)j(with)g
4285 (asymmetric)208 2846 y(k)n(ey)c(exc)n(hange)g(proto)r(cols)g(and)h
4286 (o\013ers)f(signi\014can)n(tly)h(impro)n(v)n(ed)f(p)r(erformance)g(o)n
4287 (v)n(er)f(comparably)h(strong)208 2945 y(extended)27
4288 b(metho)r(ds)h(that)g(resist)f(stolen-v)n(eri\014er)f(attac)n(ks)g(suc)
4289 n(h)h(as)g(Augmen)n(ted)h(EKE)e(or)h(B-SPEKE.)0 3220
4290 y Fm(1)135 b(In)l(tro)t(duction)0 3402 y Fo(P)n(assw)n(ord)29
4291 b(authen)n(tication)j(proto)r(cols)e(come)i(in)g(man)n(y)f(\015a)n(v)n
4292 (ors,)g(but)i(they)f(all)g(solv)n(e)e(the)j(same)e(problem:)45
4293 b(One)32 b(part)n(y)0 3501 y(m)n(ust)22 b(someho)n(w)e(pro)n(v)n(e)g
4294 (to)i(another)f(part)n(y)f(that)i(it)g(kno)n(ws)f(some)g(passw)n(ord)f
4295 Fl(P)12 b Fo(,)23 b(usually)e(set)h(in)g(adv)-5 b(ance.)34
4296 b(Suc)n(h)22 b(proto)r(cols)0 3601 y(range)d(from)i(the)g(trivial)f(to)
4297 h(the)g(incredibly)g(complex,)h(and)e(man)n(y)h(of)f(them)i(o\013er)e
4298 (some)g(form)h(of)g(protection)f(from)g(v)-5 b(arious)0
4299 3701 y(attac)n(ks)26 b(moun)n(ted)i(b)n(y)f(malicious)g(or)g(excessiv)n
4300 (ely)f(curious)h(third)g(parties.)125 3800 y(All)h(metho)r(ds)f(of)h(h)
4301 n(uman)f(authen)n(tication)h(fall)f(in)n(to)h(three)f(broad)g
4302 (categories:)125 3966 y Fk(\017)41 b Fo(Something)27
4303 b(the)h(user)f Fn(is)h Fo(\(v)n(oiceprin)n(t)f(iden)n(ti\014cation,)g
4304 (retinal)g(scanners\))125 4132 y Fk(\017)41 b Fo(Something)27
4305 b(the)h(user)f Fn(has)h Fo(\(ID)h(cards,)d(smartcards\))125
4306 4298 y Fk(\017)41 b Fo(Something)27 b(the)h(user)f Fn(knows)h
4307 Fo(\(passw)n(ords,)e(PINs\))125 4464 y(This)36 b(pap)r(er)h(deals)f
4308 (with)h(a)g(particularly)e(imp)r(ortan)n(t)h(subset)h(of)g(the)g(last)g
4309 (category)e(kno)n(wn)h(as)g Fn(dir)l(e)l(ct)h Fo(passw)n(ord)0
4310 4564 y(authen)n(tication.)59 b(Mec)n(hanisms)34 b(that)i(fall)f(in)n
4311 (to)g(this)g(rather)g(exclusiv)n(e)f(category)f(cannot)i(rely)f(on)h(p)
4312 r(ersisten)n(t)g(stored)0 4663 y(information)j(on)h(the)g(clien)n(t)g
4313 (side.)71 b(The)39 b(user's)f(passw)n(ord,)i(whic)n(h)f(is)g(a)f
4314 (memorized)h(quan)n(tit)n(y)-7 b(,)41 b(is)e(the)g(only)g(secret)0
4315 4763 y(a)n(v)-5 b(ailable)27 b(to)h(clien)n(t)h(soft)n(w)n(are.)37
4316 b(It)29 b(is)f(also)f(assumed)h(that)h(the)f(net)n(w)n(ork)f(b)r(et)n
4317 (w)n(een)i(the)f(clien)n(t)h(and)f(serv)n(er)f(is)h(vulnerable)0
4318 4863 y(to)d(b)r(oth)h(ea)n(v)n(esdropping)c(and)j(delib)r(erate)g(tamp)
4319 r(ering)g(b)n(y)g(the)g(enem)n(y)-7 b(.)36 b(In)25 b(addition,)h(no)f
4320 (trusted)g(third)g(part)n(y)f(suc)n(h)h(as)f(a)0 4962
4321 y(k)n(ey)g(serv)n(er)f(or)h(arbitrator)f(can)i(b)r(e)g(used;)h(only)e
4322 (the)i(original)d(t)n(w)n(o)h(parties)g(can)h(engage)e(in)i(the)h
4323 (authen)n(tication)e(proto)r(col.)125 5062 y(Suc)n(h)j(proto)r(cols)f
4324 (ha)n(v)n(e)g(a)g(surprisingly)g(wide)h(range)f(of)h(practical)f
4325 (applications)h(b)r(ecause)g(they)g(do)g(not)g(require)f(an)n(y-)0
4326 5162 y(thing)h(more)f(than)h(a)g(memorized)f(passw)n(ord,)f(making)i
4327 (them)g(m)n(uc)n(h)g(easier)f(to)g(use)h(and)g(less)f(exp)r(ensiv)n(e)h
4328 (to)g(deplo)n(y)f(than)0 5261 y(either)k(biometric)h(or)e(tok)n
4329 (en-based)h(metho)r(ds.)46 b(One)30 b(ob)n(vious)f(application)h(is)h
4330 (handling)f(remote,)h(passw)n(ord-protected)p 0 5330
4331 1560 4 v 91 5384 a Fj(\003)127 5407 y Fi(1998)25 b(In)n(ternet)g(So)r
4332 (ciet)n(y)g(Symp)r(osium)d(on)i(Net)n(w)n(ork)g(and)g(Distributed)g
4333 (System)g(Securit)n(y)1929 5656 y Fo(1)p eop
4334 %%Page: 2 2
4335 2 1 bop 0 390 a Fo(computer)32 b(access.)51 b(Most)32
4336 b(In)n(ternet)g(proto)r(cols)f(curren)n(tly)h(in)h(use)f(emplo)n(y)g
4337 (plain)n(text)g(passw)n(ords)e(for)i(authen)n(tication,)0
4338 490 y(and)23 b(it)h(has)f(b)r(een)h(recommended)f(that)h(they)g(b)r(e)g
4339 (replaced)f(with)h(more)f(secure)f(alternativ)n(es)g(if)j(it)f(can)f(b)
4340 r(e)h(done)f(transpar-)0 589 y(en)n(tly)k([8)o(];)g(a)f(secure)g
4341 (direct)g(authen)n(tication)h(proto)r(col)e(\014ts)i(p)r(erfectly)g(in)
4342 n(to)f(suc)n(h)g(an)g(arc)n(hitecture)g(without)h(in)n(tro)r(ducing)0
4343 689 y(signi\014can)n(t)20 b(user-visible)g(o)n(v)n(erhead.)32
4344 b(Ev)n(en)20 b(in)h(situations)f(where)h(some)f(form)g(of)h(securit)n
4345 (y)f(infrastructure)g(already)f(exists,)0 789 y(a)30
4346 b(strong)g(passw)n(ord)e(system)j(adds)f(a)g(strong)g(indep)r(enden)n
4347 (t)h(factor)f(to)h(the)g(authen)n(tication)f(mec)n(hanism)g(that)h
4348 (adds)f(to)0 888 y(the)e(o)n(v)n(erall)d(strength)j(of)f(the)h(system.)
4349 37 b(This)27 b(includes)h Fn(multi-factor)g Fo(systems)g(that)f(emplo)n
4350 (y)g(a)h(passw)n(ord)d(plus)j(either)f(a)0 988 y(hand-carried)g(or)h
4351 (biometric)h(device.)40 b(Reference)29 b([9)o(])g(con)n(tains)f(an)h
4352 (excellen)n(t)g(treatmen)n(t)f(of)h(these)g(issues,)g(and)g([1)o(])g
4353 (also)0 1088 y(lists)f(additional)f(applications)f(for)h(secure)g
4354 (direct)h(authen)n(tication)f(proto)r(cols.)125 1187
4355 y(Section)33 b(2)g(brie\015y)h(reviews)e(existing)i(authen)n(tication)f
4356 (proto)r(cols)f(and)i(explains)f(b)r(oth)h(their)g(strengths)f(and)g
4357 (their)0 1287 y(shortcomings.)125 1386 y(Section)26 b(3)h(discusses)f
4358 (the)h(new)g(authen)n(tication)f(proto)r(col)g(in)h(mathematical)f
4359 (terms,)h(suggests)e(p)r(ossible)i(implemen-)0 1486 y(tations,)g(and)h
4360 (explains)f(the)h(rationale)e(b)r(ehind)i(its)g(design.)125
4361 1586 y(Section)c(4)g(analyzes)f(the)h(securit)n(y)g(of)g(the)h(new)f
4362 (proto)r(col,)g(pro)n(v)n(es)e(its)j(securit)n(y)e(against)g(ea)n(v)n
4363 (esdropp)r(ers)f(b)n(y)i(reducing)0 1685 y(it)k(to)f(existing)h(hard)f
4364 (mathematical)g(problems,)g(and)g(discusses)g(necessary)f(conditions)h
4365 (and)g(restrictions.)125 1785 y(Section)g(5)g(addresses)f(p)r
4366 (erformance)h(and)g(implemen)n(tation)h(issues.)0 2055
4367 y Fm(2)135 b(T)-11 b(erminology)45 b(and)g(bac)l(kground)0
4368 2237 y Fo(Throughout)32 b(this)i(pap)r(er,)h(the)f(terms)g
4369 Fn(client)g Fo(and)f Fn(server)h Fo(will)g(b)r(e)g(used)g(to)f(denote)h
4370 (the)g Fn(user)f Fo(and)h Fn(host)g Fo(parties)f(in)g(a)0
4371 2337 y(direct)28 b(authen)n(tication)g(proto)r(col.)38
4372 b(Unless)28 b(stated)g(otherwise,)f(the)i(clien)n(t)f(is)g(assumed)g
4373 (to)g(b)r(e)h(a)f(h)n(uman)g(user)f(who,)h(lik)n(e)0
4374 2436 y(t)n(ypical)g(computer)f(users,)g(can)h(only)g(remem)n(b)r(er)f
4375 (relativ)n(ely)g(short)g(passw)n(ords)f([7)o(,)i(13)o(].)38
4376 b(Although)29 b(a)e(user)g(ma)n(y)h(emplo)n(y)0 2536
4377 y(a)k(piece)g(of)h(soft)n(w)n(are)e(to)h(negotiate)f(the)i(authen)n
4378 (tication)f(proto)r(col)g(in)g(practice,)h(this)g(do)r(es)f(not)g
4379 (a\013ect)h(our)f(de\014nition)0 2635 y(of)c(the)h(clien)n(t,)f(since)g
4380 (w)n(e)g(ha)n(v)n(e)f(already)f(stipulated)j(that)f(said)g(clien)n(t)g
4381 (soft)n(w)n(are)e(cannot)i(remem)n(b)r(er)f(long-term)g(k)n(eys)g(on)0
4382 2735 y(b)r(ehalf)h(of)g(the)g(user.)125 2835 y(The)35
4383 b(terms)f Fn(p)l(asswor)l(d)i Fo(and)f Fn(veri\014er)h
4384 Fo(corresp)r(ond)d(to)i(con)n(v)n(en)n(tional)e(priv)-5
4385 b(ate)35 b(and)f(public)i(k)n(eys,)g(di\013ering)e(in)h(only)0
4386 2934 y(t)n(w)n(o)c(asp)r(ects:)44 b(Unlik)n(e)32 b(t)n(ypical)f(priv)-5
4387 b(ate)31 b(k)n(eys,)h(the)g(passw)n(ord)d(has)i(limited)h(en)n(trop)n
4388 (y)-7 b(,)32 b(constrained)e(b)n(y)h(the)h(memory)f(of)0
4389 3034 y(the)j(user.)54 b(A)34 b(v)n(eri\014er)e(has)h(similar)f
4390 (mathematical)h(prop)r(erties)g(to)g(a)g(public)h(k)n(ey)-7
4391 b(,)35 b(since)e(it)h(is)f(easily)g(computed)g(from)0
4392 3134 y(the)e(passw)n(ord,)e(y)n(et)i(deriving)e(the)i(passw)n(ord)e
4393 (from)h(the)h(v)n(eri\014er)e(is)i(computationally)e(infeasible.)46
4394 b(Instead)30 b(of)h(b)r(eing)f(a)0 3233 y(publicly-kno)n(wn)j(quan)n
4395 (tit)n(y)-7 b(,)34 b(ho)n(w)n(ev)n(er,)f(the)h(v)n(eri\014er)d(is)j(k)n
4396 (ept)f(secret)g(b)n(y)g(the)g(serv)n(er.)53 b(An)34 b(authen)n
4397 (tication)f(mec)n(hanism)0 3333 y(that)22 b(requires)e(the)i(serv)n(er)
4398 d(to)j(store)e(a)h(cop)n(y)g(of)g(the)h(user's)f(passw)n(ord)e(or)i
4399 (priv)-5 b(ate)21 b(k)n(ey)g(is)g(kno)n(wn)g(as)g(a)g
4400 Fn(plaintext-e)l(quivalent)0 3432 y Fo(mec)n(hanism,)27
4401 b(while)h(one)f(that)h(only)f(requires)f(a)i(v)n(eri\014er)e(to)h(b)r
4402 (e)h(stored)f(will)h(b)r(e)g(called)f(a)g Fn(veri\014er-b)l(ase)l(d)i
4403 Fo(mec)n(hanism.)125 3532 y(V)-7 b(eri\014er-based)29
4404 b(proto)r(cols)h(ha)n(v)n(e)g(a)h(signi\014can)n(t)g(adv)-5
4405 b(an)n(tage)29 b(o)n(v)n(er)h(ones)h(that)g(are)f(plain)n(text-equiv)-5
4406 b(alen)n(t.)48 b(A)31 b(system)0 3632 y(that)j(uses)f(plain)n
4407 (text-equiv)-5 b(alen)n(t)32 b(authen)n(tication)h(b)r(ecomes)h(instan)
4408 n(tly)f(compromised)f(once)h(the)h(passw)n(ord)d(database)0
4409 3731 y(is)g(rev)n(ealed,)f(since)h(ev)n(ery)f(user's)g(passw)n(ord)f
4410 (is)i(stored)g(there.)47 b(A)31 b(database)f(of)h(v)n(eri\014ers,)f(on)
4411 h(the)h(other)e(hand,)i(can)f(b)r(e)0 3831 y(protected)f(just)i(as)e
4412 (easily)g(and)h(e\013ectiv)n(ely)g(as)f(a)g(database)g(of)h(plain)n
4413 (text-equiv)-5 b(alen)n(t)30 b(passw)n(ords,)f(except)i(that)g(failure)
4414 0 3931 y(of)d(said)f(protection)g(is)g(not)h(as)f(catastrophic)f(if)i
4415 (only)f(v)n(eri\014ers)f(are)h(compromised.)125 4030
4416 y(While)j(an)n(y)e(reasonably)f(secure)i(authen)n(tication)g(proto)r
4417 (col)f(is)i(exp)r(ected)f(not)h(to)f(leak)g(an)n(y)g(information)f(ab)r
4418 (out)i(the)0 4130 y(passw)n(ord)21 b(to)h(ea)n(v)n(esdropp)r(ers,)f
4419 (proto)r(cols)g(classi\014ed)h(as)g Fn(zer)l(o-know)t(le)l(dge)i
4420 Fo(do)e(not)h(ev)n(en)f(leak)g(an)n(y)f(information)h(ab)r(out)h(the)0
4421 4229 y(passw)n(ord)k(to)h(the)i(legitimate)e(host)h(\(except)g(the)g
4422 (fact)g(that)g(the)g(part)n(y)f(at)h(the)g(other)f(end)h(really)f(do)r
4423 (es)g(kno)n(w)g(it\).)41 b(This)0 4329 y(subset)20 b(of)h(v)n
4424 (eri\014er-based)d(proto)r(cols)h(is)h(strong)g(indeed,)i(since)e(the)h
4425 (host)f(nev)n(er)g(stores)f(plain)n(text-equiv)-5 b(alen)n(t)20
4426 b(information)0 4429 y(and)27 b(is)h(nev)n(er)e(giv)n(en)h(an)n(y)g
4427 (suc)n(h)g(information)g(during)g(the)h(course)e(of)i(authen)n
4428 (tication.)36 b(This)28 b(reduces)f(the)g(damage)g(that)0
4429 4528 y(T)-7 b(ro)5 b(jan)29 b(horses)499 4498 y Fh(1)566
4430 4528 y Fo(can)h(in\015ict,)j(and)d(it)h(enables)g(the)g(authen)n
4431 (tication)f(system)g(to)h(retain)f(some)g(degree)g(of)h(securit)n(y)f
4432 (ev)n(en)0 4628 y(in)e(the)g(case)f(of)g(complete)h(host)f(compromise.)
4433 0 4856 y Fg(2.1)112 b(Older)37 b(authen)m(tication)f(tec)m(hniques)0
4434 5009 y Fo(In)29 b(the)g(simplest)g(of)g(all)f(passw)n(ord)f(authen)n
4435 (tication)h(proto)r(cols,)g(Carol)f(\(the)j(user)e(or)g(clien)n(t\))h
4436 (sends)f(Stev)n(e)h(\(the)g(host)g(or)0 5109 y(serv)n(er\))i(her)i
4437 (username)e(and)i(her)f(plain)n(text)h(passw)n(ord,)f(and)h(Stev)n(e)f
4438 (v)n(eri\014es)g(the)h(passw)n(ord,)f(either)h(b)n(y)f(comparing)g(it)p
4439 0 5172 1560 4 v 92 5226 a Ff(1)127 5249 y Fi(One)d(h)n(uge)h(b)r
4440 (ene\014t)h(here)e(is)g(that)h(passw)n(ords)f(shared)g(b)r(et)n(w)n
4441 (een)i(di\013eren)n(t)f(systems)e(are)h(not)h(compromised)d(if)h(an)i
4442 (attac)n(k)n(er)g(installs)f(a)0 5328 y(T)-6 b(ro)t(jan)24
4443 b(horse)g(on)h(one)g(of)f(the)h(systems.)32 b(The)25
4444 b(Secure)g(Remote)f(P)n(assw)n(ord)g(proto)r(col)h(is)f(one)h(of)f(the)
4445 h(\014rst)f(authen)n(tication)j(mec)n(hanisms)c(that)0
4446 5407 y(solv)n(es)h(this)f(problem.)1929 5656 y Fo(2)p
4447 eop
4448 %%Page: 3 3
4449 3 2 bop 0 390 a Fo(directly)28 b(to)f(his)h(v)n(ersion)f(of)g(Carol's)g
4450 (passw)n(ord)e(or)i(applying)h(a)f(one-w)n(a)n(y)f(hash)h(function)i
4451 (\014rst)e(and)h(c)n(hec)n(king)f(against)f(a)0 490 y(database)f(of)h
4452 (stored)f(hashes.)35 b(Since)26 b(Carol's)f(passw)n(ord)f(is)i
4453 (immediately)g(exp)r(osed)f(to)h(an)n(y)f(ea)n(v)n(esdropping)e(attac)n
4454 (k,)j(this)0 589 y(metho)r(d)i(is)g(unacceptable)f(in)h(net)n(w)n(orks)
4455 e(where)h(suc)n(h)g(attac)n(ks)f(are)h(p)r(ossible.)125
4456 689 y(T)-7 b(o)34 b(coun)n(ter)h(this,)i(Carol)d(and)h(Stev)n(e)g(can)g
4457 (emplo)n(y)f(a)h Fn(chal)t(lenge-r)l(esp)l(onse)i Fo(proto)r(col.)59
4458 b(In)35 b(general)f(terms,)j(suc)n(h)d(a)0 789 y(proto)r(col)26
4459 b(w)n(ould)i(tak)n(e)e(the)i(follo)n(wing)f(form:)101
4460 955 y(1.)42 b(Carol)26 b(sends)h(her)g(iden)n(tit)n(y)h(to)g(Stev)n(e,)
4461 f(along)f(with)i(some)f(random)g(message.)101 1121 y(2.)42
4462 b(Stev)n(e)27 b(sends)g(Carol)f(a)i(random)e(message,)h(called)g(a)g
4463 Fn(chal)t(lenge)p Fo(.)101 1287 y(3.)42 b(Carol)21 b(p)r(erforms)h
4464 (some)h(computation)g(based)f(on)h(the)g(c)n(hallenge,)g(the)g(\014rst)
4465 g(random)f(message,)h(and)f(her)h(passw)n(ord.)208 1386
4466 y(She)30 b(sends)g(this)h Fn(r)l(esp)l(onse)g Fo(to)f(Stev)n(e,)h(who)g
4467 (p)r(erforms)e(the)i(same)f(computation)g(and)g(v)n(eri\014es)g(the)h
4468 (correctness)d(of)208 1486 y(Carol's)e(resp)r(onse.)125
4469 1652 y(Since)35 b(Stev)n(e's)f(c)n(hallenge)g(is)h(di\013eren)n(t)g
4470 (for)f(eac)n(h)g(authen)n(tication)g(attempt,)k(a)c(captured)h(resp)r
4471 (onse)f(is)g(useless)h(for)0 1752 y(future)30 b(sessions,)e(defeating)h
4472 (a)g(simple)g(repla)n(y)f(attac)n(k.)41 b(Ho)n(w)n(ev)n(er,)28
4473 b(c)n(hallenge-resp)r(onse)f(proto)r(cols)g(can)i(b)r(e)h(attac)n(k)n
4474 (ed)e(in)0 1851 y(other)g(w)n(a)n(ys.)39 b(Ev)n(e)27
4475 b(can)i(capture)f(the)h(random)f(n)n(um)n(b)r(er,)g(c)n(hallenge,)g
4476 (and)h(resp)r(onse)e(from)i(a)f(successful)g(authen)n(tication)0
4477 1951 y(attempt)22 b(and)f(start)g(guessing)f(passw)n(ords)f(un)n(til)j
4478 (she)f(\014nds)g(one)g(that)h(generates)d(a)i(resp)r(onse)g(that)g
4479 (matc)n(hes)g(the)h(captured)0 2051 y(one.)41 b(This)29
4480 b(attac)n(k)f(is)h(called)f(a)h Fn(dictionary)k(attack)d
4481 Fo(and)e(has)h(b)r(een)g(used)g(to)g(exploit)g(systems)g(in)g(the)g
4482 (past,)h(often)f(quite)0 2150 y(successfully)e([7].)125
4483 2250 y(Challenge-resp)r(onse)d(proto)r(cols)h(are)h(also)g(plain)n
4484 (text-equiv)-5 b(alen)n(t,)26 b(so)g(they)h(can)g(b)r(e)g(easily)f
4485 (defeated)h(b)n(y)f(an)h(in)n(truder)0 2350 y(who)g(captures)g(the)h
4486 (passw)n(ord)e(\014le,)h(as)g(w)n(ell)h(as)f(one)g(who)g(can)g(ea)n(v)n
4487 (esdrop.)125 2449 y(T)-7 b(o)30 b(w)n(ork)f(around)g(the)i(limitations)
4488 g(of)f(inheren)n(tly)g(w)n(eak)g(authen)n(tication)g(mec)n(hanisms,)h
4489 (proto)r(col)e(designers)g(ha)n(v)n(e)0 2549 y(traditionally)e(used)g
4490 (one)g(of)h(three)f(approac)n(hes:)125 2715 y Fk(\017)41
4491 b Fo(Increase)26 b(the)i(length)f(of)h(the)g(k)n(ey)f(with)h(an)f
4492 (external)g(device)g(lik)n(e)h(a)f(smartcard.)125 2881
4493 y Fk(\017)41 b Fo(T)-7 b(ak)n(e)31 b(adv)-5 b(an)n(tages)31
4494 b(of)i(ph)n(ysical)f(phenomena)g(to)g(construct)g(a)h(c)n(hannel)f
4495 (that)h(is)f(more)g(di\016cult)i(to)e(compromise)208
4496 2980 y(\(spread)26 b(sp)r(ectrum,)i(quan)n(tum)g(cryptograph)n(y\).)125
4497 3147 y Fk(\017)41 b Fo(Ignore)26 b(the)i(problem)f(and)g(hop)r(e)h
4498 (\\nob)r(o)r(dy)f(notices.")125 3313 y(The)35 b(\014rst)g(metho)r(d)i
4499 (c)n(hanges)d(the)i(authen)n(tication)f(system)g(so)g(that)h(it)g(is)f
4500 (no)h(longer)e(based)h(on)g(\\something)g(y)n(ou)0 3412
4501 y(kno)n(w,")25 b(losing)f(the)i(con)n(v)n(enience)e(b)r(ene\014ts)i(of)
4502 f(passw)n(ord-only)d(metho)r(ds)k(in)g(the)f(pro)r(cess.)35
4503 b(The)26 b(second)e(metho)r(d)i(is)f(only)0 3512 y(applicable)32
4504 b(to)g(a)g(limited)h(range)e(of)h(applications.)50 b(The)32
4505 b(third)g(metho)r(d)h(is)f(the)h(most)f(common,)h(and)f(exp)r(oses)f(a)
4506 h(v)n(ery)0 3611 y(dangerous)26 b(attitude)j(among)e(proto)r(col)g
4507 (designers.)37 b(This)28 b(com)n(bination)f(of)h(w)n(eak)f(authen)n
4508 (tication)h(tec)n(hnology)f(and)h(lax)0 3711 y(attitudes)22
4509 b(to)n(w)n(ards)f(passw)n(ord)f(securit)n(y)h(ha)n(v)n(e)g(giv)n(en)g
4510 (passw)n(ord)f(authen)n(tication)i(a)g(negativ)n(e)f(reputation)g(in)h
4511 (the)h(securit)n(y)0 3811 y(comm)n(unit)n(y)k([13)o(].)0
4512 4043 y Fg(2.2)112 b(Stronger)38 b(solutions)0 4196 y
4513 Fo(In)28 b(1992,)d(Bello)n(vin)i(and)g(Merritt)g([1])g(presen)n(ted)g
4514 (a)g(new)g(proto)r(col)g(kno)n(wn)f(as)h Fn(Encrypte)l(d)j(Key)g
4515 (Exchange)p Fo(,)f(or)d(EKE.)g(By)0 4296 y(using)i(a)h(com)n(bination)e
4516 (of)i(symmetric)f(and)h(public-k)n(ey)f(cryptograph)n(y)-7
4517 b(,)26 b(EKE)i(resists)f(dictionary)h(attac)n(ks)f(b)n(y)i(giving)e(a)0
4518 4396 y(passiv)n(e)22 b(attac)n(k)n(er)g(insu\016cien)n(t)i(information)
4519 f(to)h(v)n(erify)f(a)g(guessed)g(passw)n(ord.)33 b(EKE)23
4520 b(p)r(erforms)g(a)g(k)n(ey)g(exc)n(hange)f(as)h(w)n(ell,)0
4521 4495 y(so)i(b)r(oth)i(parties)e(can)g(encrypt)h(their)g(transmissions)e
4522 (once)i(authen)n(tication)f(is)h(established.)36 b(In)26
4523 b(the)g(most)g(general)e(form)0 4595 y(of)i(EKE,)e(the)i(t)n(w)n(o)f
4524 (comm)n(unicating)g(parties)g(encrypt)g(ephemeral)g(public)h(k)n(eys)f
4525 (with)h(a)g(symmetric)f(cipher,)h(using)f(their)0 4694
4526 y(shared)i(secret)g(passw)n(ord)f(as)h(a)h(k)n(ey)-7
4527 b(.)37 b(Since)28 b(it)h(w)n(as)e(in)n(v)n(en)n(ted,)g(EKE)g(has)g(b)r
4528 (een)i(dev)n(elop)r(ed)e(in)n(to)h(a)g(family)g(of)f(proto)r(cols,)0
4529 4794 y(man)n(y)20 b(of)h(whic)n(h)g(are)f(stronger)f(than)i(the)h
4530 (original)d(or)h(add)h(new)g(desirable)f(prop)r(erties.)34
4531 b(F)-7 b(or)20 b(example,)i(DH-EKE)e([17)o(])h(and)0
4532 4894 y(SPEKE)27 b([9])i(add)g(what)f(is)h(kno)n(wn)f(as)h
4533 Fn(forwar)l(d)j(se)l(cr)l(e)l(cy)p Fo(,)e(whic)n(h)f(means)f(that)h
4534 (rev)n(ealing)e(the)j(passw)n(ord)d(to)h(an)h(attac)n(k)n(er)0
4535 4993 y(do)r(es)j(not)h(help)g(him)g(obtain)g(the)g(session)f(k)n(eys)g
4536 (of)g(past)h(sessions.)51 b(It)33 b(is)g(also)e(usually)i(tak)n(en)f
4537 (to)g(mean)h(that)g(a)f(stolen)0 5093 y(session)25 b(k)n(ey)g(do)r(es)h
4538 (not)g(help)h(an)e(attac)n(k)n(er)g(carry)f(out)i(a)g(brute-force)f
4539 (guessing)g(attac)n(k)g(on)h(the)g(passw)n(ord.)35 b(Reference)25
4540 b([6])0 5193 y(describ)r(es)i(a)g(set)h(of)f(\\secret)g(public-k)n(ey")
4541 f(proto)r(cols)g(that)i(accomplish)f(the)h(same)f(ob)5
4542 b(jectiv)n(es)27 b(as)g(EKE.)125 5292 y(T)-7 b(o)35 b(date,)i(the)f
4543 (family)f(of)h(EKE)e(proto)r(cols)g(represen)n(ts)g(the)i(strongest)e
4544 (lev)n(el)h(of)g(passw)n(ord-based)d(authen)n(tication)0
4545 5392 y(proto)r(cols)e(a)n(v)-5 b(ailable.)48 b(EKE's)30
4546 b(greatest)h(failing)g(is)h(that)g(it)g(still)g(su\013ers)f(from)g
4547 (plain)n(text-equiv)-5 b(alence,)32 b(requiring)f(that)1929
4548 5656 y(3)p eop
4549 %%Page: 4 4
4550 4 3 bop 0 390 a Fo(b)r(oth)37 b(the)f(clien)n(t)h(and)f(host)g(ha)n(v)n
4551 (e)f(access)g(to)i(the)f(same)g(secret)g(passw)n(ord)e(or)h(hash)h
4552 (thereof.)63 b(There)36 b(is)g(one)g(v)-5 b(arian)n(t)0
4553 490 y(of)37 b(EKE,)f(kno)n(wn)h(as)f Fn(A)n(ugmente)l(d)i(EKE)g
4554 Fo(or)e(A-EKE)g([2)o(],)k(whic)n(h)d(mak)n(es)g(EKE)f(a)g(v)n
4555 (eri\014er-based)f(proto)r(col,)k(but)f(the)0 589 y(mo)r(di\014cation)
4556 27 b(also)g(destro)n(ys)f(forw)n(ard)g(secrecy)g([17)o(].)125
4557 689 y(Recen)n(tly)-7 b(,)38 b(additional)e(w)n(ork)f(has)g(b)r(een)i
4558 (done)f(to)g(extend)h(the)f(EKE)f(family)i(of)f(proto)r(cols)f(to)h
4559 (address)f(the)h(issue)0 789 y(of)f(holding)f(plain)n(text-equiv)-5
4560 b(alen)n(t)35 b(data)f(in)h(passw)n(ord)e(\014les)i([10)o(].)59
4561 b(B-SPEKE)33 b(is)i(an)f(example)h(of)g(suc)n(h)f(an)h(extended)0
4562 888 y(metho)r(d.)63 b(These)36 b(proto)r(cols)f(add)h(another)f(k)n(ey)
4563 h(exc)n(hange)e(round)i(to)g(v)n(erify)f(the)i(clien)n(t's)f(p)r
4564 (ossession)f(of)h(the)h(actual)0 988 y(passw)n(ord)28
4565 b(as)h(opp)r(osed)g(to)h(a)f(stolen)g(v)n(eri\014er)g(from)g(the)h
4566 (passw)n(ord)e(\014le.)43 b(This)30 b(\014xes)f(a)h(ma)5
4567 b(jor)28 b(issue)h(with)i(EKE,)d(at)i(the)0 1088 y(exp)r(ense)23
4568 b(of)g(substan)n(tially)g(increasing)f(the)h(running)g(time)h(and)f
4569 (computational)g(complexit)n(y)g(of)g(the)h(resulting)e(proto)r(col.)
4570 125 1187 y(The)35 b(issue)g(of)g(a)n(v)n(oiding)e(plain)n(text-equiv)-5
4571 b(alence)34 b(has)h(b)r(een)h(a)f(glaring)e(omission)h(in)i(secure)e
4572 (proto)r(col)g(designs)h(for)0 1287 y(quite)c(some)g(time,)h(y)n(et)f
4573 (it)g(m)n(ust)g(b)r(e)g(addressed)f(if)i(it)f(is)g(to)g(b)r(e)g
4574 (considered)f(a)g(viable)h(replacemen)n(t)f(for)g(authen)n(tication)0
4575 1386 y(systems)i(lik)n(e)h(the)g Fe(/etc/passwd)28 b
4576 Fo(\014le)33 b(in)g(Unix)g(systems)f([13)o(].)53 b(In)32
4577 b(addition,)i(p)r(o)r(or)e(p)r(erformance)g(has)g(often)h(b)r(een)g(an)
4578 0 1486 y(obstacle)24 b(to)g(the)h(adoption)f(of)h(stronger)e(proto)r
4579 (cols;)h(the)h(proto)r(cols)e(describ)r(ed)h(in)h([2])f(and)h([10)o(])g
4580 (are)e(just)j(slo)n(w)d(enough)h(to)0 1586 y(b)r(e)29
4581 b(uncomfortable)f(for)g(frequen)n(t,)h(ligh)n(t)n(w)n(eigh)n(t)e
4582 (authen)n(tication)h(purp)r(oses.)39 b(An)30 b(impro)n(v)n(emen)n(t)d
4583 (in)i(p)r(erformance)e(from,)0 1685 y(sa)n(y)-7 b(,)23
4584 b(a)f(3)h(second)f(dela)n(y)h(to)f(a)h(1.5)f(second)g(dela)n(y)h(at)f
4585 (login)h(time)g(can)g(often)g(mak)n(e)f(the)i(di\013erence)e(b)r(et)n
4586 (w)n(een)h(an)g(un)n(b)r(earable)0 1785 y(solution)k(and)h(a)f(w)n(ork)
4587 -5 b(able)26 b(one.)0 2060 y Fm(3)135 b(A)44 b(new)h(framew)l(ork)0
4588 2241 y Fo(Designing)24 b(a)g(v)n(eri\014er-based)e(proto)r(col)h(is)i
4589 (considerably)e(more)g(di\016cult)i(than)g(designing)f(a)g(con)n(v)n
4590 (en)n(tional)e(shared-secret)0 2341 y(authen)n(tication)39
4591 b(proto)r(col,)j(b)r(ecause)d(the)h(v)n(eri\014er)e(and)i(passw)n(ord)d
4592 (are)i(b)n(y)g(de\014nition)h(not)g(equiv)-5 b(alen)n(t)39
4593 b(\(though)h(the)0 2441 y(former)24 b(ma)n(y)h(b)r(e)h(deriv)n(ed)f
4594 (from)g(the)g(latter\),)h(forcing)f(the)g(computational)g(structure)g
4595 (of)g(the)h(proto)r(col)e(to)i(b)r(e)f(inheren)n(tly)0
4596 2540 y(asymmetric.)36 b(As)27 b(is)f(the)h(case)f(with)i(public-k)n(ey)
4597 e(cryptograph)n(y)-7 b(,)24 b(only)j(a)f(handful)h(of)g(metho)r(ds)g
4598 (lend)g(themselv)n(es)f(to)h(the)0 2640 y(mathematical)d(manipulation)g
4599 (necessary)f(to)h(construct)g(secure)g(v)n(eri\014er-based)e(proto)r
4600 (cols.)35 b(This)24 b(is)h(one)f(of)g(the)h(reasons)0
4601 2739 y(wh)n(y)i(suc)n(h)h(proto)r(cols)e(are)g(relativ)n(ely)h(rare)f
4602 (in)i(practice.)125 2839 y(W)-7 b(e)28 b(ha)n(v)n(e)f(already)f(seen)i
4603 (proto)r(cols)e(that)i(use)g(digital)g(signatures)e(\(A-EKE\))h(and)h
4604 (proto)r(cols)e(that)j(use)e(a)h(secondary)0 2939 y(one-sided)39
4605 b(k)n(ey)h(exc)n(hange)e(\(B-SPEKE\);)h(this)h(section)f(in)n(tro)r
4606 (duces)h(a)f(new)i(construction)e(called)g Fn(Asymmetric)j(Key)0
4607 3038 y(Exchange)p Fo(,)29 b(or)e(AKE)h(for)f(short,)g(whic)n(h)h(is)g
4608 (a)g(generalized)e(form)i(for)f(a)h(third)g(class)f(of)h(v)n
4609 (eri\014er-based)d(proto)r(cols.)37 b(Later,)0 3138 y(w)n(e)27
4610 b(will)h(in)n(tro)r(duce)f(the)h(Secure)f(Remote)g(P)n(assw)n(ord)d
4611 (proto)r(col)j(itself,)h(whic)n(h)f(will)h(refer)e(to)i(the)f(more)g(w)
4612 n(ell-de\014ned)g(and)0 3238 y(sp)r(eci\014ed)h(instance)f(of)h(AKE)f
4613 (that)h(is)f(of)h(in)n(terest)f(to)g(mo)r(dern)h(passw)n(ord)d(authen)n
4614 (tication)i(systems.)0 3470 y Fg(3.1)112 b(Asymmetric)35
4615 b(k)m(ey)j(exc)m(hange)0 3623 y Fo(Lik)n(e)d(EKE,)g(the)h(primary)e
4616 (function)j(of)e(AKE)g(is)h(to)g(exc)n(hange)e(k)n(eys)h(b)r(et)n(w)n
4617 (een)g(t)n(w)n(o)g(parties,)i(the)f(clien)n(t)g(and)g(serv)n(er,)0
4618 3723 y(and)h(to)h(use)f(this)g(k)n(ey)g(to)g(v)n(erify)g(that)h(b)r
4619 (oth)g(parties)e(actually)h(kno)n(w)g(their)g(passw)n(ords.)64
4620 b(Unlik)n(e)37 b(EKE,)g(AKE)f(do)r(es)0 3823 y(not)e(encrypt)g(an)n(y)g
4621 (of)g(the)h(proto)r(col)e(\015o)n(ws.)56 b(Instead,)36
4622 b(it)f(uses)f(prede\014ned)g(mathematical)g(relationships)f(to)i(com)n
4623 (bine)0 3922 y(exc)n(hanged)22 b(ephemeral)h(v)-5 b(alues)23
4624 b(with)h(established)g(passw)n(ord)d(parameters.)34 b(Av)n(oiding)23
4625 b(encryption)g(is)g(adv)-5 b(an)n(tageous)22 b(for)0
4626 4022 y(a)27 b(n)n(um)n(b)r(er)h(of)f(reasons:)125 4188
4627 y Fk(\017)41 b Fo(It)31 b(simpli\014es)h(the)f(proto)r(col)f(b)n(y)h
4628 (eliminating)g(the)h(need)f(to)h(negotiate)e(a)h(common)g(encryption)f
4629 (algorithm.)47 b(The)208 4287 y(alternativ)n(e,)21 b(sp)r(ecifying)h
4630 (the)g(algorithm)e(with)i(the)g(proto)r(col,)g(mak)n(es)e(the)i(proto)r
4631 (col)f(dep)r(enden)n(t)h(on)f(one)g(particular)208 4387
4632 y(encryption)27 b(algorithm.)125 4553 y Fk(\017)41 b
4633 Fo(An)n(y)29 b(w)n(eakness)f(in)i(the)g(encryption)f(will)h(usually)f
4634 (result)h(in)g(a)f(w)n(eakness)f(in)i(the)g(resulting)f(authen)n
4635 (tication)g(pro-)208 4653 y(to)r(col.)36 b(In)26 b(addition,)g(when)g
4636 (passw)n(ords)e(are)h(used)h(as)f(k)n(ey)g(material,)h(issues)f(of)h
4637 (padding)g(and)f(v)n(eri\014able)g(plain)n(text)208 4752
4638 y(can)k(op)r(en)h(the)h(proto)r(col)e(to)h(a)g(v)-5 b(ariet)n(y)29
4639 b(of)h(attac)n(ks)f([6)o(].)45 b(Not)30 b(using)g(encryption)g(in)g
4640 (the)g(proto)r(col)f(itself)i(remo)n(v)n(es)208 4852
4641 y(this)c(p)r(oten)n(tial)h(hole.)125 5018 y Fk(\017)41
4642 b Fo(In)27 b(some)f(jurisdictions,)h(soft)n(w)n(are)e(and)i(hardw)n
4643 (are)e(implemen)n(tations)i(of)g(encryption)f(algorithms)g(are)g(sub)5
4644 b(ject)27 b(to)208 5118 y(legal)c(restrictions)g(or)g(exp)r(ort)h
4645 (regulations.)34 b(A)24 b(proto)r(col)f(that)i(do)r(es)e(not)i(use)f
4646 (encryption)f(is)h(not)g(a\013ected)h(b)n(y)e(suc)n(h)208
4647 5217 y(concerns.)1929 5656 y(4)p eop
4648 %%Page: 5 5
4649 5 4 bop 125 390 a Fo(AKE)22 b(also)g(di\013ers)h(from)g(its)g
4650 (predecessors)e(in)i(another)f(w)n(a)n(y)-7 b(.)34 b(Proto)r(cols)21
4651 b(lik)n(e)i(EKE)f(use)h(prearranged)d(shared)i(secrets)0
4652 490 y(as)31 b(the)h(basis)e(for)h(authen)n(tication.)48
4653 b(This)32 b(means)f(that)g(b)r(oth)h(parties)f(k)n(eep)g(exactly)g(the)
4654 h(same)e(secret)h(string)g(and)g(use)0 589 y(it)40 b(indirectly)f(to)g
4655 (authen)n(ticate)g(eac)n(h)f(other.)71 b(Since)39 b(p)r(ossession)f(of)
4656 h(the)h(secret)e(is)h(enough)g(to)g(imp)r(ersonate)f(either)0
4657 689 y(part)n(y)-7 b(,)29 b(and)g(since)g(there)h(are)e(no)n(w)h(t)n(w)n
4658 (o)f(places)h(from)g(whic)n(h)h(the)f(secret)g(can)g(p)r(oten)n(tially)
4659 g(b)r(e)h(stolen,)g(b)r(oth)f(parties)g(are)0 789 y(resp)r(onsible)e
4660 (for)g(exc)n(hanging)f(the)i(initial)g(secret)f(securely)f(and)i
4661 (guarding)e(the)i(secret)f(carefully)-7 b(.)125 888 y(AKE,)27
4662 b(ho)n(w)n(ev)n(er,)e(describ)r(es)i(a)g(\\sw)n(app)r(ed-secret")e
4663 (approac)n(h,)h(in)i(whic)n(h)f(eac)n(h)g(part)n(y)g(computes)g(a)g
4664 (secret)g(and)h(then)0 988 y(applies)23 b(a)g(one-w)n(a)n(y)e(function)
4665 j(to)g(that)f(secret)g(to)g(generate)g(a)g(v)n(eri\014er,)f(whic)n(h)i
4666 (is)f(handed)g(to)h(the)g(other)e(part)n(y)-7 b(.)35
4667 b(Although)0 1088 y(it)27 b(is)g(still)h(imp)r(ortan)n(t)e(to)h(guard)f
4668 (the)i(v)n(eri\014er)d(to)i(prev)n(en)n(t)f(a)h(dictionary)f(attac)n
4669 (k,)g(a)h(stolen)g(v)n(eri\014er)e(is)i(no)g(longer)f(enough)0
4670 1187 y(to)h(imp)r(ersonate)g(the)h(user;)f(the)h(corresp)r(onding)e
4671 (secret)h(passw)n(ord)e(is)j(still)g(needed.)125 1287
4672 y(A)36 b(sp)r(ecial)h(case)e(of)i(this)f(tec)n(hnique,)j(in)e(whic)n(h)
4673 f(only)g(one)g(part)n(y)g(generates)f(a)h(secret)g(and)g(computes)g(a)g
4674 (v)n(eri\014er,)0 1386 y(app)r(ears)c(to)h(b)r(e)g(quite)g(useful)h(if)
4675 f(the)h(other)e(part)n(y)g(is)h(a)g(m)n(ultiuser)g(system)f(that)i
4676 (stores)e(man)n(y)g(v)n(eri\014ers.)51 b(In)34 b(suc)n(h)e(an)0
4677 1486 y(application,)25 b(the)g(user's)f(secret)g(\(i.e.)37
4678 b(the)25 b(passw)n(ord\))e(nev)n(er)h(has)g(to)h(lea)n(v)n(e)e(the)j
4679 (lo)r(cal)e(host)g(during)h(the)g(initial)g(passw)n(ord)0
4680 1586 y(setup)37 b(and)g(passw)n(ord)e(c)n(hange)h(pro)r(cedures;)41
4681 b(only)c(the)g(v)n(eri\014er)f(needs)h(to)g(b)r(e)h(sen)n(t,)h(greatly)
4682 d(impro)n(ving)g(the)h(o)n(v)n(erall)0 1685 y(securit)n(y)27
4683 b(of)g(the)h(system.)865 1949 y Fl(w)r Fo(,)g Fl(x)p
4684 Fo(,)g Fl(y)s Fo(,)g Fl(z)103 b Fo(Arbitrary)26 b(parameters)1035
4685 2049 y Fl(P)12 b Fo(\()p Fl(x)p Fo(\))101 b(A)28 b(\\one-w)n(a)n(y")c
4686 (v)n(eri\014er-generating)h(function)647 2149 y Fl(Q)p
4687 Fo(\()p Fl(x;)14 b(y)s Fo(\),)28 b Fl(R)q Fo(\()p Fl(x;)14
4688 b(y)s Fo(\))100 b(\\Mixing")26 b(functions)i(for)f(priv)-5
4689 b(ate)27 b(and)h(public)g(parameters)964 2248 y Fl(S)5
4690 b Fo(\()p Fl(x;)14 b(y)s Fo(\))100 b(The)27 b(session)g(k)n(ey)g
4691 (generation)f(function)1136 2348 y Fl(K)105 b Fo(Session)27
4692 b(k)n(ey)1192 2527 y(T)-7 b(able)27 b(1:)37 b(Mathematical)27
4693 b(Notation)g(for)g(AKE)125 2789 y(T)-7 b(able)28 b(1)g(summarizes)f
4694 (the)i(notation)f(used)g(in)h(this)g(section.)39 b(W)-7
4695 b(e)29 b(mak)n(e)f(no)g(assumptions)g(at)g(this)h(p)r(oin)n(t)f(ab)r
4696 (out)h(the)0 2888 y(domain,)e(range,)g(or)f(input/output)j(t)n(yp)r(es)
4697 e(of)h(the)g(functions)g(sa)n(v)n(e)e(for)h(the)h(follo)n(wing:)732
4698 3060 y(\()p Fk(8)p Fl(w)r(;)14 b(x;)g(y)s(;)g(z)t Fo(\))22
4699 b Fl(S)5 b Fo(\()p Fl(R)q Fo(\()p Fl(P)12 b Fo(\()p Fl(w)r
4700 Fo(\))p Fl(;)i(P)e Fo(\()p Fl(x)p Fo(\)\))p Fl(;)i(Q)p
4701 Fo(\()p Fl(y)s(;)g(z)t Fo(\)\))24 b(=)f Fl(S)5 b Fo(\()p
4702 Fl(R)q Fo(\()p Fl(P)12 b Fo(\()p Fl(y)s Fo(\))p Fl(;)i(P)e
4703 Fo(\()p Fl(z)t Fo(\)\))p Fl(;)i(Q)p Fo(\()p Fl(w)r(;)g(x)p
4704 Fo(\)\))627 b(\(1\))0 3232 y(Equation)27 b(1)h(m)n(ust)h(b)r(e)g
4705 (satis\014ed)f(for)g(AKE)f(to)i(w)n(ork)e(prop)r(erly)-7
4706 b(.)38 b(By)28 b(itself,)h(it)g(guaran)n(tees)e(nothing)h(ab)r(out)g
4707 (the)h(securit)n(y)0 3331 y(of)e(the)h(resulting)e(proto)r(col.)36
4708 b(That)27 b(is)g(en)n(tirely)f(dep)r(enden)n(t)i(on)f(the)h(c)n(hoices)
4709 e(of)h(the)g(functions)h Fl(P)12 b Fo(\(\),)27 b Fl(Q)p
4710 Fo(\(\),)h Fl(R)q Fo(\(\),)g(and)f Fl(S)5 b Fo(\(\).)0
4711 3431 y(F)-7 b(or)27 b(example,)g(the)h(function)g Fl(P)12
4712 b Fo(\(\))28 b(should)g(b)r(e)g(one-w)n(a)n(y;)d(it)j(should)g(b)r(e)g
4713 (di\016cult)g(to)g(\014nd)g Fl(x)g Fo(giv)n(en)f Fl(P)12
4714 b Fo(\()p Fl(x)p Fo(\).)125 3530 y(T)-7 b(o)29 b(set)g(things)h(up)g
4715 (for)f(the)h(AKE)f(proto)r(col,)g(Carol)f(and)i(Stev)n(e)f(select)g
4716 (parameters)f Fl(x)i Fo(and)g Fl(z)t Fo(,)f(resp)r(ectiv)n(ely)-7
4717 b(.)42 b(These)0 3630 y(serv)n(e)23 b(as)g(the)i(passw)n(ords)d(in)i
4718 (the)g(proto)r(col.)35 b(Carol)23 b(computes)h Fl(P)12
4719 b Fo(\()p Fl(x)p Fo(\))25 b(and)f(giv)n(es)e(it)j(to)f(Stev)n(e,)h(and)
4720 e(Stev)n(e)h(computes)g Fl(P)12 b Fo(\()p Fl(z)t Fo(\))0
4721 3730 y(and)24 b(giv)n(es)f(it)h(to)h(Carol.)34 b(Carol)23
4722 b(and)h(Stev)n(e)g(are)f(no)n(w)g(ready)g(to)h(use)g(AKE)g(to)g(exc)n
4723 (hange)f(k)n(eys)g(using)h(the)g(follo)n(wing)f(steps:)1110
4724 3994 y(Carol)1284 b(Stev)n(e)p 594 4027 2713 4 v 827
4725 4133 a(\(generate)27 b(random)f Fl(w)r Fo(\))1874 4079
4726 y Fd(P)9 b Fh(\()p Fd(w)r Fh(\))1883 4133 y Fk(\000)-14
4727 b(!)109 b Fl(K)28 b Fo(=)23 b Fl(S)5 b Fo(\()p Fl(R)q
4728 Fo(\()p Fl(P)12 b Fo(\()p Fl(w)r Fo(\))p Fl(;)i(P)e Fo(\()p
4729 Fl(x)p Fo(\)\))p Fl(;)i(Q)p Fo(\()p Fl(y)s(;)g(z)t Fo(\)\))644
4730 4269 y Fl(K)28 b Fo(=)23 b Fl(S)5 b Fo(\()p Fl(R)q Fo(\()p
4731 Fl(P)12 b Fo(\()p Fl(y)s Fo(\))p Fl(;)i(P)e Fo(\()p Fl(z)t
4732 Fo(\)\))p Fl(;)i(Q)p Fo(\()p Fl(w)r(;)g(x)p Fo(\)\))1881
4733 4215 y Fd(P)9 b Fh(\()p Fd(y)r Fh(\))1883 4269 y Fk( )-14
4734 b(\000)302 b Fo(\(generate)26 b(random)h Fl(y)s Fo(\))1541
4735 4448 y(T)-7 b(able)27 b(2:)37 b(Generic)27 b(AKE)125
4736 4710 y(A)n(t)g(this)g(p)r(oin)n(t,)g(Carol)e(and)i(Stev)n(e)f(ha)n(v)n
4737 (e)g(p)r(erformed)g(the)h(basic)f(AKE)g(proto)r(col)g(and)g(ha)n(v)n(e)
4738 g(their)g(resp)r(ectiv)n(e)g(session)0 4809 y(k)n(eys.)35
4739 b(If)27 b(the)f(v)-5 b(alues)25 b(of)h Fl(x)g Fo(and)g
4740 Fl(z)j Fo(used)d(to)g(compute)g(the)g(session)f(k)n(ey)g(corresp)r(ond)
4741 f(to)i(the)g(previously)f(agreed-to)e(v)-5 b(alues)0
4742 4909 y(of)34 b Fl(P)12 b Fo(\()p Fl(x)p Fo(\))35 b(and)f
4743 Fl(P)12 b Fo(\()p Fl(z)t Fo(\),)36 b(then)f(b)n(y)f(Equation)f(1,)j
4744 (the)e(t)n(w)n(o)g(v)-5 b(alues)34 b(of)g Fl(K)40 b Fo(will)34
4745 b(matc)n(h.)57 b(T)-7 b(o)34 b(complete)g(the)g(authen)n(tication)0
4746 5009 y(pro)r(cess,)22 b(Carol)g(and)g(Stev)n(e)g(can)g(use)h(an)n(y)e
4747 (m)n(utually)i(agreeable)d(metho)r(d)j(to)g(v)n(erify)e(that)i(their)g
4748 (k)n(eys)e(matc)n(h;)j(the)f(securit)n(y)0 5108 y(of)28
4749 b(the)g(resulting)f(proto)r(col)f(is)h(ob)n(viously)g(dep)r(enden)n(t)h
4750 (on)f(the)h(c)n(hoice)f(of)g(this)h(metho)r(d.)125 5208
4751 y(F)-7 b(rom)36 b(the)g(basic)g(AKE)g(proto)r(col,)i(one)e(can)g(see)g
4752 (the)h(role)f(of)g(eac)n(h)g(of)g(the)h(four)f(parameters:)53
4753 b Fl(x)37 b Fo(and)f Fl(z)k Fo(are)c(the)0 5308 y(long-term)29
4754 b(secrets)g(held)h(b)n(y)f(the)h(t)n(w)n(o)f(parties,)h(while)g
4755 Fl(w)j Fo(and)c Fl(y)k Fo(are)c(ephemeral)g(parameters)f(generated)h(b)
4756 n(y)g(eac)n(h)g(side)0 5407 y(to)d(ensure)g(that)h(the)g(session)e(k)n
4757 (ey)h(v)-5 b(aries)26 b(from)g(session)f(to)i(session.)35
4758 b(As)27 b(stated)f(earlier,)g(the)h(securit)n(y)e(of)i(AKE)f(dep)r
4759 (ends)1929 5656 y(5)p eop
4760 %%Page: 6 6
4761 6 5 bop 0 390 a Fo(on)28 b(the)h(four)g(functions)f(it)i(uses.)39
4762 b(Ob)n(viously)-7 b(,)28 b Fl(P)12 b Fo(\(\))29 b(should)f(b)r(e)h
4763 (di\016cult)h(to)e(in)n(v)n(ert,)g(and)h(its)g(output)g(should)f(also)g
4764 (rev)n(eal)0 490 y(little)35 b(or)e(no)h(information)g(ab)r(out)g(its)g
4765 (input.)58 b(The)34 b(same)f(can)h(b)r(e)h(said)f(for)f
4766 Fl(S)5 b Fo(\(\);)38 b(it)d(should)f(b)r(e)g(c)n(hosen)g(esp)r(ecially)
4767 f(to)0 589 y(protect)e(its)h(second)f(argumen)n(t)g(from)g(leak)-5
4768 b(age.)48 b(Additionally)-7 b(,)33 b(it)f(should)f(b)r(e)h(infeasible)g
4769 (to)f(reconstruct)g(either)g(v)-5 b(alue)0 689 y(of)32
4770 b Fl(K)38 b Fo(using)32 b(only)h Fl(P)12 b Fo(\()p Fl(w)r
4771 Fo(\),)34 b Fl(P)12 b Fo(\()p Fl(x)p Fo(\),)35 b Fl(P)12
4772 b Fo(\()p Fl(y)s Fo(\),)34 b(and)e Fl(P)12 b Fo(\()p
4773 Fl(z)t Fo(\).)51 b(No)33 b(closed-form)e(expression)g(that)i(do)r(es)f
4774 (this)g(should)h(exist,)g(and)0 789 y(ideally)e(w)n(e)f(w)n(ould)h(lik)
4775 n(e)g(this)g(to)g(b)r(e)g(as)g(di\016cult)h(as)e(in)n(v)n(erting)g
4776 Fl(P)12 b Fo(\(\).)48 b(F)-7 b(urther)31 b(restrictions)e(will)j(dep)r
4777 (end)f(on)g(the)h(exact)0 888 y(implemen)n(tation)c(of)f(AKE.)0
4778 1121 y Fg(3.2)112 b(SRP:)37 b(An)g(AKE)g(construction)0
4779 1274 y Fo(AKE)30 b(b)n(y)g(itself)g(is)h(merely)e(an)h(in)n(teresting)g
4780 (mathematical)g(exercise.)43 b(It)31 b(describ)r(es)f(the)g(broad)f
4781 (outline)i(of)f(a)g(family)g(of)0 1374 y(k)n(ey-exc)n(hange)24
4782 b(proto)r(cols,)i(but)i(it)f(is)g(necessary)f(to)g(\014ll)i(in)f(some)g
4783 (of)f(the)i(blanks)e(to)h(mak)n(e)g(the)g(proto)r(col)f(applicable)g
4784 (and)0 1473 y(enable)e(further)g(detailed)g(securit)n(y)g(analysis.)34
4785 b(This)24 b(section)g(presen)n(ts)f(the)i Fn(Se)l(cur)l(e)h(R)l(emote)g
4786 (Passwor)l(d)g Fo(\(SRP\))e(proto)r(col,)0 1573 y(one)j(p)r(ossible)g
4787 (in)n(terpretation)g(of)h(AKE)f(and)g(one)g(that)h(is)g(b)r(eliev)n(ed)
4788 f(to)h(b)r(e)g(simple,)f(fast,)h(and)g(highly)f(secure.)0
4789 1789 y Fp(3.2.1)94 b(SRP)31 b(sp)s(eci\014cations)0 1942
4790 y Fo(In)f(SRP)-7 b(,)29 b(all)h(computations)f(are)f(p)r(erformed)i(in)
4791 g(a)f(\014nite)h(\014eld)g(GF\()p Fl(n)p Fo(\).)44 b(In)29
4792 b(other)h(w)n(ords,)e(a)i(large)e(prime)h(n)n(um)n(b)r(er)h
4793 Fl(n)f Fo(is)0 2042 y(c)n(hosen)f(ahead)h(of)g(time,)h(and)g(all)f
4794 (additions,)g(m)n(ultiplications,)h(and)f(exp)r(onen)n(tiations)f(are)h
4795 (p)r(erformed)f(mo)r(dulo)i Fl(n)p Fo(.)42 b(All)0 2141
4796 y(input)28 b(parameters)e(and)i(outputs)g(of)f Fl(P)12
4797 b Fo(\(\),)28 b Fl(Q)p Fo(\(\),)g Fl(R)q Fo(\(\),)g(and)g
4798 Fl(S)5 b Fo(\(\))28 b(are)e(th)n(us)i(in)n(tegers)e(b)r(et)n(w)n(een)i
4799 (0)f(and)g Fl(n)19 b Fk(\000)f Fo(1)27 b(inclusiv)n(e.)125
4800 2241 y(The)g(\\one-w)n(a)n(y")e(v)n(eri\014er-generator)e
4801 Fl(P)12 b Fo(\(\))28 b(b)r(ecomes)g(a)f(mo)r(dular)g(exp)r(onen)n
4802 (tiation)g(in)h(GF\()p Fl(n)p Fo(\):)1764 2423 y Fl(P)12
4803 b Fo(\()p Fl(x)p Fo(\))24 b(=)f Fl(g)2095 2389 y Fd(x)3794
4804 2423 y Fo(\(2\))0 2606 y Fl(g)30 b Fo(is)e(a)f Fn(gener)l(ator)h
4805 Fo(in)g(GF\()p Fl(n)p Fo(\).)38 b(Remem)n(b)r(er)27 b(that)h(there)f
4806 (is)h(an)f(implicit)i(mo)r(dulo)e Fl(n)h Fo(in)f(eac)n(h)g
4807 (computation.)125 2706 y(The)g(functions)h Fl(Q)p Fo(\(\),)g
4808 Fl(R)q Fo(\(\),)g(and)f Fl(S)5 b Fo(\(\))28 b(are)f(the)h(follo)n
4809 (wing:)1568 2888 y Fl(Q)p Fo(\()p Fl(w)r(;)14 b(x)p Fo(\))84
4810 b(=)e Fl(w)21 b Fo(+)e Fl(ux)1461 b Fo(\(3\))1569 3013
4811 y Fl(R)q Fo(\()p Fl(w)r(;)14 b(x)p Fo(\))85 b(=)d Fl(w)r(x)2182
4812 2979 y Fd(u)3794 3013 y Fo(\(4\))1577 3137 y Fl(S)5 b
4813 Fo(\()p Fl(w)r(;)14 b(x)p Fo(\))85 b(=)d Fl(w)2135 3103
4814 y Fd(x)3794 3137 y Fo(\(5\))125 3320 y(The)24 b(role)f(of)h(the)h(v)-5
4815 b(ariable)23 b Fl(u)h Fo(will)g(b)r(e)h(explained)f(in)g(Section)g
4816 (3.2.4.)35 b(In)24 b(these)h(equations,)f Fl(u)f Fo(is)i(de\014ned)f
4817 (as)g(a)g(function)0 3420 y(of)34 b Fl(w)i Fo(and)d Fl(x)p
4818 Fo(:)50 b Fl(u)32 b Fo(=)h Fl(f)9 b Fo(\()p Fl(w)r(;)14
4819 b(x)p Fo(\).)56 b(By)33 b(insp)r(ection,)i(Equations)d(2{5)h(satisfy)g
4820 (Equation)f(1.)55 b(More)32 b(information)h(ab)r(out)h(the)0
4821 3519 y(n)n(um)n(b)r(er)27 b(theory)g(used)h(here)f(can)g(b)r(e)h(found)
4822 g(in)g([16)o(].)125 3619 y(As)i(stated)h(in)g(Section)g(3.1,)g(the)g(t)
4823 n(w)n(o)f(parties)g(still)h(need)g(to)g(v)n(erify)f(that)h(their)f
4824 (session)g(k)n(eys)g(matc)n(h)h(and)f(do)h(so)f(in)0
4825 3719 y(a)g(secure)g(manner.)46 b(SRP)30 b(accomplishes)g(this)h(with)g
4826 (a)f(simpli\014ed)h(MA)n(C)g(\(Message)e(Authen)n(tication)i(Co)r(de\))
4827 g(based)f(on)0 3818 y(one-w)n(a)n(y)c(hash)h(functions.)0
4828 4034 y Fp(3.2.2)94 b(The)32 b(SRP)g(proto)s(col)0 4187
4829 y Fo(What)37 b(follo)n(ws)e(is)i(a)f(complete)g(description)g(of)g(the)
4830 h(en)n(tire)f(SRP)h(authen)n(tication)f(pro)r(cess)f(from)h(b)r
4831 (eginning)g(to)h(end,)0 4287 y(starting)27 b(with)h(the)g(passw)n(ord)d
4832 (setup)j(steps.)125 4387 y(T)-7 b(able)32 b(3)g(sho)n(ws)g(the)h
4833 (notation)f(used)g(in)h(this)g(section.)52 b(The)33 b(v)-5
4834 b(alues)32 b Fl(n)h Fo(and)f Fl(g)j Fo(are)d(w)n(ell-kno)n(wn)f(v)-5
4835 b(alues,)34 b(agreed)d(to)0 4486 y(b)r(eforehand.)125
4836 4586 y(T)-7 b(o)27 b(establish)g(a)g(passw)n(ord)f Fl(P)39
4837 b Fo(with)28 b(Stev)n(e,)g(Carol)e(pic)n(ks)h(a)g(random)g(salt)g
4838 Fl(s)p Fo(,)h(and)f(computes)1730 4768 y Fl(x)d Fo(=)f
4839 Fl(H)7 b Fo(\()p Fl(s;)14 b(P)e Fo(\))1831 4951 y Fl(v)26
4840 b Fo(=)d Fl(g)2028 4917 y Fd(x)0 5100 y Fo(Stev)n(e)i(stores)f
4841 Fl(v)k Fo(and)d Fl(s)g Fo(as)g(Carol's)e(passw)n(ord)g(v)n(eri\014er)h
4842 (and)h(salt.)35 b(Remem)n(b)r(er)25 b(that)h(the)f(computation)g(of)g
4843 Fl(v)j Fo(is)d(implicitly)0 5200 y(reduced)i(mo)r(dulo)h
4844 Fl(n)p Fo(.)37 b Fl(x)28 b Fo(is)f(discarded)g(b)r(ecause)g(it)h(is)g
4845 (equiv)-5 b(alen)n(t)27 b(to)g(the)h(plain)n(text)g(passw)n(ord)d
4846 Fl(P)12 b Fo(.)125 5300 y(The)31 b(AKE)h(proto)r(col)e(also)h(allo)n
4847 (ws)f(Stev)n(e)i(to)g(ha)n(v)n(e)e(a)i(passw)n(ord)d
4848 Fl(z)36 b Fo(with)c(a)f(corresp)r(onding)f(public)i(k)n(ey)g
4849 Fl(g)3559 5270 y Fd(z)3628 5300 y Fo(held)g(b)n(y)0 5399
4850 y(Carol;)22 b(in)e(SRP)-7 b(,)21 b(w)n(e)f(set)g Fl(z)27
4851 b Fo(=)22 b(0)e(so)g(that)h(it)g(drops)e(out)i(of)f(the)h(equations.)34
4852 b(Since)21 b(this)f(priv)-5 b(ate)20 b(k)n(ey)g(is)h(0,)g(the)g
4853 (corresp)r(onding)1929 5656 y(6)p eop
4854 %%Page: 7 7
4855 7 6 bop 648 460 a Fl(n)99 b Fo(A)28 b(large)e(prime)i(n)n(um)n(b)r(er.)
4856 36 b(All)28 b(computations)f(are)g(p)r(erformed)g(mo)r(dulo)h
4857 Fl(n)p Fo(.)655 560 y Fl(g)102 b Fo(A)28 b(primitiv)n(e)f(ro)r(ot)g(mo)
4858 r(dulo)h Fl(n)f Fo(\(often)h(called)g(a)f Fn(gener)l(ator)p
4859 Fo(\))659 659 y Fl(s)99 b Fo(A)28 b(random)f(string)g(used)g(as)g(the)h
4860 (user's)f Fn(salt)633 759 y Fl(P)111 b Fo(The)28 b(user's)e(passw)n
4861 (ord)650 858 y Fl(x)100 b Fo(A)28 b(priv)-5 b(ate)27
4862 b(k)n(ey)g(deriv)n(ed)g(from)g(the)h(passw)n(ord)e(and)h(salt)654
4863 958 y Fl(v)103 b Fo(The)28 b(host's)f(passw)n(ord)e(v)n(eri\014er)650
4864 1058 y Fl(u)99 b Fo(Random)27 b(scram)n(bling)f(parameter,)h(publicly)h
4865 (rev)n(ealed)581 1157 y Fl(a;)14 b(b)99 b Fo(Ephemeral)27
4866 b(priv)-5 b(ate)27 b(k)n(eys,)g(generated)f(randomly)g(and)i(not)g
4867 (publicly)f(rev)n(ealed)531 1257 y Fl(A;)14 b(B)104 b
4868 Fo(Corresp)r(onding)26 b(public)i(k)n(eys)557 1357 y
4869 Fl(H)7 b Fo(\(\))100 b(One-w)n(a)n(y)26 b(hash)h(function)538
4870 1456 y Fl(m;)14 b(n)99 b Fo(The)28 b(t)n(w)n(o)f(quan)n(tities)g
4871 (\(strings\))g Fl(m)h Fo(and)f Fl(n)h Fo(concatenated)621
4872 1556 y Fl(K)105 b Fo(Session)27 b(k)n(ey)1202 1735 y(T)-7
4873 b(able)27 b(3:)36 b(Mathematical)27 b(Notation)h(for)f(SRP)0
4874 2067 y(public)h(k)n(ey)g(is)f(1.)38 b(Consequen)n(tly)-7
4875 b(,)27 b(instead)h(of)g(safeguarding)e(its)i(o)n(wn)f(passw)n(ord)f
4876 Fl(z)t Fo(,)h(Stev)n(e)h(needs)g(only)f(to)h(k)n(eep)g(Carol's)0
4877 2166 y(v)n(eri\014er)g Fl(v)34 b Fo(secret)29 b(to)g(assure)g(m)n
4878 (utual)h(authen)n(tication.)43 b(This)29 b(frees)h(Carol)e(from)i(ha)n
4879 (ving)e(to)i(remem)n(b)r(er)f(Stev)n(e's)h(public)0 2266
4880 y(k)n(ey)d(and)g(simpli\014es)h(the)g(proto)r(col.)125
4881 2366 y(T)-7 b(o)25 b(authen)n(ticate,)h(Carol)e(and)h(Stev)n(e)h
4882 (engage)e(in)i(the)g(proto)r(col)e(describ)r(ed)i(in)f(T)-7
4883 b(able)26 b(4.)36 b(A)26 b(description)f(of)g(eac)n(h)g(step)0
4884 2465 y(follo)n(ws:)1417 2718 y(Carol)811 b(Stev)n(e)p
4885 976 2751 1948 4 v 1026 2846 a(1.)1983 2799 y Fd(C)1942
4886 2846 y Fk(\000)-15 b(!)215 b Fo(\(lo)r(okup)27 b Fl(s)p
4887 Fo(,)h Fl(v)s Fo(\))1026 2956 y(2.)205 b Fl(x)24 b Fo(=)f
4888 Fl(H)7 b Fo(\()p Fl(s;)14 b(P)e Fo(\))1993 2909 y Fd(s)1942
4889 2956 y Fk( )-14 b(\000)1026 3081 y Fo(3.)297 b Fl(A)24
4890 b Fo(=)e Fl(g)1604 3051 y Fd(a)1984 3034 y(A)1942 3081
4891 y Fk(\000)-15 b(!)1026 3210 y Fo(4.)1953 3159 y Fd(B)s(;u)1942
4892 3210 y Fk( )h(\000)249 b Fl(B)28 b Fo(=)22 b Fl(v)g Fo(+)c
4893 Fl(g)2691 3180 y Fd(b)1026 3310 y Fo(5.)99 b Fl(S)28
4894 b Fo(=)22 b(\()p Fl(B)h Fk(\000)18 b Fl(g)1600 3280 y
4895 Fd(x)1642 3310 y Fo(\))1674 3280 y Fd(a)p Fh(+)p Fd(ux)2318
4896 3310 y Fl(S)28 b Fo(=)22 b(\()p Fl(Av)2621 3280 y Fd(u)2666
4897 3310 y Fo(\))2698 3280 y Fd(b)1026 3410 y Fo(6.)233 b
4898 Fl(K)29 b Fo(=)23 b Fl(H)7 b Fo(\()p Fl(S)e Fo(\))625
4899 b Fl(K)29 b Fo(=)22 b Fl(H)7 b Fo(\()p Fl(S)e Fo(\))1026
4900 3536 y(7.)101 b Fl(M)1273 3548 y Fh(1)1333 3536 y Fo(=)22
4901 b Fl(H)7 b Fo(\()p Fl(A;)14 b(B)t(;)g(K)6 b Fo(\))1961
4902 3488 y Fd(M)2024 3496 y Fc(1)1942 3536 y Fk(\000)-15
4903 b(!)243 b Fo(\(v)n(erify)27 b Fl(M)2662 3548 y Fh(1)2699
4904 3536 y Fo(\))1026 3662 y(8.)218 b(\(v)n(erify)28 b Fl(M)1654
4905 3674 y Fh(2)1690 3662 y Fo(\))1961 3614 y Fd(M)2024 3622
4906 y Fc(2)1942 3662 y Fk( )-14 b(\000)99 b Fl(M)2256 3674
4907 y Fh(2)2316 3662 y Fo(=)23 b Fl(H)7 b Fo(\()p Fl(A;)14
4908 b(M)2692 3674 y Fh(1)2729 3662 y Fl(;)g(K)6 b Fo(\))1078
4909 3841 y(T)-7 b(able)27 b(4:)37 b(The)27 b(Secure)h(Remote)f(P)n(assw)n
4910 (ord)e(Proto)r(col)101 4206 y(1.)42 b(Carol)26 b(sends)h(Stev)n(e)g
4911 (her)h(username,)e(\(e.g.)37 b Fe(carol)p Fo(\).)101
4912 4372 y(2.)42 b(Stev)n(e)29 b(lo)r(oks)g(up)i(Carol's)d(passw)n(ord)g
4913 (en)n(try)i(and)f(fetc)n(hes)h(her)g(passw)n(ord)e(v)n(eri\014er)h
4914 Fl(v)k Fo(and)d(her)f(salt)h Fl(s)p Fo(.)44 b(He)30 b(sends)g
4915 Fl(s)208 4472 y Fo(to)d(Carol.)36 b(Carol)26 b(computes)h(her)g
4916 (long-term)g(priv)-5 b(ate)27 b(k)n(ey)g Fl(x)h Fo(using)f
4917 Fl(s)h Fo(and)f(her)h(real)e(passw)n(ord)g Fl(P)12 b
4918 Fo(.)101 4638 y(3.)42 b(Carol)22 b(generates)h(a)g(random)g(n)n(um)n(b)
4919 r(er)h Fl(a)p Fo(,)h(1)d Fl(<)h(a)g(<)g(n)p Fo(,)h(computes)g(her)g
4920 (ephemeral)f(public)i(k)n(ey)e Fl(A)g Fo(=)g Fl(g)3460
4921 4608 y Fd(a)3500 4638 y Fo(,)i(and)e(sends)208 4737 y(it)28
4922 b(to)f(Stev)n(e.)101 4903 y(4.)42 b(Stev)n(e)27 b(generates)e(his)j(o)n
4923 (wn)e(random)h(n)n(um)n(b)r(er)g Fl(b)p Fo(,)g(1)22 b
4924 Fl(<)h(b)g(<)f(n)p Fo(,)28 b(computes)f(his)g(ephemeral)f(public)i(k)n
4925 (ey)f Fl(B)g Fo(=)c Fl(v)e Fo(+)c Fl(g)3844 4873 y Fd(b)3877
4926 4903 y Fo(,)208 5003 y(and)27 b(sends)g(it)h(bac)n(k)f(to)h(Carol,)e
4927 (along)g(with)i(the)g(randomly)f(generated)f(parameter)g
4928 Fl(u)p Fo(.)101 5169 y(5.)42 b(Carol)21 b(and)j(Stev)n(e)f(compute)g
4929 (the)h(common)f(exp)r(onen)n(tial)f(v)-5 b(alue)23 b
4930 Fl(S)28 b Fo(=)23 b Fl(g)2463 5139 y Fd(ab)p Fh(+)p Fd(bux)2712
4931 5169 y Fo(using)g(the)h(v)-5 b(alues)23 b(a)n(v)-5 b(ailable)22
4932 b(to)h(eac)n(h)208 5269 y(of)31 b(them.)48 b(If)32 b(Carol's)d(passw)n
4933 (ord)h Fl(P)43 b Fo(en)n(tered)31 b(in)g(Step)h(2)f(matc)n(hes)f(the)i
4934 (one)f(she)g(originally)e(used)j(to)f(generate)f Fl(v)s
4935 Fo(,)208 5368 y(then)e(b)r(oth)g(v)-5 b(alues)27 b(of)g
4936 Fl(S)33 b Fo(will)28 b(matc)n(h.)1929 5656 y(7)p eop
4937 %%Page: 8 8
4938 8 7 bop 101 390 a Fo(6.)42 b(Both)27 b(sides)g(hash)g(the)h(exp)r(onen)
4939 n(tial)f Fl(S)33 b Fo(in)n(to)27 b(a)g(cryptographically)e(strong)i
4940 (session)f(k)n(ey)-7 b(.)101 552 y(7.)42 b(Carol)22 b(sends)j(Stev)n(e)
4941 f Fl(M)949 564 y Fh(1)1010 552 y Fo(as)f(evidence)i(that)f(she)g(has)g
4942 (the)h(correct)e(session)g(k)n(ey)-7 b(.)35 b(Stev)n(e)24
4943 b(computes)g Fl(M)3424 564 y Fh(1)3485 552 y Fo(himself)h(and)208
4944 651 y(v)n(eri\014es)h(that)i(it)g(matc)n(hes)f(what)g(Carol)g(sen)n(t)g
4945 (him.)101 813 y(8.)42 b(Stev)n(e)21 b(sends)g(Carol)f
4946 Fl(M)940 825 y Fh(2)999 813 y Fo(as)g(evidence)i(that)f(he)h(also)e
4947 (has)h(the)h(correct)e(session)h(k)n(ey)-7 b(.)34 b(Carol)20
4948 b(also)h(v)n(eri\014es)f Fl(M)3585 825 y Fh(2)3643 813
4949 y Fo(herself,)208 913 y(accepting)27 b(only)g(if)h(it)g(matc)n(hes)f
4950 (Stev)n(e's)g(v)-5 b(alue.)125 1084 y(This)33 b(proto)r(col)g(is)h
4951 (mostly)g(the)g(result)g(of)f(substituting)i(the)f(equations)f(of)h
4952 (Section)g(3.2.1)f(in)n(to)g(the)i(generic)e(AKE)0 1184
4953 y(proto)r(col,)g(adding)g(explicit)h(\015o)n(ws)e(to)h(exc)n(hange)f
4954 (information)g(lik)n(e)h(the)h(user's)e(iden)n(tit)n(y)h(and)g(the)h
4955 (salt)f Fl(s)p Fo(.)53 b(Both)33 b(sides)0 1283 y(will)f(agree)e(on)i
4956 (the)g(session)f(k)n(ey)g Fl(S)k Fo(=)30 b Fl(g)1305
4957 1253 y Fd(ab)p Fh(+)p Fd(bux)1563 1283 y Fo(if)i(all)g(steps)g(are)e
4958 (executed)i(correctly)-7 b(.)49 b(SRP)31 b(also)g(adds)h(the)g(t)n(w)n
4959 (o)f(\015o)n(ws)0 1383 y(at)c(the)h(end)g(to)f(v)n(erify)g(session)f(k)
4960 n(ey)h(agreemen)n(t)f(using)h(a)g(one-w)n(a)n(y)e(hash)i(function.)37
4961 b(Once)27 b(the)h(proto)r(col)e(run)h(completes)0 1483
4962 y(successfully)-7 b(,)27 b(b)r(oth)h(parties)f(ma)n(y)g(use)g
4963 Fl(K)34 b Fo(to)27 b(encrypt)g(subsequen)n(t)h(session)e(tra\016c.)0
4964 1697 y Fp(3.2.3)94 b(Computation)30 b(of)i Fl(B)0 1850
4965 y Fo(Observ)-5 b(an)n(t)34 b(readers)g(will)i(notice)f(that)h(Stev)n
4966 (e's)f(ephemeral)g(public)h(k)n(ey)f(in)h(Step)g(4)f(is)h(the)g(sum)f
4967 (of)h(t)n(w)n(o)f(exp)r(onen)n(tial)0 1949 y(residues.)h(Wh)n(y)28
4968 b(not)f(just)i(mak)n(e)d Fl(B)h Fo(=)c Fl(g)1297 1919
4969 y Fd(b)1358 1949 y Fo(and)k(simplify)h(the)g(proto)r(col?)125
4970 2049 y(Unfortunately)-7 b(,)31 b(that)g(simpli\014cation)f(op)r(ens)h
4971 (the)g(proto)r(col)e(to)i(the)g(an)f(activ)n(e)g(dictionary)g(attac)n
4972 (k,)g(carried)g(out)g(b)n(y)0 2149 y(an)e(attac)n(k)n(er)e(who)i
4973 (masquerades)e(as)h(a)h(legitimate)g(host)f(and)h(con)n(vinces)f(Carol)
4974 g(to)h(mak)n(e)f(an)h(authen)n(tication)f(attempt.)0
4975 2248 y(The)h(attac)n(k)n(er,)e(Sue,)h(captures)g Fl(s)h
4976 Fo(from)f(a)g(legitimate)h(session)e(and)i(pro)r(ceeds)e(as)h(follo)n
4977 (ws:)101 2420 y(1.)42 b(Carol)26 b(sends)h(Sue)h(her)f(username.)101
4978 2581 y(2.)42 b(Sue)27 b(sends)h(Carol)e(the)i(salt)f
4979 Fl(s)h Fo(she)f(sno)r(op)r(ed)h(earlier.)101 2743 y(3.)42
4980 b(Carol)26 b(sends)h(Sue)h(her)f(public)h(exp)r(onen)n(tial)f(residue)g
4981 Fl(A)p Fo(.)101 2905 y(4.)42 b(Sue)27 b(pic)n(ks)g(her)h(o)n(wn)f
4982 (random)f Fl(b)i Fo(and)f Fl(u)p Fo(,)g(computes)h(her)f(o)n(wn)g
4983 (residue)g Fl(B)32 b Fo(and)27 b(sends)g Fl(B)32 b Fo(and)c
4984 Fl(u)f Fo(to)g(Carol.)101 3066 y(5.)42 b(Carol)31 b(computes)i(her)g
4985 (session)f(k)n(ey)h Fl(S)k Fo(=)32 b Fl(B)1650 3036 y
4986 Fd(a)p Fh(+)p Fd(ux)1818 3066 y Fo(,)j(computes)e Fl(K)38
4987 b Fo(from)33 b Fl(S)5 b Fo(,)34 b(and)f(happily)h(sends)e(Sue)i(a)f
4988 (pro)r(of)f(of)208 3166 y(that)27 b Fl(K)6 b Fo(.)101
4989 3327 y(6.)42 b(Sue)27 b(sim)n(ulates)g(net)n(w)n(ork)g(failure)g(or)f
4990 (simply)i(noti\014es)g(Carol)e(that)i(the)g(passw)n(ord)d(w)n(as)i
4991 (incorrect.)125 3499 y(No)n(w,)32 b(Sue)h(has)e Fl(A)i
4992 Fo(and)f(her)f(o)n(wn)h Fl(b)p Fo(,)h(along)e(with)h(a)g(pro)r(of)f(of)
4993 h Fl(K)38 b Fo(from)32 b(Carol.)49 b(She)32 b(can)g(guess)f(at)h(a)g
4994 (passw)n(ord)e Fl(p)3854 3469 y Fb(0)3877 3499 y Fo(,)0
4995 3599 y(compute)e Fl(x)384 3569 y Fb(0)436 3599 y Fo(from)g(it)g(and)g
4996 (then)h Fl(v)1111 3569 y Fb(0)1162 3599 y Fo(from)f(that,)g(construct)g
4997 Fl(S)1984 3569 y Fb(0)2035 3599 y Fo(as)f Fl(S)2193 3569
4998 y Fb(0)2240 3599 y Fo(=)d(\()p Fl(Av)2466 3569 y Fb(0)p
4999 Fd(u)2529 3599 y Fo(\))2561 3569 y Fd(b)2595 3599 y Fo(,)k(and)g
5000 (\014nally)g Fl(K)3137 3569 y Fb(0)3183 3599 y Fo(=)23
5001 b Fl(H)7 b Fo(\()p Fl(S)3435 3569 y Fb(0)3459 3599 y
5002 Fo(\),)28 b(and)g(c)n(hec)n(k)0 3698 y(it)g(against)e(Carol's)g(pro)r
5003 (of)i(of)f(the)h(real)f Fl(K)6 b Fo(.)36 b(If)28 b(they)g(matc)n(h,)f
5004 (the)h(guessed)f(passw)n(ord)f(is)h(correct.)125 3798
5005 y(Since)k(this)h(attac)n(k)e(comes)h(from)g(an)g(imp)r(ostor)g(who)g
5006 (do)r(es)g(not)g(kno)n(w)f Fl(v)35 b Fo(\(an)n(y)n(one)30
5007 b(who)h Fn(do)l(es)h Fo(kno)n(w)f Fl(v)k Fo(can)c(already)0
5008 3898 y(p)r(erform)26 b(a)h(dictionary)f(attac)n(k\),)g(one)g(w)n(a)n(y)
5009 g(to)h(th)n(w)n(art)f(it)h(is)g(to)f(force)g(the)h(host)g(to)g(commit)g
5010 (to)f(its)h(v)-5 b(alue)27 b(of)g Fl(v)j Fo(in)d(Step)g(4.)0
5011 3997 y(Ho)n(w)n(ev)n(er,)g(the)h(w)n(a)n(y)f(in)i(whic)n(h)f(the)h
5012 (residues)e Fl(g)1509 3967 y Fd(b)1570 3997 y Fo(and)h
5013 Fl(v)k Fo(are)27 b(com)n(bined)h(m)n(ust)h(b)r(e)f(selected)h
5014 (carefully)-7 b(.)38 b(If)29 b(w)n(e)e(denote)i(the)0
5015 4097 y(\\com)n(bining)34 b(function")h(used)g(to)g(compute)g
5016 Fl(B)k Fo(as)34 b Fl(B)39 b Fo(=)c Fl(f)9 b Fo(\()p Fl(v)s(;)14
5017 b(g)2090 4067 y Fd(b)2123 4097 y Fo(\),)37 b(then)f(w)n(e)e(wish)h(to)g
5018 (a)n(v)n(oid)e(using)i(functions)g Fl(f)44 b Fo(that)0
5019 4212 y(ha)n(v)n(e)30 b(the)h(prop)r(ert)n(y)f(that)h
5020 Fl(f)9 b Fo(\()p Fl(g)992 4182 y Fd(x)1034 4212 y Fl(;)14
5021 b(g)1114 4182 y Fd(y)1153 4212 y Fo(\))29 b(=)f Fl(g)1364
5022 4166 y Fh(^)1350 4182 y Fd(f)7 b Fh(\()p Fd(x;y)r Fh(\))1569
5023 4212 y Fo(for)31 b(some)f(easily-deriv)n(ed)2452 4190
5024 y(^)2434 4212 y Fl(f)9 b Fo(\(\).)47 b(The)32 b(attac)n(k)e(describ)r
5025 (ed)g(ab)r(o)n(v)n(e)g(can)h(b)r(e)0 4311 y(extended)d(to)f(situations)
5026 g(where)h Fl(f)9 b Fo(\(\))27 b(has)g(this)h(undesirable)f(prop)r(ert)n
5027 (y)-7 b(.)36 b(This)28 b(rules)f(out,)g(for)g(example,)h
5028 Fl(f)9 b Fo(\()p Fl(x;)14 b(y)s Fo(\))23 b(=)f Fl(xy)s
5029 Fo(.)125 4411 y(In)k(addition,)g(w)n(e)g(also)f(wish)h(the)g(v)-5
5030 b(alue)26 b(of)g Fl(B)k Fo(to)c(leak)f(as)h(little)h(information)e(ab)r
5031 (out)h Fl(v)j Fo(as)d(p)r(ossible,)g(whic)n(h)g(rules)f(out)0
5032 4511 y Fl(f)9 b Fo(\()p Fl(x;)14 b(y)s Fo(\))30 b(=)g
5033 Fl(x)22 b Fk(\010)e Fl(y)35 b Fo(\(i.e.)50 b(\\exclusiv)n(e-or"\))29
5034 b(or)i Fl(f)9 b Fo(\()p Fl(x;)14 b(y)s Fo(\))30 b(=)f
5035 Fl(E)1888 4523 y Fd(y)1929 4511 y Fo(\()p Fl(x)p Fo(\),)34
5036 b(where)d Fl(E)2402 4523 y Fd(k)2443 4511 y Fo(\(\))h(is)g(a)f
5037 (symmetric)h(encryption)f(algorithm.)0 4610 y(In)g(either)g(of)g(these)
5038 g(cases,)f(an)h(attac)n(k)n(er)e(can)h(carry)g(out)h(a)f
5039 Fn(p)l(artition)k(attack,)e Fo(whic)n(h)f(facilitates)g(an)f
5040 (o\013-line)h(passw)n(ord)0 4710 y(searc)n(h)26 b(b)n(y)i(eliminating)g
5041 (imp)r(ossible)g(passw)n(ords.)35 b(F)-7 b(or)28 b(example,)f(if)i(w)n
5042 (e)e(used)h Fl(B)g Fo(=)23 b Fl(v)f Fk(\010)c Fl(g)2885
5043 4680 y Fd(b)2918 4710 y Fo(,)28 b(an)g(attac)n(k)n(er)e(could)i
5044 (capture)0 4809 y Fl(B)33 b Fo(and)c(compute)g(a)f(guessed)h(v)n
5045 (eri\014er)e Fl(v)1291 4779 y Fb(0)1344 4809 y Fo(for)h(eac)n(h)g
5046 (passw)n(ord)f(guess.)40 b(If)29 b Fl(B)24 b Fk(\010)19
5047 b Fl(v)2572 4779 y Fb(0)2621 4809 y Fl(>)25 b(n)p Fo(,)k(then)g(that)g
5048 (particular)f(passw)n(ord)0 4909 y(guess)g(can)h(b)r(e)h(ruled)f(out)h
5049 (as)e(imp)r(ossible.)42 b(If)30 b(this)g(is)f(done)g(o)n(v)n(er)e(a)i
5050 (n)n(um)n(b)r(er)g(of)h(sessions,)e(an)h(attac)n(k)n(er)f(ma)n(y)g(b)r
5051 (e)i(able)f(to)0 5009 y(reduce)e(the)h(n)n(um)n(b)r(er)f(of)h(p)r
5052 (ossible)f(passw)n(ords)f(to)h(a)g(n)n(um)n(b)r(er)h(small)f(enough)g
5053 (to)g(p)r(ermit)h(brute-force)f(guessing.)125 5108 y(Mo)r(dular)j
5054 (addition)h(app)r(ears)f(to)h(b)r(e)h(the)g(simplest)f(op)r(eration)f
5055 (that)i(leaks)e(no)h(information)f(ab)r(out)i Fl(v)i
5056 Fo(while)e(at)f(the)0 5208 y(same)g(time)i(enabling)f(SRP)g(to)f
5057 (resist)h(a)g(dictionary)f(attac)n(k)g(b)n(y)h(a)f(fak)n(e)h(host.)50
5058 b(Additionally)-7 b(,)33 b Fl(g)i Fo(m)n(ust)d(b)r(e)h(a)e(primitiv)n
5059 (e)0 5308 y(ro)r(ot)i(of)g(GF\()p Fl(n)p Fo(\))h(in)g(order)e(to)h(mak)
5060 n(e)g(all)g(v)-5 b(alues)33 b(of)g Fl(B)38 b Fo(equiprobable)32
5061 b(for)h(an)n(y)g Fl(v)s Fo(.)54 b(If)34 b(this)g(requiremen)n(t)e(is)i
5062 (not)f(met,)i(a)0 5407 y(partition)27 b(attac)n(k)g(again)f(b)r(ecomes)
5063 h(p)r(ossible.)1929 5656 y(8)p eop
5064 %%Page: 9 9
5065 9 8 bop 0 390 a Fp(3.2.4)94 b(The)32 b(role)f(of)h Fl(u)0
5066 543 y Fo(Wh)n(y)g(is)g(the)h(parameter)e Fl(u)h Fo(used)g(at)g(all)g
5067 (in)h(the)f(SRP)h(proto)r(col)e(when)h(it)h(is)f(broadcast)f(in)h(the)h
5068 (clear)e(in)h(Step)h(4?)51 b(Let)0 643 y(us)30 b(assume,)h(for)f(the)h
5069 (momen)n(t,)g(that)g(an)f(in)n(truder,)h(Chris,)g(who)f(has)g(captured)
5070 g Fl(v)k Fo(p)r(oses)c(as)g(a)g(fak)n(e)g(clien)n(t)h(attempting)0
5071 743 y(to)e(gain)f(access)f(to)i(the)g(host.)40 b(Let)29
5072 b(us)g(also)e(assume)h(that)i(Chris)e(has)g(someho)n(w)f(disco)n(v)n
5073 (ered)g(the)i(v)-5 b(alue)29 b(of)g Fl(u)f Fo(in)h(Step)g(3,)0
5074 842 y(p)r(erhaps)h(through)f(psyc)n(hic)h(abilit)n(y)g(or)g(\(more)f
5075 (lik)n(ely\))i(as)e(a)h(result)g(of)h(a)e(\015a)n(w)h(in)h(Stev)n(e's)f
5076 (random)f(n)n(um)n(b)r(er)h(generator.)0 942 y(Under)e(these)f
5077 (circumstances,)g(Chris)g(can)g(gain)g(access)f(to)i(the)g(host)f
5078 (using)g(the)h(follo)n(wing)f(steps:)101 1117 y(1.)42
5079 b(Chris)27 b(sends)g(Carol's)f(username)h(to)g(Stev)n(e.)101
5080 1280 y(2.)42 b(Stev)n(e)27 b(sends)g(Carol's)f(salt)i
5081 Fl(s)f Fo(to)h(Chris.)101 1443 y(3.)42 b(Chris)27 b(computes)1857
5082 1542 y Fl(A)c Fo(=)g Fl(g)2073 1508 y Fd(a)2112 1542
5083 y Fl(v)2155 1508 y Fb(\000)p Fd(u)208 1687 y Fo(and)k(sends)g(it)h(to)g
5084 (Stev)n(e)f(instead)h(of)f(using)g(the)h(regular)e(form)n(ula)h(for)g
5085 Fl(A)p Fo(.)101 1850 y(4.)42 b(Stev)n(e)27 b(sends)g
5086 Fl(B)g Fo(=)c Fl(v)f Fo(+)c Fl(g)1017 1820 y Fd(b)1077
5087 1850 y Fo(bac)n(k)27 b(to)h(Chris)f(as)g(exp)r(ected.)101
5088 2013 y(5.)42 b(Chris)27 b(computes)g(the)h(session)f(k)n(ey)f(K)i(as:)
5089 1604 2188 y Fl(K)h Fo(=)22 b Fl(H)7 b Fo(\(\()p Fl(B)23
5090 b Fk(\000)18 b Fl(v)s Fo(\))2175 2154 y Fd(a)2239 2188
5091 y Fo(mo)r(d)23 b Fl(n)p Fo(\))101 2395 y(6.)42 b(Chris)27
5092 b(sends)g(Stev)n(e)g(a)h(pro)r(of)f(of)g(this)h Fl(K)33
5093 b Fo(and)28 b(logs)e(in)i(as)f(Carol.)125 2570 y(This)g(attac)n(k)g(w)n
5094 (orks)f(b)r(ecause)h(Stev)n(e)g(computes)h(his)f(session)g(k)n(ey)g
5095 (as:)1374 2761 y Fl(S)h Fo(=)22 b(\()p Fl(Av)1677 2726
5096 y Fd(u)1721 2761 y Fo(\))1753 2726 y Fd(b)1810 2761 y
5097 Fo(=)h(\()p Fl(g)1973 2726 y Fd(a)2013 2761 y Fl(v)2056
5098 2726 y Fb(\000)p Fd(u)2151 2761 y Fl(v)2194 2726 y Fd(u)2238
5099 2761 y Fo(\))2270 2726 y Fd(b)2327 2761 y Fo(=)f Fl(g)2457
5100 2726 y Fd(ab)125 2936 y Fo(Note)30 b(that)g(this)g(v)-5
5101 b(alue)30 b(is)g(indep)r(enden)n(t)h(of)f(the)g(long-term)f(k)n(eys,)h
5102 (and)f(can)h(easily)f(b)r(e)h(computed)h(b)n(y)e(Chris.)44
5103 b(Since)0 3035 y(he)25 b(has)g(the)h(same)f(session)f(k)n(ey)g(that)i
5104 (Stev)n(e)f(has,)g(he)h(can)f(fo)r(ol)g(Stev)n(e)g(in)n(to)g(b)r
5105 (elieving)g(that)h(he)f(is)h(Carol.)34 b(Ob)n(viously)-7
5106 b(,)25 b(this)0 3135 y(attac)n(k)i(can)g(also)f(b)r(e)i(carried)f(out)g
5107 (if)h Fl(u)f Fo(is)h(\014xed)g(to)f(a)g(publicly-kno)n(wn)g(v)-5
5108 b(alue.)125 3235 y(T)e(o)22 b(prev)n(en)n(t)g(Chris)g(from)g(b)r(eing)h
5109 (able)f(to)g(cancel)g(out)h(the)g Fl(v)j Fo(term)d(in)f(this)h(manner,)
5110 g(Stev)n(e)g(m)n(ust)g(not)f(rev)n(eal)f(the)i(v)-5 b(alue)0
5111 3334 y(of)28 b Fl(u)f Fo(un)n(til)h(after)f(he)h(receiv)n(es)e
5112 Fl(A)i Fo(from)f(the)h(user.)37 b(Since)27 b Fl(u)h Fo(is)f(comm)n
5113 (unicated)g(publicly)-7 b(,)29 b(it)f(is)f(p)r(ossible)g(to)h
5114 (\\piggybac)n(k")0 3434 y(it)g(on)f(top)g(of)g(another)g(public)g(v)-5
5115 b(alue,)28 b(th)n(us)f(transmitting)g(it)h(implicitly)-7
5116 b(.)37 b(F)-7 b(or)27 b(example,)g(b)r(oth)h(sides)f(can)f(compute)i
5117 Fl(u)f Fo(as)0 3533 y(a)h(simple)i(function)f(of)g Fl(B)t
5118 Fo(,)g(in)g(whic)n(h)g(case)f(Stev)n(e)h(m)n(ust)g(w)n(ait)f(for)h
5119 (Carol)e(to)i(send)g(out)g Fl(A)g Fo(b)r(efore)g(he)g(sends)f(bac)n(k)g
5120 Fl(B)33 b Fo(and)0 3633 y(rev)n(eals)26 b Fl(u)p Fo(.)36
5121 b(In)28 b(either)g(case,)e Fl(u)d Fo(=)g(0)k(m)n(ust)g(b)r(e)h(a)n(v)n
5122 (oided)f(for)g(ob)n(vious)f(reasons.)0 3906 y Fm(4)135
5123 b(Securit)l(y)45 b(analysis)0 4088 y Fo(It)30 b(is)f(easy)g(to)g(pro)n
5124 (v)n(e)f(that)i(b)r(oth)g(AKE)f(and)g(SRP)h(are)e(\\correct")f(in)j
5125 (the)g(sense)f(that)h(b)r(oth)g(parties)f(are)f(guaran)n(teed)g(to)0
5126 4188 y(agree)21 b(on)g(a)h(session)f(k)n(ey)g(if)i(the)g(correct)d
5127 (passw)n(ords)g(are)h(supplied)i(and)f(the)g(soft)n(w)n(are)e(on)i(b)r
5128 (oth)h(sides)f(functions)g(prop)r(erly)-7 b(.)0 4287
5129 y(It)23 b(is)f(more)g(di\016cult)h(to)g(sho)n(w,)g(as)e(this)i(section)
5130 f(attempts)h(to)g(do,)g(that)g(these)g(proto)r(cols)e(are)g(in)i(fact)g
5131 (secure.)34 b(This)23 b(means)0 4387 y(man)n(y)30 b(things)g(in)h(the)g
5132 (con)n(text)f(of)g(authen)n(tication)g(proto)r(cols.)44
5133 b(In)31 b(general)e(terms,)i(an)f(in)n(truder,)g(who)g(is)h(de\014ned)g
5134 (here)0 4487 y(as)f(a)h(malicious)f(third)h(part)n(y)f(in)n(terested)g
5135 (in)h(sub)n(v)n(erting)f(comm)n(unications)f(b)r(et)n(w)n(een)i(Carol)f
5136 (and)g(Stev)n(e,)i(m)n(ust)f(not)g(b)r(e)0 4586 y(able)f(to)g(gain)g
5137 (access)f(to)h(the)g(host)g(merely)g(b)n(y)g(observing)f(the)h
5138 (messages)f(exc)n(hanged)g(during)h(a)f(successful)h(run)g(of)h(the)0
5139 4686 y(proto)r(col.)36 b(In)27 b(the)h(case)f(of)h(SRP)-7
5140 b(,)27 b(w)n(e)h(w)n(ould)f(lik)n(e)g(to)g(strengthen)h(this)f
5141 (de\014nition)h(further)g(in)g(the)g(follo)n(wing)e(w)n(a)n(ys:)101
5142 4846 y(1.)42 b(No)e(useful)i(information)e(ab)r(out)h(the)g(passw)n
5143 (ord)e Fl(P)53 b Fo(or)40 b(its)h(asso)r(ciated)f(priv)-5
5144 b(ate)40 b(k)n(ey)g Fl(x)i Fo(is)f(rev)n(ealed)e(during)h(a)208
5145 4945 y(successful)18 b(run.)34 b(Sp)r(eci\014cally)-7
5146 b(,)20 b(w)n(e)e(wish)h(to)f(prev)n(en)n(t)g(an)g(attac)n(k)n(er)f
5147 (from)h(b)r(eing)h(able)f(to)g(guess)g(and)h(v)n(erify)e(passw)n(ords)
5148 208 5045 y(based)27 b(on)g(exc)n(hanged)f(messages.)101
5149 5208 y(2.)42 b(No)26 b(useful)h(information)f(ab)r(out)h(the)g(session)
5150 e(k)n(ey)h Fl(K)33 b Fo(is)26 b(rev)n(ealed)f(to)i(an)f(ea)n(v)n
5151 (esdropp)r(er)e(during)j(a)f(successful)g(run.)208 5308
5152 y(Since)f Fl(K)31 b Fo(is)26 b(a)f(cryptographically)e(strong)i(k)n(ey)
5153 g(instead)g(of)h(a)f(limited-en)n(trop)n(y)f(passw)n(ord,)h(w)n(e)g
5154 (are)f(not)i(concerned)208 5407 y(ab)r(out)h(guessing)f(attac)n(ks)h
5155 (on)g Fl(K)6 b Fo(,)27 b(as)g(long)g(as)g Fl(K)33 b Fo(cannot)27
5156 b(b)r(e)h(computed)g(directly)g(b)n(y)f(an)g(in)n(truder.)1929
5157 5656 y(9)p eop
5158 %%Page: 10 10
5159 10 9 bop 101 390 a Fo(3.)42 b(Ev)n(en)37 b(if)h(an)g(in)n(truder)f(has)
5160 h(the)g(abilit)n(y)g(to)g(alter)f(or)g(create)g(his)h(o)n(wn)f
5161 (messages)g(and)g(mak)n(e)h(them)g(app)r(ear)f(to)208
5162 490 y(originate)23 b(from)h(Carol)g(or)f(Stev)n(e,)j(the)f(proto)r(col)
5163 e(should)i(prev)n(en)n(t)f(the)h(in)n(truder)f(from)g(gaining)g(access)
5164 g(to)g(the)h(host)208 589 y(or)d(learning)g(an)n(y)h(information)g(ab)r
5165 (out)g(passw)n(ords)e(or)i(session)f(k)n(eys.)35 b(A)n(t)23
5166 b(w)n(orst,)g(an)h(in)n(truder)e(should)i(only)f(b)r(e)g(able)208
5167 689 y(to)k(cause)g(authen)n(tication)g(to)h(fail)f(b)r(et)n(w)n(een)h
5168 (the)g(t)n(w)n(o)f(parties)f(\(often)j(termed)e(a)g Fn
5169 (denial-of-servic)l(e)k Fo(attac)n(k\).)101 852 y(4.)42
5170 b(If)30 b(the)h(host's)f(passw)n(ord)e(\014le)j(is)f(captured)g(and)g
5171 (the)h(in)n(truder)f(learns)f(the)i(v)-5 b(alue)30 b(of)h
5172 Fl(v)s Fo(,)g(it)g(should)f(still)h(not)f(allo)n(w)208
5173 951 y(the)e(in)n(truder)f(to)g(imp)r(ersonate)g(the)h(user)f(without)h
5174 (an)f(exp)r(ensiv)n(e)g(dictionary)g(searc)n(h.)101 1114
5175 y(5.)42 b(If)c(the)h(session)e(k)n(ey)h(of)g(an)n(y)g(past)g(session)f
5176 (is)i(compromised,)h(it)e(should)h(not)f(help)h(the)f(in)n(truder)g
5177 (guess)g(at)g(or)208 1213 y(otherwise)26 b(deduce)i(the)g(user's)f
5178 (passw)n(ord.)101 1376 y(6.)42 b(If)28 b(the)h(user's)f(passw)n(ord)f
5179 (itself)i(is)f(compromised,)g(it)g(should)h(not)f(allo)n(w)g(the)g(in)n
5180 (truder)g(to)h(determine)f(the)h(session)208 1476 y(k)n(ey)j
5181 Fl(K)39 b Fo(for)33 b(past)g(sessions)f(and)h(decrypt)g(them.)55
5182 b(Ev)n(en)32 b(presen)n(t)h(sessions)f(should)h(at)g(least)g(b)r(e)g
5183 (protected)g(from)208 1575 y(passiv)n(e)26 b(ea)n(v)n(esdropping.)125
5184 1734 y(A)39 b(proto)r(col)g(with)h(these)f(prop)r(erties)g(is)g
5185 Fn(r)l(obust)p Fo(;)45 b(in)40 b(other)f(w)n(ords,)i(it)f(resists)f(b)r
5186 (eing)g(compromised)g(ev)n(en)g(if)h(the)0 1834 y(participan)n(ts)33
5187 b(in)i(the)g(proto)r(col)e(are)g(not)h(completely)h(reliable)e(or)h
5188 (secure.)56 b(Informally)-7 b(,)35 b(suc)n(h)f(a)g(proto)r(col)f
5189 (tolerates)g(a)0 1934 y(wide)38 b(range)e(of)i(attac)n(ks,)h(prev)n(en)
5190 n(ting)d(an)i(attac)n(k)e(on)i(an)n(y)e(part)i(or)e(parts)h(of)h(the)g
5191 (system)f(from)h(leading)f(to)g(further)0 2033 y(securit)n(y)32
5192 b(compromises.)53 b(If)34 b(an)f(attac)n(k)n(er)f(manages)g(to)h
5193 (obtain)g(a)g(user's)f(passw)n(ord,)h(for)g(example,)i(the)e(p)r(oten)n
5194 (tial)h(for)0 2133 y(damage)g(should)h(stop)g(as)f(so)r(on)h(as)f(the)i
5195 (user)e(c)n(hanges)g(that)h(passw)n(ord.)58 b(This)35
5196 b(ties)g(in)h(closely)e(with)i(the)f(concept)g(of)0 2233
5197 y(forw)n(ard)26 b(secrecy)-7 b(,)26 b(whic)n(h)i(protects)f(past)g
5198 (information)g(from)g(future)h(compromises.)0 2463 y
5199 Fg(4.1)112 b(Reduction)37 b(to)g(Di\016e-Hellman)0 2617
5200 y Fo(F)-7 b(ortunately)g(,)22 b(the)e(mathematical)g(structure)g(of)h
5201 (the)g(SRP)f(proto)r(col)f(is)i(su\016cien)n(tly)f(similar)g(to)g(the)h
5202 (Di\016e-Hellman)g(\(DH\))0 2716 y(problem)30 b([4)o(],)h(a)f(problem)g
5203 (that)g(is)g(b)r(eliev)n(ed)g(to)g(b)r(e)h(computationally)e
5204 (infeasible)h(with)h(su\016cien)n(tly)f(large)f(parameters,)0
5205 2816 y(that)h(it)h(is)f(p)r(ossible)g(to)g(construct)g(a)f(pro)r(of)h
5206 (linking)g(the)g(in)n(tractabilit)n(y)g(of)g(DH)h(to)f(that)g(of)g
5207 (compromising)f(SRP)-7 b(.)30 b(This)0 2916 y(pro)r(of)d(establishes)g
5208 (the)h(securit)n(y)f(of)g(SRP)h(against)e(passiv)n(e)g(ea)n(v)n
5209 (esdropp)r(er)f(attac)n(k.)125 3015 y(W)-7 b(e)37 b(b)r(egin)g(b)n(y)g
5210 (presuming)g(the)g(existence)g(of)g(an)g(algorithm)f(or)h(metho)r(d)g
5211 (that)h(yields)f(the)g(SRP)g(session)f(k)n(ey)h(in)0
5212 3115 y(p)r(olynomial)d(time)h(giv)n(en)f(all)h(the)g(information)f
5213 (that)h(is)f(publicly)h(kno)n(wn)f(or)g(transmitted)h(during)f(a)h
5214 (legitimate)f(and)0 3214 y(successful)e(run)h(of)f(the)h(SRP)g(proto)r
5215 (col,)g Fn(as)h(wel)t(l)i(as)f(the)f(user's)h(p)l(asswor)l(d)p
5216 Fo(.)53 b(The)33 b(reason)e(for)h(giving)g(a)n(w)n(a)n(y)e(this)j
5217 (piece)0 3314 y(of)e(information)f(will)h(b)r(e)g(eviden)n(t)g(shortly)
5218 -7 b(.)46 b(Suc)n(h)30 b(an)h(algorithm)e(can)i(b)r(e)g(mo)r(deled)g
5219 (as)f(an)h(oracle)e Fl(Q)h Fo(that)h(accepts)g(the)0
5220 3414 y(v)-5 b(alues)27 b Fl(A)p Fo(,)h Fl(B)t Fo(,)g
5221 Fl(u)p Fo(,)f Fl(g)s Fo(,)h Fl(n)p Fo(,)f(and)h Fl(x)g
5222 Fo(from)f(T)-7 b(able)27 b(4)h(and)f(computes)g(the)h(session)f(k)n(ey)
5223 g Fl(S)h Fo(=)22 b Fl(g)2807 3384 y Fd(ab)p Fh(+)p Fd(bux)3061
5224 3414 y Fo(from)27 b(this)h(input.)1337 3604 y Fl(Q)p
5225 Fo(\()p Fl(g)1478 3570 y Fd(a)1518 3604 y Fl(;)14 b(g)1598
5226 3570 y Fd(b)1649 3604 y Fo(+)k Fl(g)1775 3570 y Fd(x)1816
5227 3604 y Fl(;)c(u;)g(g)s(;)g(n;)g(x)p Fo(\))23 b(=)f Fl(g)2337
5228 3570 y Fd(ab)p Fh(+)p Fd(bux)125 3778 y Fo(The)28 b(DH)i(conjecture)e
5229 (claims)h(that)g(it)g(is)f(di\016cult)i(to)f(compute)g
5230 Fl(g)2246 3748 y Fd(ab)2343 3778 y Fo(in)g(GF\()p Fl(n)p
5231 Fo(\))h(giv)n(en)e Fl(g)2965 3748 y Fd(a)3033 3778 y
5232 Fo(and)h Fl(g)3239 3748 y Fd(b)3272 3778 y Fo(.)40 b(By)29
5233 b(\014xing)f Fl(u)d Fo(=)f(2)0 3877 y(and)j Fl(x)d Fo(=)f(\()p
5234 Fl(n)18 b Fk(\000)g Fo(1\))p Fl(=)p Fo(2,)27 b(w)n(e)g(can)g(de\014ne)h
5235 (the)g(DH)g(oracle)1780 3856 y(^)1761 3877 y Fl(Q)g Fo(in)g(terms)f(of)
5236 g(the)h(SRP)g(oracle)e Fl(Q)h Fo(as)g(follo)n(ws:)1026
5237 4051 y(^)1007 4072 y Fl(Q)p Fo(\()p Fl(A;)14 b(B)t(;)g(g)s(;)g(n)p
5238 Fo(\))23 b(=)g Fl(Q)p Fo(\()p Fl(A;)14 b(B)23 b Fo(+)18
5239 b Fl(g)1990 4038 y Fh(\()p Fd(n)p Fb(\000)p Fh(1\))p
5240 Fd(=)p Fh(2)2238 4072 y Fl(;)c Fo(2)p Fl(;)g(g)s(;)g(n;)g
5241 Fo(\()p Fl(n)j Fk(\000)h Fo(1\))p Fl(=)p Fo(2\))125 4246
5242 y(Substituting)28 b Fl(A)23 b Fo(=)g Fl(g)816 4216 y
5243 Fd(a)883 4246 y Fo(and)28 b Fl(B)f Fo(=)c Fl(g)1266 4216
5244 y Fd(b)1299 4246 y Fo(,)k(w)n(e)h(ha)n(v)n(e:)1612 4415
5245 y(^)1593 4436 y Fl(Q)o Fo(\()p Fl(g)1733 4402 y Fd(a)1773
5246 4436 y Fl(;)14 b(g)1853 4402 y Fd(b)1886 4436 y Fl(;)g(g)s(;)g(n)p
5247 Fo(\))23 b(=)f Fl(g)2238 4402 y Fd(ab)125 4610 y Fo(Th)n(us,)33
5248 b(if)g(there)g(existed)f(a)g(metho)r(d)h(to)g(compromise)e(the)i
5249 (session)e(k)n(ey)h(used)h(in)f(SRP)h(through)f(a)g(passiv)n(e)f(attac)
5250 n(k,)0 4710 y(that)f(same)f(metho)r(d)i(could)f(b)r(e)g(used)g(to)f
5251 (break)g(a)h(DH)g(k)n(ey)g(exc)n(hange)e(in)i(p)r(olynomially-equiv)-5
5252 b(alen)n(t)29 b(time.)44 b(This)30 b(pro)r(of)0 4809
5253 y(establishes)d(that)h(SRP)f(resists)g(passiv)n(e)f(attac)n(k)h(at)g
5254 (least)g(as)g(w)n(ell)h(as)f(the)h(Di\016e-Hellman)g(proto)r(col.)125
5255 4909 y(In)e(terms)f(of)h(our)f(securit)n(y)g(requiremen)n(ts,)h(this)g
5256 (directly)g(satis\014es)f(Requiremen)n(t)g(6)h(in)g(our)f(securit)n(y)g
5257 (analysis,)g(since)0 5009 y(rev)n(ealing)18 b(the)j(passw)n(ord)d(do)r
5258 (es)i(not)g(p)r(ermit)h(the)g(computation)e(of)i(an)n(y)e
5259 (previously-used)g(session)g(k)n(ey)-7 b(.)34 b(This)20
5260 b(also)f(satis\014es)0 5108 y(Requiremen)n(t)32 b(2,)h(since)f(an)g(in)
5261 n(truder)g(who)g(do)r(es)g(not)g(kno)n(w)g(the)g(passw)n(ord)f
5262 Fl(x)h Fo(has)g(ev)n(en)g(less)g(information)f(ab)r(out)i(the)0
5263 5208 y(session)27 b(k)n(ey)-7 b(.)125 5308 y(The)25 b(preceding)g(pro)r
5264 (of)g(establishes)f(that)i(it)g(is)f(computationally)g(infeasible)g(to)
5265 h(construct)e(a)h(session)g(k)n(ey)g(ev)n(en)g(with)0
5266 5407 y(the)g(user's)f(passw)n(ord)e Fl(x)j Fo(and)f(all)h(public)f
5267 (information.)36 b(This)24 b(applies)g(to)h(all)f(p)r(ossible)g(v)-5
5268 b(alues)24 b(of)g Fl(x)p Fo(,)i(not)f(just)g(the)f(correct)1908
5269 5656 y(10)p eop
5270 %%Page: 11 11
5271 11 10 bop 0 390 a Fo(one.)46 b(In)30 b(other)g(w)n(ords,)h(an)f(in)n
5272 (truder)g(who)g(ea)n(v)n(esdrops)e(on)j(a)f(successful)g(SRP)h(run)f
5273 (cannot)g(construct)g(a)g(guess)g(at)h(the)0 490 y(session)22
5274 b(k)n(ey)h(using)f(only)h(publicly-visible)g(information)g(and)g(a)g
5275 (guessed)f(v)-5 b(alue)23 b(of)g Fl(x)p Fo(.)36 b(Without)24
5276 b(the)g(abilit)n(y)f(to)g(construct)0 589 y(guesses)i(at)h
5277 Fl(K)6 b Fo(,)26 b(the)g(messages)e Fl(M)1084 601 y Fh(1)1147
5278 589 y Fo(and)i Fl(M)1388 601 y Fh(2)1451 589 y Fo(leak)g(no)f
5279 (information)h(to)g(the)g(passiv)n(e)f(o\013-line)h(attac)n(k)n(er)3275
5280 559 y Fh(2)3310 589 y Fo(.)36 b(Since)27 b Fl(A)f Fo(and)g
5281 Fl(B)0 689 y Fo(do)h(not)h(leak)f(an)n(y)g(information)g(either)g
5282 (\(see)h(Section)f(3.2.3\),)g(a)g(passiv)n(e)f(attac)n(k)n(er)g(cannot)
5283 h(v)n(erify)g(guesses)f(at)i(the)g(user's)0 789 y(passw)n(ord.)35
5284 b(Th)n(us,)27 b(SRP)h(resists)e(passiv)n(e)h(dictionary)f(attac)n(ks)h
5285 (and)g(satis\014es)g(Requiremen)n(t)g(1.)0 1021 y Fg(4.2)112
5286 b(Resistance)37 b(to)g(the)h(Denning-Sacco)g(attac)m(k)0
5287 1174 y Fo(The)33 b Fn(Denning-Sac)l(c)l(o)h(A)n(ttack)f
5288 Fo([3)o(])h(o)r(ccurs)e(when)h(an)f(in)n(truder)h(captures)f(the)h
5289 (session)f(k)n(ey)g Fl(K)39 b Fo(from)32 b(an)h(ea)n(v)n(esdropp)r(ed)0
5290 1274 y(session)g(and)h(uses)f(it)i(either)f(to)g(gain)f(the)h(abilit)n
5291 (y)g(to)g(imp)r(ersonate)f(the)h(user)g(directly)g(or)f(to)h(conduct)g
5292 (a)f(brute-force)0 1374 y(searc)n(h)26 b(against)g(the)i(user's)f
5293 (passw)n(ord.)125 1473 y(If)h Fl(K)34 b Fo(is)28 b(rev)n(ealed)f(to)i
5294 (a)e(passiv)n(e)g(ea)n(v)n(esdropp)r(er)f(Ev)n(e,)i(she)g(do)r(es)g
5295 (not)g(learn)g(an)n(y)g(new)g(information)g(from)g(com)n(bining)0
5296 1573 y Fl(K)37 b Fo(with)c Fl(M)383 1585 y Fh(1)452 1573
5297 y Fo(or)e Fl(M)639 1585 y Fh(2)675 1573 y Fo(.)50 b(This)32
5298 b(is)g(true)g(b)r(ecause)f(b)r(oth)i Fl(M)1803 1585 y
5299 Fh(1)1872 1573 y Fo(and)e Fl(M)2118 1585 y Fh(2)2187
5300 1573 y Fo(can)h(b)r(e)g(computed)g(directly)g(from)f(publicly-visible)0
5301 1672 y(data)e(and)f Fl(K)6 b Fo(.)41 b(W)-7 b(e)30 b(ha)n(v)n(e)e
5302 (already)f(established)i(that)g(Ev)n(e)f(cannot)h(construct)f
5303 (meaningful)i(guesses)d(at)i(the)h(session)e(k)n(ey)0
5304 1772 y Fl(K)i Fo(from)23 b(guessed)h(passw)n(ords,)e(and)i(there)g(do)r
5305 (es)g(not)g(app)r(ear)g(to)g(b)r(e)g(an)n(y)g(easier)e(w)n(a)n(y)h(for)
5306 h(her)g(to)g(carry)e(out)i(a)g(brute-force)0 1872 y(dictionary)j(attac)
5307 n(k.)36 b(It)27 b(is)h(th)n(us)g(conjectured)f(that)h(Requiremen)n(t)f
5308 (5)g(is)h(satis\014ed.)125 1971 y(Note)d(that)h(this)f(di\013ers)g
5309 (from)g(the)h(Augmen)n(ted-EKE)e(proto)r(col)g(in)i([2)o(])g(b)r
5310 (ecause)f(A-EKE)e(requires)h(the)i(user)f(to)g(send)0
5311 2071 y(a)j(message)g(that)h(is)g(dep)r(enden)n(t)g(on)f(b)r(oth)i(the)f
5312 (long-term)f(priv)-5 b(ate)28 b(k)n(ey)g(and)h(the)g(session)f(k)n(ey)
5313 -7 b(.)40 b(It)29 b(is)f(this)h(message)f(that)0 2171
5314 y(enables)f(the)h(Denning-Sacco)f(attac)n(k)f(against)h(that)h(proto)r
5315 (col.)0 2403 y Fg(4.3)112 b(Resistance)37 b(to)g(activ)m(e)g(attac)m
5316 (ks)0 2556 y Fo(SRP)21 b(has)g(b)r(een)h(carefully)f(designed)g(to)g
5317 (th)n(w)n(art)f(the)i(activ)n(e)f(attac)n(ks)f(illustrated)h(in)h
5318 (Sections)f(3.2.3)f(and)h(3.2.4.)34 b(Although)0 2656
5319 y(it)26 b(is)g(di\016cult)g(to)g(determine)g(conclusiv)n(ely)e(whether)
5320 i(or)f(not)g(these)h(precautions)f(bulletpro)r(of)h(the)g(proto)r(col)e
5321 (completely)0 2756 y(from)30 b(all)g(p)r(ossible)h(activ)n(e)e(attac)n
5322 (ks,)h(SRP)h(resists)e(all)i(the)g(w)n(ell-kno)n(wn)e(attac)n(ks)g
5323 (that)i(ha)n(v)n(e)e(plagued)h(existing)g(authen-)0 2855
5324 y(tication)h(mec)n(hanisms,)g(suc)n(h)f(as)g(the)h(Denning-Sacco)f
5325 (attac)n(k)g(men)n(tioned)h(previously)-7 b(.)45 b(While)31
5326 b(no)g(successful)f(attac)n(ks)0 2955 y(ha)n(v)n(e)c(b)r(een)i(disco)n
5327 (v)n(ered)e(against)h(SRP)-7 b(,)27 b(a)g(more)g(formal)g(analysis)f
5328 (of)i(activ)n(e)f(attac)n(k)f(scenarios)g(w)n(ould)h(b)r(e)h(w)n
5329 (elcome.)125 3054 y(Activ)n(e)23 b(attac)n(ks)f(can)g(tak)n(e)h(man)n
5330 (y)f(di\013eren)n(t)h(forms,)h(dep)r(ending)f(on)g(what)g(information)g
5331 (is)g(a)n(v)-5 b(ailable)21 b(to)i(the)h(attac)n(k)n(er.)0
5332 3154 y(An)30 b(attac)n(k)n(er)e(who)i(kno)n(ws)f(Carol's)f(priv)-5
5333 b(ate)30 b(k)n(ey)f Fl(x)h Fo(can)g(ob)n(viously)e(pretend)i(to)g(b)r
5334 (e)g(Carol)e(when)i(accessing)f(the)h(host)3840 3124
5335 y Fh(3)3877 3154 y Fo(.)0 3254 y(Lik)n(ewise,)22 b(an)g(attac)n(k)n(er)
5336 f(with)h Fl(v)k Fo(can)21 b(masquerade)g(as)g(Stev)n(e)h(when)g(Carol)f
5337 (tries)h(to)g(con)n(tact)f(him.)36 b(Although)22 b(the)h(amoun)n(t)0
5338 3353 y(of)30 b(damage)e(that)j(can)e(b)r(e)h(caused)g(b)n(y)f(a)g(leak)
5339 n(ed)g(v)n(eri\014er)g(is)h(limited)g(compared)f(to)h(plain)n
5340 (text-equiv)-5 b(alen)n(t)29 b(systems,)h(the)0 3453
5341 y(v)n(eri\014er)c(should)i(not)f(b)r(e)h(treated)f(as)g(a)g(public)i
5342 (quan)n(tit)n(y)-7 b(.)125 3553 y(A)31 b(man-in-the-middle)f(attac)n
5343 (k,)h(whic)n(h)f(requires)g(an)g(attac)n(k)n(er)f(to)h(fo)r(ol)h(b)r
5344 (oth)g(sides)f(of)h(a)f(legitimate)h(con)n(v)n(ersation,)0
5345 3652 y(cannot)26 b(b)r(e)h(carried)e(out)i(b)n(y)f(an)h(attac)n(k)n(er)
5346 d(who)j(do)r(es)f(not)g(kno)n(w)g(Carol's)f(passw)n(ord.)35
5347 b(An)27 b(attac)n(k)n(er)e(who)h(do)r(es)g(not)h(kno)n(w)0
5348 3752 y Fl(x)33 b Fo(cannot)f(fo)r(ol)h(Stev)n(e)g(in)n(to)f(thinking)h
5349 (he)g(is)f(talking)h(to)f(Carol,)h(so)f(at)g(least)h(one)f(half)h(of)g
5350 (the)g(deception)f(fails.)53 b(If)33 b(the)0 3851 y(attac)n(k)n(er)24
5351 b(do)r(esn't)j(kno)n(w)e Fl(v)30 b Fo(either,)c(he)g(is)g(in)h(w)n
5352 (orse)d(shap)r(e,)j(b)r(ecause)e(he)i(also)e(can't)h(fo)r(ol)g(Carol)f
5353 (in)n(to)h(b)r(elieving)g(that)g(she)0 3951 y(is)h(comm)n(unicating)g
5354 (with)h(Stev)n(e.)0 4183 y Fg(4.4)112 b(Securit)m(y)37
5355 b(assumptions)g(and)h(constrain)m(ts)0 4337 y Fo(The)32
5356 b(v)-5 b(alidit)n(y)31 b(of)g(the)h(preceding)f(securit)n(y)g(analysis)
5357 f(dep)r(ends)i(on)f(a)g(n)n(um)n(b)r(er)g(of)h(conditions,)g(most)f(of)
5358 h(whic)n(h)f(concern)0 4436 y(the)i(prop)r(er)f(generation)g(and)h
5359 (screening)f(of)h(v)-5 b(arious)31 b(parameters)h(in)h(the)g(SRP)g
5360 (proto)r(col.)52 b(This)33 b(section)f(will)i(discuss)0
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5362 (constrain)n(ts)f(that)i(will)g(satisfy)f(them.)0 4752
5363 y Fp(4.4.1)94 b(Discrete)31 b(logarithms)0 4905 y Fo(In)c(Section)g
5364 (3.1,)g(w)n(e)f(men)n(tioned)h(that)h(the)f(function)h
5365 Fl(P)12 b Fo(\(\))27 b(selected)g(for)g(use)g(in)g(AKE)f(m)n(ust)i(b)r
5366 (e)f(di\016cult)h(to)f(in)n(v)n(ert.)36 b(It)27 b(is)0
5367 5005 y(ob)n(vious)d(wh)n(y)h(this)h(is)f(imp)r(ortan)n(t:)35
5368 b(The)26 b(securit)n(y)e(of)i(SRP)f(and)g(an)n(y)g(other)f
5369 (construction)h(of)g(AKE)g(dep)r(ends)h(on)f(k)n(eeping)p
5370 0 5074 1560 4 v 92 5128 a Ff(2)127 5151 y Fi(This)c(assumes)g(that)h
5371 (the)h(hash)f(function)g(used)g(to)g(generate)h Fa(M)1854
5372 5160 y Ff(1)1910 5151 y Fi(and)f Fa(M)2113 5160 y Ff(2)2169
5373 5151 y Fi(is)f(cryptographically)h(secure,)g(a)g(concept)i(that)e(is)f
5374 (b)r(ey)n(ond)i(the)0 5230 y(scop)r(e)i(of)e(this)h(pap)r(er.)92
5375 5286 y Ff(3)127 5309 y Fi(In)j(a)g(t)n(ypical)g(clien)n(t/serv)n(er)g
5376 (en)n(vironmen)n(t,)h(man)n(y)e(do)h(not)g(consider)g(this)g(an)g
5377 (activ)n(e)g(attac)n(k,)i(since)e(a)g(user)f(can)i(initiate)f(con)n
5378 (tact)i(with)0 5388 y(the)c(host)f(from)e(an)n(y)i(lo)r(cation.)32
5379 b(In)24 b(an)n(y)g(ev)n(en)n(t,)h(this)f(is)f(m)n(uc)n(h)g(easier)g(to)
5380 i(carry)e(out)h(compared)g(to)g(a)g(more)f(con)n(v)n(en)n(tional)i
5381 (activ)n(e)g(attac)n(k.)1908 5656 y Fo(11)p eop
5382 %%Page: 12 12
5383 12 11 bop 0 390 a Fo(the)28 b(priv)-5 b(ate)27 b(v)-5
5384 b(alues)27 b Fl(w)k Fo(and)c Fl(y)k Fo(secret)c(while)g(publicly)h(rev)
5385 n(ealing)e Fl(P)12 b Fo(\()p Fl(w)r Fo(\))29 b(and)e
5386 Fl(P)12 b Fo(\()p Fl(y)s Fo(\).)125 490 y(Recall)27 b(that)h(in)f(the)h
5387 (case)f(of)h(SRP)-7 b(,)27 b(w)n(e)h(ha)n(v)n(e)1764
5388 677 y Fl(P)12 b Fo(\()p Fl(x)p Fo(\))24 b(=)f Fl(g)2095
5389 642 y Fd(x)125 847 y Fo(where)32 b(the)h(base)f Fl(g)j
5390 Fo(and)e(the)g(implied)h(mo)r(dulus)f Fl(n)f Fo(are)g(publicly)h(kno)n
5391 (wn)f(and)h(agreed-up)r(on)e(v)-5 b(alues.)52 b(Computing)0
5392 947 y Fl(P)12 b Fo(\()p Fl(x)p Fo(\))29 b(is)f(kno)n(wn)f(as)h
5393 Fn(discr)l(ete)i(exp)l(onentiation)p Fo(,)f(and)f(its)g(in)n(v)n(erse)f
5394 (is)h(kno)n(wn)f(as)g(a)h Fn(discr)l(ete)j(lo)l(garithm)p
5395 Fo(.)39 b(Finding)29 b(discrete)0 1047 y(logarithms)20
5396 b(is)h(a)g(problem)g(long)g(b)r(eliev)n(ed)g(to)h(b)r(e)g
5397 (computationally)e(di\016cult)i(for)f(large)f(v)-5 b(alues)21
5398 b(of)h Fl(n)f Fo(\(512)g(bits)g(or)g(longer\))3864 1017
5399 y Fh(4)0 1146 y Fo(and)30 b(has)f(b)r(een)h(the)g(sub)5
5400 b(ject)30 b(of)g(a)f(great)f(deal)i(of)f(researc)n(h)f([11)o(].)44
5401 b(The)29 b(apparen)n(t)g(securit)n(y)g(of)g(discrete)h(exp)r(onen)n
5402 (tiation)0 1246 y(as)d(a)g(one-w)n(a)n(y)f(trap)r(do)r(or)g(is)i(used)f
5403 (b)n(y)g(other)g(k)n(ey-exc)n(hange)e(proto)r(cols,)i(most)g(notably)g
5404 (Di\016e-Hellman)h([4].)125 1346 y(Note)d(that)h(the)g(pro)r(of-b)n
5405 (y-reduction)d(of)j(Section)f(4.1)g(actually)g(relied)g(on)g(the)h(in)n
5406 (tractabilit)n(y)e(of)i(the)g(Di\016e-Hellman)0 1445
5407 y(problem)j(itself,)h(not)f(the)h(in)n(tractabilit)n(y)e(of)i
5408 (computing)f(discrete)g(logarithms)e(in)j(GF\()p Fl(n)p
5409 Fo(\).)43 b(While)29 b(the)h(abilit)n(y)f(to)g(solv)n(e)0
5410 1545 y(discrete)35 b(logarithms)g(implies)h(the)g(abilit)n(y)g(to)g
5411 (break)f(DH,)h(the)h(implication)f(in)g(the)g(other)f(direction)h(has)f
5412 (y)n(et)h(to)g(b)r(e)0 1644 y(pro)n(v)n(en.)k(Without)30
5413 b(loss)e(of)h(generalit)n(y)-7 b(,)28 b(the)i(most)f(accurate)e
5414 (assessmen)n(t)h(of)h(SRP)g(at)g(this)h(time)f(is)g(that)h(its)f
5415 (securit)n(y)f(is)0 1744 y(link)n(ed)f(to)h(that)g(of)f(the)h
5416 (underlying)f(Di\016e-Hellman)h(problem.)0 1958 y Fp(4.4.2)94
5417 b(Group)32 b(parameter)f(agreemen)m(t)0 2111 y Fo(Both)k([4])h(and)f
5418 ([1])h(discuss)f(the)h(safe)f(generation)f(of)i Fl(n)f
5419 Fo(and)h Fl(g)s Fo(.)61 b(F)-7 b(or)35 b(SRP)-7 b(,)35
5420 b(w)n(e)h(wish)f(to)h(maximize)f(the)h(di\016cult)n(y)g(of)0
5421 2211 y(calculating)25 b(discrete)g(logarithms)f(in)i(GF\()p
5422 Fl(n)p Fo(\).)37 b(F)-7 b(or)25 b(this)h(reason,)f Fl(n)g
5423 Fo(m)n(ust)h(b)r(e)g(a)f(non-)p Fn(smo)l(oth)h Fo(prime,)g(whic)n(h)g
5424 (means)f(that)0 2310 y Fl(n)18 b Fk(\000)g Fo(1)27 b(m)n(ust)h(not)g
5425 (consist)f(en)n(tirely)g(of)g(small)h(factors)e([15)o(].)125
5426 2410 y(Some)37 b(authen)n(tication)h(proto)r(cols)e(based)i(on)f
5427 (discrete)h(logarithms)e(are)h(p)r(oten)n(tially)h(susceptible)g(to)g
5428 (a)f Fn(sub)l(gr)l(oup)0 2510 y(c)l(on\014nement)e(attack)g
5429 Fo([9],)i(where)d(an)g(attac)n(k)n(er)f(forces)h(the)h(session)f(k)n
5430 (ey)g(used)h(b)n(y)f(either)h(part)n(y)e(to)i(b)r(e)g(con\014ned)g(to)f
5431 (a)0 2609 y(small)c(subgroup)f(of)h(GF\()p Fl(n)p Fo(\).)46
5432 b(Because)29 b(of)h(the)h(w)n(a)n(y)e(it)i(computes)f(session)f(k)n
5433 (eys,)h(SRP)g(resists)g(this)g(attac)n(k.)44 b(Since)31
5434 b(the)0 2709 y(probabilit)n(y)21 b(of)g(generating)g(a)g(smo)r(oth)h
5435 (prime)f(at)h(random)f(is)g(quite)i(small)e([11)o(],)i
5436 Fl(n)f Fo(can,)g(in)h(practice,)f(b)r(e)g(safely)f(generated)0
5437 2808 y(b)n(y)27 b(selecting)g(a)h(random,)e(large)h(prime.)125
5438 2908 y(Nev)n(ertheless,)e(for)g(maximal)g(securit)n(y)-7
5439 b(,)25 b(the)h(author)e(recommends)h(that)h Fl(n)g Fo(b)r(e)g(a)f
5440 Fn(safe)k(prime)p Fo(,)e(whic)n(h)e(is)h(a)f(n)n(um)n(b)r(er)g(of)0
5441 3008 y(the)j(form)1757 3178 y Fl(n)22 b Fo(=)h(2)p Fl(p)18
5442 b Fo(+)g(1)125 3349 y(where)33 b Fl(p)g Fo(is)h(also)f(prime.)55
5443 b(These)33 b(n)n(um)n(b)r(ers)g(resist)h(discrete)f(logarithm)f
5444 (computation)i(and)f(con)n(tain)g(the)i(smallest)0 3449
5445 y(p)r(ossible)c(n)n(um)n(b)r(er)g(of)g(subgroups,)g(since)g
5446 Fl(n)20 b Fk(\000)h Fo(1)31 b(con)n(tains)f(the)h(few)n(est)h(p)r
5447 (ossible)e(n)n(um)n(b)r(er)h(of)h(factors,)f(2.)47 b(If)31
5448 b Fl(n)h Fo(is)f(a)f(safe)0 3548 y(prime,)e(an)f(attempted)h(subgroup)f
5449 (con\014nemen)n(t)g(attac)n(k)g(can)g(b)r(e)h(easily)f(detected)h(and)f
5450 (a)n(v)n(oided)f(in)i(all)g(cases.)125 3648 y(The)e(proto)r(col)g
5451 (descriptions)f(un)n(til)i(no)n(w)f(ha)n(v)n(e)g(assumed)g(that)h(the)g
5452 (parameters)e Fl(n)h Fo(and)h Fl(g)i Fo(ha)n(v)n(e)c(b)r(een)j
5453 (established)e(in)0 3748 y(adv)-5 b(ance)31 b(of)g(the)h(authen)n
5454 (tication)f(attempt.)49 b(One)31 b(w)n(a)n(y)f(to)i(accomplish)e(this)i
5455 (is)f(to)h(ha)n(v)n(e)e(the)i(serv)n(er)d(send)j Fl(n)f
5456 Fo(and)g Fl(g)j Fo(to)0 3847 y(the)d(clien)n(t)f(as)g(part)g(of)g(the)h
5457 (proto)r(col.)44 b(Alternativ)n(ely)-7 b(,)31 b(as)e(suggested)h(in)g
5458 ([9],)h(parameters)e(can)h(b)r(e)h(em)n(b)r(edded)g(in)n(to)f(the)0
5459 3947 y(soft)n(w)n(are)d(at)i(b)r(oth)h(ends.)41 b(The)30
5460 b(former)e(approac)n(h)f(has)i(the)g(adv)-5 b(an)n(tage)28
5461 b(of)h(b)r(eing)g(more)f(\015exible)h(b)n(y)g(allo)n(wing)f(di\013eren)
5462 n(t)0 4047 y(parameters)j(to)h(b)r(e)g(used)h(for)e(eac)n(h)h(host)g
5463 (and)g(ev)n(en)g(eac)n(h)f(user)h(according)e(to)i(individual)h
5464 (securit)n(y)e(and)h(p)r(erformance)0 4146 y(requiremen)n(ts.)47
5465 b(The)31 b(latter)g(approac)n(h)f(can)h(b)r(e)h(used)f(to)g(a)n(v)n
5466 (oid)f(issues)h(of)g(testing)g(ephemeral)g(parameters)f(for)h(safet)n
5467 (y)-7 b(,)0 4246 y(issues)27 b(that)h(will)g(b)r(e)g(discussed)f(in)h
5468 (the)g(next)f(section.)0 4460 y Fp(4.4.3)94 b(Constrain)m(t)32
5469 b(c)m(hec)m(ks)0 4613 y Fo(The)23 b(follo)n(wing)g(is)g(a)g(list)h(of)f
5470 (constrain)n(t)f(c)n(hec)n(ks)h(that)g(m)n(ust)h(b)r(e)g(p)r(erformed)f
5471 (b)n(y)g(b)r(oth)h(sides)f(to)g(ensure)g(the)h(securit)n(y)e(of)i(the)0
5472 4712 y(SRP)j(proto)r(col.)36 b(Clien)n(t)27 b(testing)g(of)g
5473 Fl(n)h Fo(and)f Fl(g)j Fo(is)d(only)f(necessary)g(if)i(these)f(v)-5
5474 b(alues)27 b(are)f(transmitted)h(and)g(not)h(em)n(b)r(edded)0
5475 4812 y(or)f(prearranged.)0 4983 y Fl(n)32 b Fp(is)f(a)h(large)f(safe)h
5476 (prime)e(\(clien)m(t\))42 b Fo(The)30 b(clien)n(t)h(m)n(ust)f(ensure)g
5477 (that)g Fl(n)g Fo(is)h(large)d(enough)i(to)g(resist)g(attac)n(k;)h(see)
5478 e(Sec-)208 5082 y(tion)k(4.4.1)e(for)i(recommendations.)52
5479 b(Using)33 b(a)f(probabilistic)h(primalit)n(y)f(tester,)i(the)g(clien)n
5480 (t)f(should)g(also)f(ensure)208 5182 y(that)27 b(b)r(oth)h
5481 Fl(n)g Fo(and)f(\()p Fl(n)19 b Fk(\000)f Fo(1\))p Fl(=)p
5482 Fo(2)26 b(are)h(prime.)p 0 5251 1560 4 v 92 5305 a Ff(4)127
5483 5328 y Fi(As)d(computational)h(sp)r(eeds)f(creep)h(up)n(w)n(ards,)f
5484 (the)h(lo)n(w)n(er)f(size)g(b)r(ound)h(for)e Fa(n)h Fi(will)f
5485 (gradually)h(increase)g(as)g(w)n(ell.)32 b(F)-6 b(or)24
5486 b(that)h(reason,)f(man)n(y)0 5407 y(are)g(recommending)e(1024)j(bits)e
5487 (for)g(long-term)g(securit)n(y)-6 b(.)1908 5656 y Fo(12)p
5488 eop
5489 %%Page: 13 13
5490 13 12 bop 0 390 a Fl(g)34 b Fp(is)d(a)i(primitiv)m(e)d(ro)s(ot)h(of)h
5491 (GF\()p Fl(n)p Fp(\))g(\(clien)m(t\))41 b Fo(Assuming)e(the)g
5492 (factorization)e(of)i Fl(n)25 b Fk(\000)h Fo(1)38 b(is)g(kno)n(wn,)j
5493 (the)e(algorithm)208 490 y(describ)r(ed)g(in)h([16)o(])f(for)g(testing)
5494 h(generators)d(can)i(b)r(e)h(used)f(to)h(v)n(erify)e
5495 Fl(g)s Fo(.)72 b(If)40 b Fl(n)g Fo(is)f(a)g(safe)g(prime,)k(this)c
5496 (test)h(is)208 589 y(particularly)26 b(easy)g(and)i(fast.)0
5497 756 y Fl(A)23 b Fk(6)p Fo(=)g(0)31 b Fp(\(serv)m(er\))43
5498 b Fo(This)27 b(prev)n(en)n(ts)g(the)h(serv)n(er's)d(session)i(k)n(ey)g
5499 (from)g(b)r(eing)h(forced)f(to)g(a)g(kno)n(wn)g(v)-5
5500 b(alue,)28 b(namely)f(zero.)0 922 y Fl(B)g Fk(6)p Fo(=)c(0)31
5501 b Fp(\(clien)m(t\))42 b Fo(This)27 b(c)n(hec)n(k)g(prev)n(en)n(ts)f(a)i
5502 (dictionary)e(attac)n(k)h(on)g(the)h(passw)n(ord)e(from)h(a)g
5503 (masquerading)f(host.)0 1088 y Fl(a;)14 b(b)22 b(>)h
5504 Fo(log)334 1108 y Fd(g)387 1088 y Fl(n)41 b Fo(The)36
5505 b(computations)f(of)h Fl(g)1328 1057 y Fd(a)1404 1088
5506 y Fo(and)g Fl(g)1617 1057 y Fd(b)1685 1088 y Fo(in)h(GF\()p
5507 Fl(n)p Fo(\))f(m)n(ust)g(\\wrap)f(around")f(to)i(prev)n(en)n(t)f(an)g
5508 (attac)n(k)n(er)f(from)208 1187 y(taking)e(the)h(algebraic)e(logarithm)
5509 g(of)i Fl(g)1499 1157 y Fd(a)1572 1187 y Fo(to)f(reco)n(v)n(er)f
5510 Fl(a)p Fo(.)52 b(The)33 b(probabilit)n(y)f(of)g(this)h(happ)r(ening)g
5511 (is)g(in\014nitesimal)208 1287 y(\(less)27 b(than)h(2)629
5512 1257 y Fb(\000)p Fh(1014)844 1287 y Fo(for)f(1024-bit)f
5513 Fl(n)p Fo(\),)i(but)g(the)g(c)n(hec)n(k)f(is)g(trivial.)0
5514 1561 y Fm(5)135 b(Optimizing)46 b(SRP)0 1743 y Fo(Implemen)n(ting)32
5515 b(a)g(proto)r(col)f(suc)n(h)g(as)h(SRP)f(for)h(use)g(in)g(real)f
5516 (systems)g(brings)h(practical)e(issues)i(lik)n(e)f(p)r(erformance)g(in)
5517 n(to)0 1843 y(pla)n(y)-7 b(.)39 b(The)28 b(n)n(um)n(b)r(er)g(of)h
5518 (message)e(rounds,)h(the)g(size)g(of)h(the)g(exc)n(hanged)e(messages,)g
5519 (and)h(the)h(exp)r(ected)f(execution)h(time)0 1942 y(of)24
5520 b(a)g(successful)g(authen)n(tication)g(attempt)h(are)e(all)h(imp)r
5521 (ortan)n(t)g(factors)f(in)i(designing)e(concrete)h(proto)r(col)f(sp)r
5522 (eci\014cations.)0 2042 y(Eliminating)33 b(ev)n(en)f(one)h(net)n(w)n
5523 (ork)e(message)h(or)g(computational)g(round)g(can)h(signi\014can)n(tly)
5524 f(impro)n(v)n(e)g(the)h(utilit)n(y)g(of)g(an)0 2142 y(authen)n
5525 (tication)27 b(system)h([5)o(].)0 2374 y Fg(5.1)112 b(Message)39
5526 b(rounds)p 1641 2550 618 4 v 1639 2650 4 100 v 1691 2620
5527 a Fl(C)29 b Fo(=)-14 b Fk(\))23 b Fl(S)131 b(C)p 2257
5528 2650 V 1639 2749 V 1691 2719 a(C)29 b Fk(\()-14 b Fo(=)23
5529 b Fl(S)144 b(s)p 2257 2749 V 1639 2849 V 1691 2819 a(C)29
5530 b Fo(=)-14 b Fk(\))23 b Fl(S)132 b(A)p 2257 2849 V 1639
5531 2949 V 1691 2919 a(C)29 b Fk(\()-14 b Fo(=)23 b Fl(S)130
5532 b(B)p 2257 2949 V 1639 3048 V 1691 3018 a(C)29 b Fo(=)-14
5533 b Fk(\))23 b Fl(S)104 b(M)2172 3030 y Fh(1)p 2257 3048
5534 V 1639 3148 V 1691 3118 a Fl(C)29 b Fk(\()-14 b Fo(=)23
5535 b Fl(S)104 b(M)2172 3130 y Fh(2)p 2257 3148 V 1641 3151
5536 618 4 v 1542 3300 a Fo(T)-7 b(able)27 b(5:)36 b(Original)27
5537 b(SRP)125 3579 y(Recall)g(from)h(Section)f(3.2.2)g(that)h(the)g(full)h
5538 (SRP)f(proto)r(col)e(in)n(v)n(olv)n(ed)h(a)g(total)h(of)f(three)h
5539 (round)f(trips)h(b)r(et)n(w)n(een)g(clien)n(t)0 3679
5540 y(and)g(serv)n(er,)f(as)h(sho)n(wn)g(in)g(T)-7 b(able)29
5541 b(5.)39 b(This)28 b(section)g(will)h(assume)f(that)g
5542 Fl(u)g Fo(is)h(transmitted)f(implicitly)i(along)d(with)i
5543 Fl(B)t Fo(,)g(as)0 3778 y(discussed)d(in)h(Section)g(3.2.4.)36
5544 b(It)27 b(is)g(p)r(ossible)f(to)h(reduce)f(the)h(total)g(n)n(um)n(b)r
5545 (er)f(of)h(messages)e(exc)n(hanged)h(b)n(y)g(consolidating)0
5546 3878 y(some)k(of)g(the)h(individual)g(transactions,)e(grouping)g
5547 (together)h(pieces)g(of)g(information)g(that)h(do)f(not)g(dep)r(end)h
5548 (on)g(earlier)0 3978 y(messages.)45 b(F)-7 b(or)31 b(example,)g(since)g
5549 (the)g(salt)g Fl(s)g Fo(and)f(the)i(clien)n(t's)f(exp)r(onen)n(t)f(are)
5550 g(indep)r(enden)n(t)i(of)f(eac)n(h)f(other,)h(they)g(can)0
5551 4077 y(b)r(e)26 b(sen)n(t)g(in)g(either)f(order.)35 b(By)26
5552 b(rearranging)c(additional)j(messages,)g(it)h(is)g(p)r(ossible)f(to)h
5553 (reduce)f(SRP)g(to)h(t)n(w)n(o)f(round)g(trips,)0 4177
5554 y(as)i(sho)n(wn)g(in)h(T)-7 b(able)27 b(6.)p 1620 4363
5555 660 4 v 1618 4463 4 100 v 1670 4433 a Fl(C)i Fo(=)-14
5556 b Fk(\))23 b Fl(S)104 b(C)q(;)14 b(A)p 2278 4463 V 1618
5557 4562 V 1670 4532 a(C)29 b Fk(\()-14 b Fo(=)23 b Fl(S)113
5558 b(s;)14 b(B)p 2278 4562 V 1618 4662 V 1670 4632 a(C)29
5559 b Fo(=)-14 b Fk(\))23 b Fl(S)125 b(M)2172 4644 y Fh(1)p
5560 2278 4662 V 1618 4761 V 1670 4732 a Fl(C)29 b Fk(\()-14
5561 b Fo(=)23 b Fl(S)125 b(M)2172 4744 y Fh(2)p 2278 4761
5562 V 1620 4765 660 4 v 1500 4914 a Fo(T)-7 b(able)28 b(6:)36
5563 b(Optimized)28 b(SRP)125 5212 y(It)41 b(is)g(p)r(ossible)g(to)g(reduce)
5564 f(the)i(n)n(um)n(b)r(er)e(of)h(messages)f(ev)n(en)g(further)h(if)h(one)
5565 e(is)h(willing)g(to)g(settle)h(for)e(one-w)n(a)n(y)0
5566 5312 y(authen)n(tication)29 b(instead)f(of)h(the)h(m)n(utual)f(authen)n
5567 (tication)f(that)i(is)f(pro)n(vided)f(b)n(y)g(b)r(oth)i(Original)d(SRP)
5568 i(and)g(Optimized)1908 5656 y(13)p eop
5569 %%Page: 14 14
5570 14 13 bop 1620 394 660 4 v 1618 493 4 100 v 1670 463
5571 a Fl(C)29 b Fo(=)-14 b Fk(\))23 b Fl(S)104 b(C)q(;)14
5572 b(A)p 2278 493 V 1618 593 V 1670 563 a(C)29 b Fk(\()-14
5573 b Fo(=)23 b Fl(S)113 b(s;)14 b(B)p 2278 593 V 1618 692
5574 V 1670 663 a(C)29 b Fo(=)-14 b Fk(\))23 b Fl(S)125 b(M)2172
5575 675 y Fh(1)p 2278 692 V 1620 696 660 4 v 1318 845 a Fo(T)-7
5576 b(able)27 b(7:)37 b(One-W)-7 b(a)n(y)26 b(Optimized)i(SRP)0
5577 1193 y(SRP)-7 b(.)31 b(T)-7 b(able)30 b(7)h(sho)n(ws)f(a)g
5578 (three-message,)g(one-and-a-half)f(round)h(trip)h(implemen)n(tation)g
5579 (of)g(SRP)f(that)i(authen)n(ticates)0 1293 y(the)c(clien)n(t)g(to)f
5580 (the)h(serv)n(er,)e(but)i(not)g(the)g(other)f(w)n(a)n(y)-7
5581 b(.)125 1392 y(Three)32 b(messages)g(app)r(ears)g(to)h(b)r(e)g(the)h
5582 (theoretical)e(lo)n(w)n(er)g(b)r(ound)h(for)g(a)g(secure)f(authen)n
5583 (tication)h(proto)r(col,)g(whic)n(h)0 1492 y(also)d(matc)n(hes)g(the)i
5584 (minimal)f(proto)r(col)f(presen)n(ted)h(in)g([17)o(].)47
5585 b(This)31 b(is)g(based)g(on)g(the)g(observ)-5 b(ation)30
5586 b(that)h(a)g(t)n(w)n(o-message)0 1591 y(proto)r(col)k(\(one)g(in)h
5587 (whic)n(h)g(the)g(clien)n(t)g(sends)g(a)f(message)f(to)i(the)g(serv)n
5588 (er)e(and)i(the)g(serv)n(er)e(sends)h(a)h(message)e(bac)n(k\))h(is)0
5589 1691 y(trivially)23 b(vulnerable)g(to)g(a)g(repla)n(y)g(attac)n(k,)g
5590 (assuming)g(that)h(no)f(out-of-band)g(comm)n(unication)g(is)h(used,)g
5591 (lik)n(e)f(a)g(biometric)0 1791 y(input)28 b(device)g(or)e(sync)n
5592 (hronized)h(clo)r(c)n(ks.)0 2023 y Fg(5.2)112 b(Execution)37
5593 b(sp)s(eed)0 2176 y Fo(Of)27 b(all)g(the)h(op)r(erations)e(executed)h
5594 (in)h(the)f(course)f(of)i(negotiating)e(secure)g(proto)r(cols)g(lik)n
5595 (e)h(SRP)-7 b(,)27 b(the)h(slo)n(w)n(est)e(one)h(b)n(y)g(far)0
5596 2276 y(is)j(the)h(iterated)f(group)f(op)r(eration,)h(mo)r(dular)g(exp)r
5597 (onen)n(tiation)g(in)h(this)f(case.)44 b(By)31 b(comparison,)e(other)h
5598 (functions)g(suc)n(h)0 2376 y(as)j(hashing,)h(addition,)g(and)f(m)n
5599 (ultiplication)h(require)e(a)h(negligible)f(amoun)n(t)h(of)g(pro)r
5600 (cessor)e(time.)54 b(An)n(y)34 b(discussion)e(of)0 2475
5601 y(p)r(erformance)27 b(issues)g(necessarily)e(cen)n(ters)i(around)g(the)
5602 h(sp)r(eed)g(of)f(the)h(group)f(op)r(eration.)125 2575
5603 y(Instead)d(of)h(lumping)h(all)f(mo)r(dular)f(exp)r(onen)n(tiation)h
5604 (op)r(erations)f(in)n(to)g(the)i(same)f(category)e(and)i(coun)n(ting)f
5605 (them,)i(w)n(e)0 2674 y(can)g(arriv)n(e)e(at)i(more)g(accurate)f(p)r
5606 (erformance)g(estimates)h(b)n(y)g(sub)r(dividing)h(them)g(in)n(to)f
5607 (three)g(categories.)34 b(Our)26 b(notation)0 2774 y(will)i(b)r(e)g
5608 (the)g(follo)n(wing:)0 2957 y Fl(t)30 2969 y Fd(g)110
5609 2957 y Fo(The)g(amoun)n(t)f(of)g(time)i(required)d(to)i(execute)f(a)g
5610 (mo)r(dular)g(exp)r(onen)n(tiation)g(with)h(a)g(tin)n(y)f(base)g
5611 (\(e.g.)37 b Fl(g)26 b Fo(=)c(2\).)0 3123 y Fl(t)30 3135
5612 y Fd(e)107 3123 y Fo(The)28 b(amoun)n(t)f(of)g(time)i(required)d(if)i
5613 (the)g(exp)r(onen)n(t)g(is)f(tin)n(y)-7 b(.)0 3289 y
5614 Fl(t)30 3301 y Fd(b)105 3289 y Fo(The)27 b(amoun)n(t)h(of)f(time)h
5615 (required)f(if)h(neither)g(base)f(or)f(exp)r(onen)n(t)i(is)f(tin)n(y)-7
5616 b(.)125 3471 y(F)g(or)19 b(the)i(purp)r(oses)f(of)g(our)g(b)r(enc)n
5617 (hmark)g(data,)h(w)n(e)f(will)h(use)f(a)g(1024-bit)f(safe)h(prime)g(mo)
5618 r(dulus)h(and)f(256-bit)f(exp)r(onen)n(ts.)0 3571 y(Tin)n(y)25
5619 b(exp)r(onen)n(ts)f(are)g(32)g(bits)i(long.)35 b(Although)25
5620 b(p)r(erformance)f(\014gures)g(will)h(v)-5 b(ary)24 b(with)i
5621 (di\013ering)f(parameter)e(sizes,)i(host)0 3671 y(arc)n(hitectures,)h
5622 (and)i(soft)n(w)n(are)d(implemen)n(tations,)j(their)g(relativ)n(e)e(v)
5623 -5 b(alues)27 b(should)h(remain)f(consisten)n(t.)p 932
5624 3873 2037 4 v 930 3972 4 100 v 1568 3943 a(Proto)r(col)p
5625 1925 3972 V 210 w(Clien)n(t)298 b(Serv)n(er)p 2966 3972
5626 V 932 3976 2037 4 v 932 3992 V 930 4092 4 100 v 982 4062
5627 a(Di\016e-Hellman/DH-EKE)p 1925 4092 V 202 w Fl(t)2110
5628 4074 y Fd(g)2167 4062 y Fo(+)19 b Fl(t)2281 4074 y Fd(b)2601
5629 4062 y Fl(t)2631 4074 y Fd(g)2688 4062 y Fo(+)f Fl(t)2801
5630 4074 y Fd(b)p 2966 4092 V 930 4192 V 1596 4162 a Fo(SPEKE)p
5631 1925 4192 V 267 w(2)p Fl(t)2217 4174 y Fd(b)2666 4162
5632 y Fo(2)p Fl(t)2738 4174 y Fd(b)p 2966 4192 V 932 4195
5633 2037 4 v 930 4295 4 100 v 1609 4265 a Fo(A-EKE)p 1925
5634 4295 V 98 w(2)p Fl(t)2048 4277 y Fd(g)2105 4265 y Fo(+)g
5635 Fl(t)2218 4277 y Fd(e)2272 4265 y Fo(+)g Fl(t)2385 4277
5636 y Fd(b)2560 4265 y Fo(2)p Fl(t)2632 4277 y Fd(g)2688
5637 4265 y Fo(+)g(2)p Fl(t)2843 4277 y Fd(b)p 2966 4295 V
5638 930 4394 V 1510 4364 a Fo(B-SPEKE)p 1925 4394 V 266 w(3)p
5639 Fl(t)2217 4376 y Fd(b)2581 4364 y Fl(t)2611 4376 y Fd(g)2668
5640 4364 y Fo(+)g(3)p Fl(t)2823 4376 y Fd(b)p 2966 4394 V
5641 930 4494 V 1713 4464 a Fo(SRP)p 1925 4494 V 183 w(2)p
5642 Fl(t)2132 4476 y Fd(g)2188 4464 y Fo(+)g Fl(t)2301 4476
5643 y Fd(b)2518 4464 y Fl(t)2548 4476 y Fd(g)2605 4464 y
5644 Fo(+)g Fl(t)2718 4476 y Fd(e)2772 4464 y Fo(+)g Fl(t)2885
5645 4476 y Fd(b)p 2966 4494 V 932 4497 2037 4 v 1317 4646
5646 a Fo(T)-7 b(able)27 b(8:)36 b(Reference)28 b(Running)g(Times)125
5647 4928 y(T)-7 b(able)30 b(8)h(giv)n(es)e(the)j(amoun)n(t)e(of)h(time)h
5648 (required)e(to)g(negotiate)g(some)h(w)n(ell-kno)n(wn)e(proto)r(cols,)i
5649 (including)g(the)g(three)0 5028 y(v)n(eri\014er-based)21
5650 b(proto)r(cols)g(curren)n(tly)h(in)h(existence.)35 b(In)23
5651 b(this)h(table,)f(Augmen)n(ted-EKE)f(is)h(ev)-5 b(aluated)22
5652 b(with)i(the)f Fp(p-NEW)0 5128 y Fo(digital)h(signature)f(algorithm)g
5653 (disco)n(v)n(ered)g(b)n(y)h(Nyb)r(erg)f(and)h(Ruepp)r(el)h([14],)g(one)
5654 f(of)g(the)h(fastest)f(suc)n(h)g(algorithms)f(usable)0
5655 5227 y(with)28 b(A-EKE.)1908 5656 y(14)p eop
5656 %%Page: 15 15
5657 15 14 bop 125 390 a Fo(T)-7 b(o)25 b(sa)n(v)n(e)f(time,)i(one)g(could)f
5658 (easily)g(implemen)n(t)h(the)g(clien)n(t)g(and)f(serv)n(er)f(so)h(that)
5659 h(they)g(do)f(some)g(of)h(the)g(computations)0 490 y(in)k(parallel.)43
5660 b(A)30 b(reasonable)e(lo)n(w)n(er)g(b)r(ound)j(on)e(execution)h(time)g
5661 (can)g(b)r(e)g(calculated)g(simply)g(b)n(y)f(taking)h(the)g(greater)e
5662 (of)0 589 y(the)g(t)n(w)n(o)f(times,)h(since)f(that)h(will)g(determine)
5663 f(the)h(critical)f(path)h(of)g(the)g(proto)r(col.)125
5664 689 y(T)-7 b(able)20 b(9)f(sho)n(ws)h(p)r(erformance)f(\014gures)g
5665 (gathered)h(from)g(a)f(167)g(MHz)i(single-pro)r(cessor)c(Sun)k(UL)-7
5666 b(TRASparc-1)19 b(running)0 789 y(Solaris)g(2.5.)34 b(The)20
5667 b(GNU)h(MP)f(library)-7 b(,)21 b(built)g(with)f(the)h(GNU)g(C)f
5668 (compiler,)i(w)n(as)d(used)h(to)g(p)r(erform)g(the)h(m)n
5669 (ultiple-precision)0 888 y(arithmetic.)37 b(F)-7 b(or)27
5670 b(this)h(platform,)f Fl(t)1137 900 y Fd(g)1199 888 y
5671 Fo(=)g(247)f(ms,)i Fl(t)1626 900 y Fd(e)1684 888 y Fo(=)g(45)e(ms,)i
5672 (and)f Fl(t)2231 900 y Fd(b)2288 888 y Fo(=)g(379)f(ms.)p
5673 857 1098 2187 4 v 855 1198 4 100 v 1493 1168 a(Proto)r(col)p
5674 1849 1198 V 98 w(Execution)h(Time)100 b(Normalized)p
5675 3042 1198 V 857 1201 2187 4 v 857 1218 V 855 1317 4 100
5676 v 906 1287 a(Di\016e-Hellman/DH-EKE)p 1849 1317 V 425
5677 w(626)26 b(ms)211 b(1.000)p 3042 1317 V 855 1417 V 1521
5678 1387 a(SPEKE)p 1849 1417 V 424 w(758)26 b(ms)211 b(1.211)p
5679 3042 1417 V 857 1420 2187 4 v 855 1520 4 100 v 1638 1490
5680 a(SRP)p 1849 1520 V 425 w(873)26 b(ms)211 b(1.395)p 3042
5681 1520 V 855 1619 V 1534 1590 a(A-EKE)p 1849 1619 V 382
5682 w(1252)26 b(ms)211 b(2.000)p 3042 1619 V 855 1719 V 1435
5683 1689 a(B-SPEKE)p 1849 1719 V 381 w(1384)26 b(ms)211 b(2.211)p
5684 3042 1719 V 857 1722 2187 4 v 999 1871 a(T)-7 b(able)27
5685 b(9:)37 b(Benc)n(hmarks)26 b(on)h(a)g(167)f(MHz)i(UL)-7
5686 b(TRASparc-1)125 2146 y(SRP)29 b(ends)i(up)f(b)r(eing)g(the)h(fastest)f
5687 (v)n(eri\014er-based)d(proto)r(col)i(in)i(the)f(table.)45
5688 b(Compared)29 b(to)h(SRP)-7 b(,)30 b(A-EKE)e(requires)0
5689 2246 y(41\045)37 b(more)g(running)g(time,)k(while)c(B-SPEKE)f(is)h
5690 (nearly)g(60\045)g(slo)n(w)n(er.)65 b(T)-7 b(ests)37
5691 b(with)i(other)e(implemen)n(tations)g(yield)0 2345 y(results)27
5692 b(that)h(di\013er)g(b)n(y)f(a)g(constan)n(t)g(factor,)g(so)g(the)h
5693 (\\normalized")d(column)j(remains)f(accurate)f(across)g(platforms.)125
5694 2445 y(SRP)39 b(has)h(other)f(p)r(erformance)g(adv)-5
5695 b(an)n(tages)38 b(that)i(these)g(tables)g(do)f(not)h(necessarily)e(sho)
5696 n(w.)73 b(F)-7 b(or)40 b(example,)i(to)0 2545 y(reduce)36
5697 b(running)h(times)g(ev)n(en)f(further,)j(the)e(v)-5 b(alues)37
5698 b Fl(g)1786 2514 y Fd(a)1863 2545 y Fo(and)f Fl(g)2076
5699 2514 y Fd(b)2146 2545 y Fo(can)g(b)r(e)i(precomputed)e(b)r(efore)h
5700 (either)f(part)n(y)g(b)r(egins)0 2644 y(authen)n(tication.)51
5701 b(This)32 b(is)g(practical)f(when)i(the)f(group)f(parameters)g
5702 Fl(n)h Fo(and)g Fl(g)j Fo(are)d(kno)n(wn)f(to)h(b)r(oth)h(parties)f
5703 (ahead)f(of)0 2744 y(time)22 b(instead)f(of)g(b)r(eing)g(exc)n(hanged)f
5704 (during)h(the)g(course)f(of)h(the)h(proto)r(col.)34 b(Not)21
5705 b(all)g(proto)r(cols)f(can)g(emplo)n(y)h(this)g(strategy;)0
5706 2843 y(in)30 b(particular,)f(the)i(SPEKE)d(family)-7
5707 b(,)31 b(b)r(ecause)e(its)h(exp)r(onen)n(tials)f(are)g(functions)h(of)g
5708 (the)g(shared)f(passw)n(ord,)g(cannot)g(do)0 2943 y(this)f([10)o(].)125
5709 3043 y(T)-7 b(o)20 b(impro)n(v)n(e)f(the)i(running)g(time)g(an)n(y)f
5710 (further,)i(w)n(e)f(w)n(ould)f(need)h(to)g(switc)n(h)f(to)h(another)f
5711 (AKE)g(construction)g(that)h(used)0 3142 y(something)31
5712 b(other)g(than)g(discrete)g(exp)r(onen)n(tiation.)47
5713 b(One)31 b(promising)f(candidate)h(is)g(the)h(elliptic)g(curv)n(e)e
5714 (cryptosystem)0 3242 y([12)o(],)25 b(whic)n(h)e(can)g(p)r(oten)n
5715 (tially)g(o\013er)g(the)h(same)f(lev)n(el)g(of)h(securit)n(y)e(as)h
5716 (cryptosystems)f(based)h(on)g(the)h(di\016cult)n(y)g(of)g(discrete)0
5717 3342 y(logarithms)31 b(but)i(with)g(m)n(uc)n(h)f(shorter)f(k)n(eys.)50
5718 b(Jablon)31 b([10)o(])i(claims)f(that)g(elliptic)h(curv)n(e)f(metho)r
5719 (ds)g(impro)n(v)n(e)f(the)i(sp)r(eed)0 3441 y(of)h(group)g(op)r
5720 (erations)f(b)n(y)h(a)g(factor)g(of)g(6)h(to)f(7)g(while)h(main)n
5721 (taining)f(an)g(equiv)-5 b(alen)n(t)34 b(lev)n(el)g(of)h(securit)n(y)-7
5722 b(.)56 b(It)35 b(is)g(still)f(to)r(o)0 3541 y(early)25
5723 b(to)h(mak)n(e)f(an)n(y)h(\014rm)g(pronouncemen)n(ts)f(on)h(the)g
5724 (securit)n(y)g(of)g(elliptic)g(curv)n(es,)g(ho)n(w)n(ev)n(er,)e(since)i
5725 (they)g(ha)n(v)n(e)f(not)i(b)r(een)0 3640 y(analyzed)32
5726 b(as)h(extensiv)n(ely)f(as)h(discrete)f(exp)r(onen)n(ts.)54
5727 b(In)33 b(addition,)i(elliptic)e(curv)n(es)f(are)g(encum)n(b)r(ered)h
5728 (b)n(y)g(ro)n(y)n(alt)n(y)e(and)0 3740 y(paten)n(t)g(restrictions,)f
5729 (whic)n(h)h(is)g(not)g(the)g(case)f(for)h(simple)g(discrete)f(exp)r
5730 (onen)n(tiation.)47 b(In)31 b(the)g(author's)f(opinion,)h(SRP)0
5731 3840 y(is)c(e\016cien)n(t)f(enough,)h(ev)n(en)f(on)g(to)r(da)n(y's)g
5732 (hardw)n(are,)f(that)i(p)r(erformance)f(is)g(not)h(a)f(signi\014can)n
5733 (t)g(issue.)36 b(In)27 b(most)g(cases,)f(the)0 3939 y(time)31
5734 b(required)e(to)h(negotiate)f(the)h(authen)n(tication)g(proto)r(col)f
5735 (is)h(not)g(ev)n(en)f(noticeable)h(\(under)g(1)g(second\))f(to)h(the)h
5736 (user,)0 4039 y(and)h(this)h(will)g(only)f(impro)n(v)n(e)f(as)h(hardw)n
5737 (are)e(b)r(ecomes)i(faster.)51 b(The)33 b(w)n(ell-established)e
5738 (securit)n(y)h(a\013orded)f(b)n(y)i(discrete)0 4139 y(exp)r(onen)n
5739 (tiation)27 b(should)g(satisfy)h(ev)n(en)f(the)h(most)f(conserv)-5
5740 b(ativ)n(e)26 b(securit)n(y)h(requiremen)n(ts.)0 4413
5741 y Fm(6)135 b(Conclusion)0 4595 y Fo(P)n(assw)n(ord)26
5742 b(authen)n(tication)j(proto)r(cols)f(ha)n(v)n(e)f(traditionally)i(used)
5743 g(symmetric)f(encryption,)h(public-k)n(ey)g(encryption,)g(or)0
5744 4695 y(a)36 b(com)n(bination)g(of)h(the)g(t)n(w)n(o)f(approac)n(hes)f
5745 (to)h(resist)g(common)h(attac)n(ks.)63 b(Only)36 b(recen)n(tly)-7
5746 b(,)39 b(ho)n(w)n(ev)n(er,)e(has)f(there)h(b)r(een)0
5747 4794 y(signi\014can)n(t)24 b(atten)n(tion)g(paid)g(to)g(designing)g
5748 (strong)f(direct)i(authen)n(tication)f(proto)r(cols)f(that)h(could)g(b)
5749 r(e)h(deplo)n(y)n(ed)f(without)0 4894 y(dep)r(ending)41
5750 b(on)f(exp)r(ensiv)n(e)g(external)f(infrastructure.)74
5751 b(In)41 b(this)f(pap)r(er,)k(w)n(e)c(sho)n(w)n(ed)f(that)h(existing)g
5752 (proto)r(cols)f(ha)n(v)n(e)0 4993 y(started)31 b(to)h(address)f(this)h
5753 (problem)g(with)g(some)f(success,)i(but)f(that)g(there)g(w)n(as)f
5754 (still)h(ro)r(om)f(for)h(impro)n(v)n(emen)n(t.)49 b(While)0
5755 5093 y(curren)n(t)27 b(direct)h(authen)n(tication)g(tec)n(hnology)e
5756 (o\013ers)i(a)f(v)-5 b(ariet)n(y)27 b(of)h(tradeo\013s)f(b)r(et)n(w)n
5757 (een)h(securit)n(y)g(and)g(p)r(erformance,)f(the)0 5193
5758 y(compromise)f(has)h(b)r(een)h(somewhat)f(unsatisfying)g(to)h(implemen)
5759 n(tors.)125 5292 y(Next,)41 b(w)n(e)d(presen)n(ted)f(the)i(groundw)n
5760 (ork)d(for)h(a)h(new)g(family)h(of)f(authen)n(tication)g(proto)r(cols)f
5761 (called)g(AKE,)h(whic)n(h)0 5392 y(emplo)n(y)n(ed)33
5762 b(a)g(sw)n(app)r(ed-secret)f(instead)i(of)g(a)f(traditional)g
5763 (shared-secret)f(arrangemen)n(t)f(and)j(whic)n(h)f(did)i(not)e(use)h
5764 (an)n(y)1908 5656 y(15)p eop
5765 %%Page: 16 16
5766 16 15 bop 0 390 a Fo(form)30 b(of)h(symmetric)f(encryption)g(to)h(ac)n
5767 (hiev)n(e)e(its)i(securit)n(y)-7 b(.)45 b(Section)31
5768 b(3.1)f(outlined)g(some)g(of)h(the)g(b)r(ene\014ts)g(of)g(a)n(v)n
5769 (oiding)0 490 y(encryption)c(in)h(an)f(authen)n(tication)g(proto)r
5770 (col.)125 589 y(W)-7 b(e)24 b(then)h(presen)n(ted)f(a)g(construction)g
5771 (of)g(AKE,)g(kno)n(wn)g(as)f(SRP)-7 b(,)25 b(based)f(on)g(discrete)g
5772 (exp)r(onen)n(tiation)g(and)g(outlined)0 689 y(a)31 b(pro)r(of)f
5773 (\(Section)i(4.1\))e(that)i(established)f(a)f(lo)n(w)n(er)g(b)r(ound)h
5774 (on)g(the)h(securit)n(y)e(of)h(SRP)-7 b(.)31 b(In)h(our)e(analysis,)h
5775 (w)n(e)f(put)i(forth)0 789 y(a)37 b(series)f(of)h(requiremen)n(ts)f
5776 (for)h(a)g(secure)f(passw)n(ord)f(proto)r(col,)k(emphasizing)d(those)h
5777 (that)g(existing)g(proto)r(cols)f(failed)0 888 y(to)e(meet.)58
5778 b(W)-7 b(e)34 b(demonstrated)g(that)g(SRP)-7 b(,)35 b(as)e(a)h(v)n
5779 (eri\014er-based,)g(zero-kno)n(wledge)e(proto)r(col)h(resistan)n(t)g
5780 (to)h(dictionary)0 988 y(attac)n(ks,)26 b(o\013ered)i(a)f(n)n(um)n(b)r
5781 (er)g(of)h(new)f(b)r(ene\014ts)h(for)g(passw)n(ord)d(system)i(implemen)
5782 n(tors:)125 1171 y Fk(\017)41 b Fo(An)31 b(attac)n(k)n(er)d(with)j
5783 (neither)g(the)g(user's)e(passw)n(ord)g(nor)g(the)i(host's)f(passw)n
5784 (ord)f(\014le)h(cannot)h(moun)n(t)f(a)g(dictionary)208
5785 1270 y(attac)n(k)c(on)i(the)g(passw)n(ord.)34 b(Mutual)28
5786 b(authen)n(tication)f(is)h(ac)n(hiev)n(ed)e(in)i(this)g(scenario.)125
5787 1436 y Fk(\017)41 b Fo(An)31 b(attac)n(k)n(er)e(who)h(captures)g(the)h
5788 (host's)f(passw)n(ord)f(\014le)h(cannot)h(directly)f(compromise)f
5789 (user-to-host)g(authen)n(ti-)208 1536 y(cation)e(and)g(gain)g(access)f
5790 (to)i(the)g(host)f(without)h(an)f(exp)r(ensiv)n(e)h(dictionary)e(searc)
5791 n(h.)125 1702 y Fk(\017)41 b Fo(An)29 b(attac)n(k)n(er)f(who)h
5792 (compromises)f(the)i(host)f(do)r(es)g(not)g(obtain)g(the)h(the)g(passw)
5793 n(ord)d(from)i(a)g(legitimate)g(authen)n(ti-)208 1802
5794 y(cation)e(attempt.)125 1968 y Fk(\017)41 b Fo(An)26
5795 b(attac)n(k)n(er)e(who)i(captures)f(the)h(session)f(k)n(ey)g(cannot)g
5796 (use)h(it)g(to)g(moun)n(t)g(a)f(dictionary)g(attac)n(k)g(on)h(the)g
5797 (passw)n(ord.)125 2134 y Fk(\017)41 b Fo(An)33 b(attac)n(k)n(er)f(who)h
5798 (captures)f(the)i(user's)e(passw)n(ord)f(cannot)i(use)g(it)h(to)f
5799 (compromise)f(the)i(session)e(k)n(eys)g(of)h(past)208
5800 2233 y(sessions.)125 2416 y(It)28 b(is)g(b)r(eliev)n(ed)g(that)g(this)h
5801 (set)f(of)g(prop)r(erties)f(is)h(at)g(or)f(near)g(the)i(theoretical)e
5802 (limit)i(of)f(securit)n(y)f(that)h(can)g(b)r(e)h(o\013ered)0
5803 2516 y(b)n(y)j(a)g(purely)f(passw)n(ord-based)f(proto)r(col.)49
5804 b(SRP)-7 b(,)32 b(whic)n(h)g(bases)g(its)g(securit)n(y)f(on)h(the)h
5805 (di\016cult)n(y)f(of)g(solving)f(the)i(Di\016e-)0 2615
5806 y(Hellman)24 b(problem)g(in)g(the)h(m)n(ultiplicativ)n(e)f(\014eld)g
5807 (mo)r(dulo)h(a)e(large)g(safe)h(prime,)g(meets)h(these)f(requiremen)n
5808 (ts)f(and)h(do)r(es)g(so)0 2715 y(using)g(only)f(one)h(exp)r(onen)n
5809 (tial)f(k)n(ey)h(exc)n(hange)e(round,)j(making)e(it)h(useful)h(for)e
5810 (applications)h(in)g(whic)n(h)g(go)r(o)r(d)f(p)r(erformance)0
5811 2814 y(is)i(an)h(issue.)35 b(It)26 b(solv)n(es)e(some)h(outstanding)g
5812 (issues)g(with)h(proto)r(cols)e(lik)n(e)h(EKE)f(and)i(SPEKE)d(without)j
5813 (sacri\014cing)e(either)0 2914 y(p)r(erformance)30 b(or)g(securit)n(y)
5814 -7 b(.)45 b(SRP's)30 b(securit)n(y)-7 b(,)31 b(simplicit)n(y)-7
5815 b(,)32 b(and)f(sp)r(eed)f(mak)n(e)g(it)i(ideal)e(for)g(a)h(wide)f
5816 (range)g(of)g(real-w)n(orld)0 3014 y(applications)d(in)h(whic)n(h)f
5817 (secure)g(passw)n(ord)e(authen)n(tication)j(is)f(required.)0
5818 3288 y Fm(Ac)l(kno)l(wledgemen)l(ts)0 3470 y Fo(The)g(author)g(w)n
5819 (ould)g(lik)n(e)g(to)g(thank)h(Dan)f(Boneh)g(\(Stanford\),)h(John)f
5820 (Gill)h(\(Stanford\),)f(Doug)g(T)n(ygar)f(\(CMU\),)i(Li)g(Gong)0
5821 3570 y(\(Ja)n(v)-5 b(aSoft\),)30 b(Da)n(vid)f(Jablon)g(\(In)n(tegrit)n
5822 (y)g(Sciences\),)h(and)g(the)g(man)n(y)f(readers)f(of)i
5823 Fe(sci.crypt)c Fo(for)j(their)h(commen)n(ts)f(and)0 3669
5824 y(feedbac)n(k)k(regarding)f(this)i(pap)r(er.)55 b(The)34
5825 b(author)f(gratefully)g(ac)n(kno)n(wledges)e(the)j(supp)r(ort)g(of)f
5826 (the)i(Defense)f(Adv)-5 b(anced)0 3769 y(Researc)n(h)23
5827 b(Pro)5 b(jects)23 b(Agency)i(under)f(Con)n(tract)g(D)n
5828 (ABT63-94-C-0055.)31 b(The)25 b(author)f(w)n(ould)g(also)f(lik)n(e)i
5829 (to)f(thank)h(Eugene)0 3869 y(Jhong)c(for)g(his)h(help)g(with)h(soft)n
5830 (w)n(are)d(co)r(ding)i(and)f(dev)n(elopmen)n(t)h(and)f(P)n(aul)g
5831 (Losleb)r(en)h(for)f(helping)h(to)g(mak)n(e)f(this)h(researc)n(h)0
5832 3968 y(p)r(ossible.)0 4243 y Fm(References)42 4425 y
5833 Fo([1])41 b(S.M.)g(Bello)n(vin)g(and)g(M.)g(Merritt.)78
5834 b(Encrypted)40 b(k)n(ey)h(exc)n(hange:)63 b(P)n(assw)n(ord-based)37
5835 b(proto)r(cols)j(secure)g(against)171 4524 y(dictionary)e(attac)n(ks.)
5836 70 b(In)40 b Fn(Pr)l(o)l(c)l(e)l(e)l(dings)h(of)g(the)g(1992)h(IEEE)f
5837 (Computer)g(So)l(ciety)g(Confer)l(enc)l(e)h(on)e(R)l(ese)l(ar)l(ch)h
5838 (in)171 4624 y(Se)l(curity)29 b(and)h(Privacy)p Fo(,)g(pages)c(72{84,)g
5839 (1992.)42 4790 y([2])41 b(S.M.)28 b(Bello)n(vin)f(and)h(M.)g(Merritt.)
5840 38 b(Augmen)n(ted)28 b(encrypted)f(k)n(ey)h(exc)n(hange:)36
5841 b(A)28 b(passw)n(ord-based)d(proto)r(col)i(secure)171
5842 4890 y(against)j(dictionary)h(attac)n(ks)g(and)h(passw)n(ord)e(\014le)i
5843 (compromise.)49 b(T)-7 b(ec)n(hnical)31 b(rep)r(ort,)i(A)-7
5844 b(T&T)32 b(Bell)g(Lab)r(oratories,)171 4989 y(1994.)42
5845 5155 y([3])41 b(D.)36 b(Denning)h(and)f(G.)h(Sacco.)61
5846 b(Timestamps)36 b(in)h(k)n(ey)e(distribution)i(systems.)62
5847 b Fn(Communic)l(ations)38 b(of)h(the)e(A)n(CM)p Fo(,)171
5848 5255 y(August)27 b(1981.)1908 5656 y(16)p eop
5849 %%Page: 17 17
5850 17 16 bop 42 390 a Fo([4])41 b(W.)d(Di\016e)h(and)g(M.E.)f(Hellman.)69
5851 b(New)38 b(directions)g(in)g(cryptograph)n(y)-7 b(.)67
5852 b Fn(IEEE)40 b(T)-6 b(r)l(ansactions)40 b(on)g(Information)171
5853 490 y(The)l(ory)p Fo(,)29 b(IT-22\(6\):644{654,)23 b(No)n(v)n(em)n(b)r
5854 (er)j(1976.)42 656 y([5])41 b(L.)f(Gong.)75 b(E\016cien)n(t)40
5855 b(net)n(w)n(ork)f(authen)n(tication)h(proto)r(cols:)61
5856 b(Lo)n(w)n(er)39 b(b)r(ounds)i(and)f(optimal)g(implemen)n(tations.)171
5857 756 y Fn(Distribute)l(d)29 b(Computing)p Fo(,)g(9\(3\):131{145,)24
5858 b(1995.)42 922 y([6])41 b(L.)34 b(Gong,)i(M.A.)f(Lomas,)h(R.)e
5859 (Needham,)j(and)d(J.)h(Saltzer.)57 b(Protecting)33 b(p)r(o)r(orly)h(c)n
5860 (hosen)f(secrets)h(from)g(guessing)171 1021 y(attac)n(ks.)h
5861 Fn(IEEE)c(Journal)f(on)f(Sele)l(cte)l(d)h(A)n(r)l(e)l(as)g(in)f
5862 (Communic)l(ations)p Fo(,)g(11\(5\):648{656,)23 b(June)28
5863 b(1993.)42 1187 y([7])41 b(F.T.)35 b(Grampp)g(and)g(R.H.)h(Morris.)59
5864 b(Unix)35 b(op)r(erating)g(system)g(securit)n(y)-7 b(.)59
5865 b Fn(A)-6 b(T&T)36 b(Bel)t(l)i(L)l(ab)l(or)l(atories)h(T)-6
5866 b(e)l(chnic)l(al)171 1287 y(Journal)p Fo(,)27 b(63\(8\):1649{1672,)c
5867 (Octob)r(er)k(1984.)42 1453 y([8])41 b(N.)35 b(Haller)f(and)g(R.)h(A)n
5868 (tkinson.)58 b Fn(On)36 b(Internet)f(A)n(uthentic)l(ation)p
5869 Fo(.)58 b(Na)n(v)-5 b(al)34 b(Researc)n(h)f(Lab)r(oratory)-7
5870 b(,)34 b(Octob)r(er)g(1994.)171 1553 y(Request)27 b(F)-7
5871 b(or)27 b(Commen)n(ts)g(\(RF)n(C\))i(1704.)42 1719 y([9])41
5872 b(D.)h(Jablon.)78 b(Strong)41 b(passw)n(ord-only)e(authen)n(ticated)i
5873 (k)n(ey)g(exc)n(hange.)78 b Fn(Computer)43 b(Communic)l(ation)g(R)l
5874 (eview)p Fo(,)171 1818 y(26\(5\):5{26,)25 b(Octob)r(er)h(1996.)0
5875 1984 y([10])41 b(D.)c(Jablon.)65 b(Extended)37 b(passw)n(ord)e(metho)r
5876 (ds)j(imm)n(une)f(to)g(dictionary)g(attac)n(k.)64 b(In)37
5877 b Fn(WETICE)j('97)g(Enterprise)171 2084 y(Se)l(curity)29
5878 b(Workshop)p Fo(,)h(Cam)n(bridge,)c(MA,)i(June)g(1997.)0
5879 2250 y([11])41 b(B.A.)21 b(LaMacc)n(hia)f(and)i(A.M.)g(Odlyzk)n(o.)j
5880 (Computation)d(of)f(discrete)g(logarithms)f(in)i(prime)g(\014elds.)27
5881 b Fn(Designs,)e(Co)l(des,)171 2350 y(and)30 b(Crypto)l(gr)l(aphy)p
5882 Fo(,)g(1:46{62,)25 b(1991.)0 2516 y([12])41 b(A.)34 b(Menezes)g(and)g
5883 (S.A.)h(V)-7 b(anstone.)56 b(Elliptic)34 b(curv)n(e)f(cryptosystems)g
5884 (and)h(their)g(implemen)n(tations.)56 b Fn(Journal)36
5885 b(of)171 2615 y(Cryptolo)l(gy)p Fo(,)29 b(6\(4\):209{224,)24
5886 b(1993.)0 2781 y([13])41 b(R.H.)36 b(Morris)f(and)h(K.)f(Thompson.)62
5887 b(Unix)36 b(passw)n(ord)e(securit)n(y)-7 b(.)61 b Fn(Communic)l(ations)
5888 38 b(of)h(the)e(A)n(CM)p Fo(,)g(22\(11\):594,)171 2881
5889 y(No)n(v)n(em)n(b)r(er)26 b(1979.)0 3047 y([14])41 b(K.)27
5890 b(Nyb)r(erg)g(and)h(R.A.)g(Ruepp)r(el.)37 b(Message)26
5891 b(reco)n(v)n(ery)f(for)i(signature)g(sc)n(hemes)g(based)g(on)g(the)h
5892 (discrete)f(logarithm)171 3147 y(problem.)36 b(In)28
5893 b Fn(A)l(dvanc)l(es)i(in)g(Cryptolo)l(gy|EUR)n(OCR)-6
5894 b(YPT)30 b('94)h(Pr)l(o)l(c)l(e)l(e)l(dings)p Fo(.)e(Springer-V)-7
5895 b(erlag,)25 b(1995.)0 3313 y([15])41 b(S.C.)c(P)n(ohling)e(and)h(M.E.)h
5896 (Hellman.)63 b(An)37 b(impro)n(v)n(ed)f(algorithm)f(for)h(computing)h
5897 (logarithms)e(in)i(gf\()p Fl(p)p Fo(\))f(and)h(its)171
5898 3412 y(cryptographic)25 b(signi\014cance.)36 b Fn(IEEE)31
5899 b(T)-6 b(r)l(ansactions)30 b(on)g(Information)h(The)l(ory)p
5900 Fo(,)e(24\(1\):106{111,)23 b(Jan)n(uary)j(1978.)0 3578
5901 y([16])41 b(Bruce)27 b(Sc)n(hneier.)36 b Fn(Applie)l(d)31
5902 b(Crypto)l(gr)l(aphy)p Fo(.)39 b(John)28 b(Wiley)f(&)h(Sons,)f(Inc.,)h
5903 (New)g(Y)-7 b(ork,)26 b(1996.)0 3744 y([17])41 b(M.)30
5904 b(Steiner,)h(G.)g(Tsudik,)g(and)f(M.)h(W)-7 b(aidner.)44
5905 b(Re\014nemen)n(t)31 b(and)f(extension)g(of)g(encrypted)g(k)n(ey)g(exc)
5906 n(hange.)44 b Fn(A)n(CM)171 3844 y(Op)l(er)l(ating)29
5907 b(Systems)h(R)l(eview)p Fo(,)e(29\(3\),)f(July)g(1995.)1908
5908 5656 y(17)p eop
5909 %%Trailer
5910 end
5911 userdict /end-hook known{end-hook}if
5912 %%EOF