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[gsasl.git] / doc / specification / srp6.ps
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1 %!PS-Adobe-2.0
2 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software
3 %%Title: srp6.dvi
4 %%Pages: 5
5 %%PageOrder: Ascend
6 %%BoundingBox: 0 0 596 842
7 %%EndComments
8 %DVIPSWebPage: (www.radicaleye.com)
9 %DVIPSCommandLine: dvips -o srp6.ps srp6.dvi
10 %DVIPSParameters: dpi=600, compressed
11 %DVIPSSource:  TeX output 2002.10.29:0201
12 %%BeginProcSet: texc.pro
14 /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S
15 N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72
16 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0
17 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{
18 landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize
19 mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[
20 matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round
21 exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{
22 statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0]
23 N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin
24 /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array
25 /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2
26 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N
27 df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A
28 definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get
29 }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub}
30 B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr
31 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3
32 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx
33 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx
34 sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{
35 rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp
36 gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B
37 /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{
38 /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{
39 A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy
40 get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse}
41 ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp
42 fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17
43 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add
44 chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{
45 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop}
46 forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn
47 /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put
48 }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{
49 bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A
50 mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{
51 SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{
52 userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X
53 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4
54 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N
55 /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{
56 /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)
57 (LaserWriter 16/600)]{A length product length le{A length product exch 0
58 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse
59 end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask
60 grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot}
61 imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round
62 exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto
63 fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p
64 delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}
65 B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{
66 p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S
67 rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end
69 %%EndProcSet
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1143 y Fe(2)1701 4887 y Fj(\))1971 4839 y Fg(M)2034 4847 y
1144 Fd(2)1952 4887 y Ff( )-14 b(\000)99 b Fh(M)2266 4899
1145 y Fe(2)2326 4887 y Fj(=)23 b Fh(H)7 b Fj(\()p Fh(A;)14
1146 b(M)2702 4899 y Fe(1)2739 4887 y Fh(;)g(S)5 b Fj(\))p
1147 2912 4917 V 984 5017 4 100 v 1036 4987 a(8.)234 b Fh(K)28
1148 b Fj(=)23 b Fh(H)7 b Fj(\()p Fh(S)e Fj(\))615 b Fh(K)29
1149 b Fj(=)22 b Fh(H)7 b Fj(\()p Fh(S)e Fj(\))p 2912 5017
1150 V 986 5020 1928 4 v 915 5174 a(T)-7 b(able)28 b(1:)36
1151 b(The)28 b(Secure)f(Remote)h(P)n(assw)n(ord)c(Proto)r(col)i(\(SRP-3\))
1152 1929 5656 y(1)p eop
1153 %%Page: 2 2
1154 2 1 bop 125 390 a Fh(H)29 b Fj(is)23 b(a)g(secure)f(hash)h(function,)i
1155 (and)e(the)g(v)-5 b(alues)23 b Fh(a)p Fj(,)h Fh(b)p Fj(,)f(and)g
1156 Fh(u)g Fj(are)f(generated)g(randomly)-7 b(.)34 b(A)n(t)24
1157 b(the)f(end)h(of)f(a)f(successful)0 490 y(proto)r(col)k(run,)i(b)r(oth)
1158 g(sides)f(will)h(share)e(a)i(secret)f(session)f(k)n(ey)h
1159 Fh(K)6 b Fj(.)125 589 y(As)32 b(a)h Fi(str)l(ong)h(p)l(asswor)l(d)i(pr)
1160 l(oto)l(c)l(ol)p Fj(,)f(SRP)e(attempts)g(to)g(prev)n(en)n(t)f(passiv)n
1161 (e)f(adv)n(ersaries)f(from)i(obtaining)h(an)n(y)f(useful)0
1162 689 y(information)22 b(ab)r(out)g(the)g(passw)n(ord)e(b)n(y)i
1163 (observing)f(successful)h(proto)r(col)f(runs,)i(and)f(it)g(seeks)g(to)g
1164 (limit)h(activ)n(e)e(adv)n(ersaries)0 789 y(to)27 b(a)f(single)g
1165 (on-line)g(passw)n(ord)f(guess)h(for)g(ev)n(ery)f(imp)r(ersonation)h
1166 (attempt.)37 b(It)27 b(is)g(easy)f(to)g(sho)n(w)g(that,)h(for)f(eac)n
1167 (h)g(session)0 888 y(that)34 b(he)f(in)n(terferes)f(with,)k(an)d(activ)
1168 n(e)f(adv)n(ersary)f(can)i(alw)n(a)n(ys)e(get)i(one)g(passw)n(ord)f
1169 (guess)g(b)n(y)h(noting)g(that)h(b)r(oth)f(sides)0 988
1170 y(of)d(the)f(proto)r(col)g(ha)n(v)n(e)f(only)h(the)h(passw)n(ord)e(as)h
1171 (a)g(shared)f(secret,)i(and)f(that)h(an)f(activ)n(e)g(attac)n(k)g(can)g
1172 (simply)g(guess)g(at)g(a)0 1088 y(passw)n(ord)i(and)i("pretend")f(to)h
1173 (b)r(e)g(one)f(of)h(the)h(authen)n(ticating)e(parties,)i(using)e(that)h
1174 (passw)n(ord)e(guess)h(as)h(the)g(shared)0 1187 y(secret.)j(Ideally)-7
1175 b(,)26 b(a)f(strong)g(passw)n(ord)f(proto)r(col)h(seeks)g(to)h(limit)h
1176 (an)f(attac)n(k)n(er)e(to)i(that)g(theoretical)f(minim)n(um)i(if)g(suc)
1177 n(h)e(an)0 1287 y(activ)n(e)i(attac)n(k)g(is)g(attempted.)125
1178 1386 y(SRP)d(in)h(its)g(curren)n(t)f(form)g(allo)n(ws)f(an)i(activ)n(e)
1179 f(attac)n(k)n(er)e(to)j(mak)n(e)f(and)g(v)n(erify)g Fi(two)h
1180 Fj(passw)n(ord)e(guesses)g(p)r(er)i(imp)r(erson-)0 1486
1181 y(ation)30 b(attempt[2].)46 b(This)31 b(prop)r(ert)n(y)e(do)r(es)h(not)
1182 h(p)r(ose)f(a)g(signi\014can)n(t)g(practical)f(securit)n(y)h(threat)g
1183 (to)h(existing)f(implemen-)0 1586 y(tations,)h(since)f(eac)n(h)g
1184 (guessing)f(attempt)i(results)f(in)h(a)f(failure)h(detectable)f(to)h(b)
1185 r(oth)f(sides)h(and)f(w)n(ould)g(still)h(require)e(an)0
1186 1685 y(unrealistic)h(n)n(um)n(b)r(er)h(of)g(on-line)g(attempts,)h(ev)n
1187 (en)f(with)g(the)h(n)n(um)n(b)r(er)f(required)f(cut)h(in)h(half.)47
1188 b(Nev)n(ertheless,)31 b(this)g(falls)0 1785 y(short)c(of)h(the)g
1189 (theoretical)f(limit,)i(and)f(a)f(simple)h(c)n(hange)f(to)h(the)g
1190 (proto)r(col)f(that)h(eliminates)f(this)i(\\t)n(w)n(o-for-one")24
1191 b(attac)n(k)0 1885 y(will)k(b)r(e)g(presen)n(ted.)125
1192 1984 y(SRP)-7 b(,)26 b(as)g(originally)f(prop)r(osed,)h(also)g(imp)r
1193 (oses)h(a)f(limitation)h(on)f(the)i(ordering)d(of)h(its)h(proto)r(col)f
1194 (messages.)35 b(In)27 b(Steps)0 2084 y(3)i(and)g(4)h(of)f(T)-7
1195 b(able)29 b(1,)h(the)g(serv)n(er)d(m)n(ust)j(w)n(ait)f(for)g(the)h
1196 (clien)n(t's)g(v)-5 b(alue)29 b(of)g Fh(A)h Fj(b)r(efore)f(rev)n
1197 (ealing)f(its)i(v)-5 b(alue)29 b(of)h Fh(u)p Fj(.)42
1198 b(In)30 b(some)0 2183 y(cases,)h(this)g(restriction)f(prev)n(en)n(ts)g
1199 (certain)h(forms)f(of)h(optimization)g(when)g(SRP)g(is)g(in)n(tegrated)
1200 f(in)n(to)h(existing)g(securit)n(y)0 2283 y(and)i(authen)n(tication)f
1201 (proto)r(cols.)51 b(It)33 b(is)g(sometimes)f(b)r(ene\014cial)h(to)f(ha)
1202 n(v)n(e)g(the)h(\015exibilit)n(y)g(to)g(send)f(b)r(oth)h(k)n(ey)g(exc)n
1203 (hange)0 2383 y(messages)k(async)n(hronously)e(to)j(sa)n(v)n(e)f(time)i
1204 (on)e(high-latency)h(links,)j(or)c(to)h(send)g(all)g(of)g(the)h(serv)n
1205 (er's)d(k)n(ey)i(exc)n(hange)0 2482 y(messages)25 b(\014rst)h(to)h
1206 (reduce)f(the)h(n)n(um)n(b)r(er)g(of)f(net)n(w)n(ork)f(round)i(trips.)
1207 36 b(A)27 b(relativ)n(ely)e(minor)h(mo)r(di\014cation)h(to)f(SRP)h
1208 (will)g(b)r(e)0 2582 y(presen)n(ted)g(whic)n(h)h(eliminates)f(this)h
1209 (\\message-ordering")23 b(limitation.)0 2857 y Fk(2)135
1210 b(Tw)l(o-for-one)45 b(guessing)0 3038 y Fj(As)26 b(noted)g(previously)
1211 -7 b(,)25 b(an)h(activ)n(e)f(attac)n(k)n(er)g(can)g(v)-5
1212 b(alidate)26 b(t)n(w)n(o)f(passw)n(ord)f(guesses)h(p)r(er)h(imp)r
1213 (ersonation)f(attempt.)37 b(Note)0 3138 y(that)28 b(the)h(serv)n(er)d
1214 (is)i(supp)r(osed)f(to)h(send)g(the)h(clien)n(t)f(the)g(v)-5
1215 b(alue)28 b Fh(v)22 b Fj(+)c Fh(g)2213 3108 y Fg(b)2246
1216 3138 y Fj(,)28 b(whic)n(h)g(is)g(just)h Fh(g)2827 3108
1217 y Fg(x)2887 3138 y Fj(+)18 b Fh(g)3013 3108 y Fg(b)3046
1218 3138 y Fj(.)38 b(An)29 b(attac)n(k)n(er)d(who)h(do)r(es)0
1219 3238 y(not)32 b(kno)n(w)f(either)h Fh(x)h Fj(or)e Fh(v)k
1220 Fj(can)d(mak)n(e)f(a)h(single)f(guess)g(at)h Fh(v)j Fj(while)e
1221 (attempting)f(to)g(imp)r(ersonate)f(the)i(serv)n(er)d(b)n(y)h(using)0
1222 3337 y(that)h(guessed)f(v)-5 b(alue)32 b(of)g Fh(v)j
1223 Fj(in)e(the)f(serv)n(er's)e(calculation.)49 b(Ho)n(w)n(ev)n(er,)31
1224 b(b)r(ecause)h(of)g(the)g(symmetry)g(of)g(the)g(equation)g(for)0
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1226 (ossible)g(for)g(the)h(attac)n(k)n(er)e(to)i(insert)f(an)h(additional)f
1227 (passw)n(ord)f(guess)h(b)n(y)g(sending)h(the)0 3537 y(clien)n(t)25
1228 b(the)h(v)-5 b(alue)25 b Fh(g)617 3506 y Fg(x)671 3537
1229 y Fj(+)13 b Fh(g)792 3506 y Fg(y)832 3537 y Fj(,)26 b(where)e
1230 Fh(x)i Fj(and)f Fh(y)i Fj(are)d(guessed)h(passw)n(ords;)e(the)j(second)
1231 e(passw)n(ord)f(guess)i Fh(y)i Fj(simply)f(tak)n(es)e(the)0
1232 3636 y(place)30 b(of)h(the)h(random)e(exp)r(onen)n(t)g
1233 Fh(b)p Fj(.)47 b(If)31 b(the)g(actual)g(passw)n(ord)e(is)h
1234 Fh(x)p Fj(,)j(the)e(clien)n(t)g(will)g(subtract)g(out)f
1235 Fh(g)3328 3606 y Fg(x)3401 3636 y Fj(and)h(use)f Fh(g)3755
1236 3606 y Fg(y)3826 3636 y Fj(as)0 3736 y(the)h(base)e(in)h(its)h(session)
1237 e(k)n(ey)g(calculation.)44 b(In)30 b(this)h(case,)f(the)g(attac)n(k)n
1238 (er)f(can)g(use)h Fh(y)j Fj(as)d(its)g Fh(b)g Fj(v)-5
1239 b(alue)30 b(in)g(its)h(o)n(wn)e(session)0 3835 y(k)n(ey)e(calculation,)
1240 g(since)g(it)h(is)g(the)g(discrete)f(log)f(of)i Fh(g)1682
1241 3805 y Fg(y)1721 3835 y Fj(,)g(the)g(clien)n(t's)g(base.)36
1242 b(The)28 b(same)f(holds)g(if)h Fh(x)g Fj(and)g Fh(y)i
1243 Fj(are)c(sw)n(app)r(ed.)125 3935 y(In)f(fact,)h(this)f(attac)n(k)f
1244 (applies)h(to)g(an)n(y)f(v)-5 b(arian)n(t)25 b(of)g(the)g(proto)r(col)f
1245 (in)h(whic)n(h)h(an)e(attac)n(king)g(serv)n(er)g(can)g(send)h(the)h
1246 (clien)n(t)0 4035 y(a)j(k)n(ey)f(exc)n(hange)g(v)-5 b(alue)29
1247 b(that)g(results)g(in)g(the)h(clien)n(t)f(using)g(a)f(base)h(v)-5
1248 b(alue)29 b(whose)f(discrete)h(log)f(is)h(kno)n(wn)f(to)h(the)h(serv)n
1249 (er)0 4134 y(if)e(the)g(clien)n(t's)g(passw)n(ord)d(is)j(either)f(of)h
1250 (t)n(w)n(o)f(v)-5 b(alues)27 b(c)n(hosen)f(b)n(y)i(the)g(serv)n(er.)125
1251 4234 y(One)33 b(simple)i(w)n(a)n(y)d(to)i(remo)n(v)n(e)f(the)h
1252 (symmetry)g(in)g(the)h(serv)n(er's)d(k)n(ey)h(exc)n(hange)g(v)-5
1253 b(alue)34 b(is)g(to)g(m)n(ultiply)g Fh(v)k Fj(b)n(y)c(some)0
1254 4334 y(v)-5 b(alue)27 b Fh(k)k Fj(agreed)26 b(to)i(b)n(y)f(b)r(oth)h
1255 (sides:)1728 4433 y Fh(B)f Fj(=)c Fh(k)s(v)e Fj(+)d Fh(g)2139
1256 4399 y Fg(b)0 4583 y Fj(Inciden)n(tally)-7 b(,)35 b(this)g(v)-5
1257 b(arian)n(t)33 b(can)g(also)g(b)r(e)i(implemen)n(ted)f(b)n(y)g(m)n
1258 (ultiplying)g(the)g Fh(g)2646 4552 y Fg(b)2713 4583 y
1259 Fj(v)-5 b(alue)34 b(b)n(y)g Fh(k)j Fj(with)d(no)g(di\013erence)g(in)0
1260 4682 y(securit)n(y;)c(ho)n(w)n(ev)n(er)d(doing)i(it)h(this)g(w)n(a)n(y)
1261 e(requires)h(the)h(clien)n(t)f(to)h(implemen)n(t)g(mo)r(dular)f
1262 (division)g(or)g(mo)r(dular)g(in)n(v)n(ersion)0 4782
1263 y(to)e(compute)h(his)g(session)e(k)n(ey)-7 b(,)27 b(whereas)g(the)h(v)
1264 -5 b(arian)n(t)26 b(as)h(curren)n(tly)g(prop)r(osed)f(do)r(es)i(not.)
1265 125 4881 y(It)i(is)h(easy)e(to)h(see)g(that)h(this)g(v)-5
1266 b(arian)n(t)29 b(do)r(es)h(not)h(protect)f(against)f(the)i(serv)n(er)d
1267 (guessing)i(t)n(w)n(o)f(passw)n(ords)f(at)j(once)f(if)0
1268 4981 y(the)f(attac)n(k)n(er)f(kno)n(ws)f(the)j(discrete)e(log)g(of)h
1269 Fh(k)j Fj(in)d(the)h(SRP)f(group.)40 b(If)29 b Fh(k)f
1270 Fj(=)d Fh(g)2470 4951 y Fg(j)2505 4981 y Fj(,)k(where)g(the)g(adv)n
1271 (ersary)d(kno)n(ws)i Fh(j)5 b Fj(,)29 b(he)g(can)0 5081
1272 y(send)f(the)g(clien)n(t:)1681 5180 y Fh(B)f Fj(=)c Fh(k)s(g)1948
1273 5146 y Fg(x)2008 5180 y Fj(+)18 b Fh(k)s(g)2180 5146
1274 y Fg(y)0 5330 y Fj(If)29 b(the)g(actual)f(passw)n(ord)f(is)i
1275 Fh(x)p Fj(,)g(the)h(clien)n(t)e(will)h(subtract)g(out)f
1276 Fh(k)s(g)2116 5300 y Fg(x)2186 5330 y Fj(from)h(this)g(v)-5
1277 b(alue,)29 b(lea)n(ving)e(it)i(with)h Fh(k)s(g)3432 5300
1278 y Fg(y)3500 5330 y Fj(as)e(its)h(base.)1929 5656 y(2)p
1280 %%Page: 3 3
1281 3 2 bop 0 390 a Fj(But)28 b Fh(k)s(g)254 360 y Fg(y)317
1282 390 y Fj(=)22 b Fh(g)447 360 y Fg(j)482 390 y Fh(g)525
1283 360 y Fg(y)588 390 y Fj(=)h Fh(g)719 360 y Fg(j)s Fe(+)p
1284 Fg(y)840 390 y Fj(,)28 b(so)f(the)h(attac)n(k)n(er)e(kno)n(ws)g(the)j
1285 (discrete)e(log)g(of)g(the)h(clien)n(t's)g(base)f(and)h(can)f
1286 (determine)h(if)g Fh(x)g Fj(is)0 490 y(the)g(correct)e(passw)n(ord.)35
1287 b(The)28 b(same)f(holds)g(if)h Fh(x)g Fj(and)g Fh(y)i
1288 Fj(are)d(sw)n(app)r(ed.)125 589 y(The)i(v)-5 b(alue)29
1289 b(of)h Fh(k)i Fj(can)d(c)n(hange)f(from)h(one)g(run)g(of)h(the)g(proto)
1290 r(col)e(to)h(the)h(next,)g(it)g(can)f(b)r(e)h(asso)r(ciated)e(with)h
1291 (the)h(SRP)0 689 y(group)e(parameters)f Fh(N)37 b Fj(and)29
1292 b Fh(g)s Fj(,)f(or)g(it)h(can)g(b)r(e)g(a)f(constan)n(t.)40
1293 b(Although)28 b(the)h(last)g(option)f(is)h(the)g(simplest,)g(care)f(m)n
1294 (ust)h(b)r(e)0 789 y(tak)n(en)e(to)g(ensure)g(that)h
1295 Fh(k)j Fj(is)c(nev)n(er)g(a)g(kno)n(wn)g(exp)r(onen)n(tial)g(of)h
1296 Fh(g)s Fj(,)f(in)h(ligh)n(t)f(of)h(the)g(previous)e(analysis.)125
1297 888 y(Note)e(that)g(as)f(a)h(safe)g(prime,)g Fh(N)33
1298 b Fj(can)24 b(b)r(e)g(expressed)f(as)h(2)p Fh(q)14 b
1299 Fj(+)d(1,)24 b(where)f Fh(q)28 b Fj(is)c(an)f(o)r(dd)i(prime.)35
1300 b(Also)24 b(note)g(that)g Fh(N)33 b Fj(m)n(ust)0 988
1301 y(b)r(e)c(2)f(\(mo)r(d)i(3\))e(b)r(ecause)g(a)h(v)-5
1302 b(alue)28 b(of)h Fh(N)38 b Fj(that)29 b(w)n(as)e(1)h(\(mo)r(d)i(3\))e
1303 (w)n(ould)h(mak)n(e)e Fh(q)32 b Fj(divisible)d(b)n(y)f(3.)40
1304 b(The)29 b(Legendre)f(sym)n(b)r(ol)0 1088 y(\()55 1055
1305 y Fe(3)p 42 1069 59 4 v 42 1116 a Fg(N)111 1088 y Fj(\))g(can)f(th)n
1306 (us)h(b)r(e)g(computed:)315 1197 y Fc(\022)404 1258 y
1307 Fj(3)p 386 1295 76 4 v 386 1371 a Fh(N)472 1197 y Fc(\023)556
1308 1314 y Fj(=)644 1197 y Fc(\022)715 1258 y Fh(N)p 715
1309 1295 V 732 1371 a Fj(3)801 1197 y Fc(\023)876 1314 y
1310 Fj(\()p Ff(\000)p Fj(1\))1047 1280 y Fe(\()p Fg(N)6 b
1311 Fb(\000)p Fe(1\)\(3)p Fb(\000)p Fe(1\))p Fg(=)p Fe(4)1506
1312 1314 y Fj(=)1594 1197 y Fc(\022)1665 1258 y Fh(N)p 1665
1313 1295 V 1682 1371 a Fj(3)1751 1197 y Fc(\023)1826 1314
1314 y Fj(\()p Ff(\000)p Fj(1\))1997 1280 y Fg(q)2056 1314
1315 y Fj(=)23 b Ff(\000)2223 1197 y Fc(\022)2293 1258 y Fh(N)p
1316 2293 1295 V 2310 1371 a Fj(3)2379 1197 y Fc(\023)2463
1317 1314 y Fj(=)g Ff(\000)2630 1197 y Fc(\022)2700 1258 y
1318 Fj(2)p 2700 1295 42 4 v 2700 1371 a(3)2752 1197 y Fc(\023)2836
1319 1314 y Fj(=)g Ff(\000)p Fj(\()p Ff(\000)p Fj(1\))3160
1320 1280 y Fe(\(3)3219 1255 y Fd(2)3250 1280 y Fb(\000)p
1321 Fe(1\))p Fg(=)p Fe(8)3455 1314 y Fj(=)g(1)125 1528 y(This)31
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1323 n(ys)e(a)i(quadratic)f(residue)g(mo)r(dulo)h Fh(N)9 b
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1325 1628 y Fj(could)d(nev)n(er)g(b)r(e)h(c)n(hosen)e(to)i(b)r(e)g(equal)e
1326 (to)i Fh(k)s Fj(.)39 b(Since)29 b(3)f(is)g(also)g(not)g(an)g(in)n
1327 (tegral)g(p)r(o)n(w)n(er)f(of)h(an)n(y)g(other)g(in)n(teger,)g(it)h(is)
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1329 Fj(to)c(b)r(e)i(a)e(kno)n(wn)h(ro)r(ot)f(of)h Fh(k)i
1330 Fj(b)n(y)e(acciden)n(t.)36 b(Using)26 b Fh(k)f Fj(=)e(3)j(ensures)f
1331 (that)h(an)n(y)f(set)h(of)g(parameters)0 1827 y Fh(N)39
1332 b Fj(and)30 b Fh(g)j Fj(that)e(are)e(safe)h(to)g(use)g(with)h(SRP)f
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1334 (standp)r(oin)n(t)f(of)g(eliminating)h(the)0 1927 y(\\t)n(w)n
1335 (o-for-one")24 b(attac)n(k.)0 2199 y Fk(3)135 b(Message)46
1336 b(ordering)0 2381 y Fj(The)39 b(implications)f(of)g(the)h
1337 (\\message-ordering")34 b(prop)r(ert)n(y)k(of)g(SRP)h(can)f(b)r(e)h(b)r
1338 (etter)g(understo)r(o)r(d)f(b)n(y)g(studying)h(the)0
1339 2480 y(v)-5 b(arious)38 b(prop)r(osals)f(to)i(optimize)g(SRP)g(and)g
1340 (in)n(tegrate)e(it)j(in)n(to)f(existing)f(proto)r(cols.)70
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1342 2580 y(SRP)31 b(suggested)f(in)i([3])f(that)h(required)e(only)h(three)g
1343 (messages,)g(with)g(an)g(optional)g(fourth)g(message)f(for)h(the)h
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1346 (the)h(parameter)d Fh(u)h Fj(is)h(no)f(longer)f(an)i(explicit)0
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1348 (as)g(a)g(function)h(of)g(the)g(serv)n(er's)d Fh(B)32
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1350 b Fh(S)286 b(I)7 b(;)14 b(A)1497 3059 y(C)29 b Ff(\()-14
1351 b Fj(=)23 b Fh(S)286 b(s;)14 b(B)1497 3158 y(C)29 b Fj(=)-14
1352 b Ff(\))23 b Fh(S)298 b(M)2172 3170 y Fe(1)1497 3258
1353 y Fh(C)29 b Ff(\()-14 b Fj(=)23 b Fh(S)105 b(M)1979 3270
1354 y Fe(2)2043 3258 y Fj(\(optional\))1350 3437 y(T)-7 b(able)28
1355 b(2:)36 b(Original)26 b(optimized)i(SRP)125 3714 y(This)d(v)n(ersion)g
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1359 b(the)g(clien)n(t)g(needs)g(to)g(kno)n(w)f(them)h(in)g(order)f(to)h
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1361 b(In)20 b(practice,)h(ho)n(w)n(ev)n(er,)e(this)h(is)0
1362 3913 y(di\016cult)25 b(to)e(arrange.)34 b(Since)24 b(the)g(passw)n(ord)
1363 e(v)n(eri\014er)g(v)-5 b(alue)24 b(\(i.e.)36 b Fh(v)26
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1365 (particular)e(user)h(on)h(a)f(particular)g(serv)n(er)0
1366 4012 y(is)h(tied)g(to)g(a)g(particular)f(set)h(of)g(parameters,)f(the)h
1367 (clien)n(t)g(cannot)g(unilaterally)f(select)h(the)g(parameters)f(the)h
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1369 b(an)f(unauthen)n(ticated)i(Di\016e-Hellman)f(k)n(ey)f(exc)n(hange.)37
1370 b(Ev)n(en)27 b(if)i(SRP)f(group)f(parameters)f(w)n(ere)h(standardized)0
1371 4212 y(b)n(y)39 b(bit)g(length,)j(the)e(clien)n(t)f(w)n(ould)g(still)g
1372 (need)g(to)g(kno)n(w)f(the)i(user's)e(group)g(size)h(b)r(efore)f
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1374 (ose)g(problems)f(for)h(b)r(oth)g(usabilit)n(y)g(and)g(implemen)n
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1378 (issue,)g(but)g(the)g(loss)e(of)h(\015exibilit)n(y)0
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1380 (w)n(ould)i(b)r(e)g(a)g(serious)f(problem)g(if)i(the)f(proto)r(col)f(w)
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1382 (nature.)125 4710 y(In)c(practice,)g(it)g(is)g(more)f(natural)g(for)h
1383 (the)g(serv)n(er)f(to)g(send)h(the)h(clien)n(t)f(the)g(v)-5
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1385 4809 y(user)33 b(after)f(receiving)h(the)g(username)f(in)i(the)g
1386 (\014rst)f(proto)r(col)f(\015o)n(w)g(from)h(the)h(clien)n(t.)54
1387 b(This)33 b(w)n(a)n(y)-7 b(,)33 b(the)h(clien)n(t)f(do)r(es)g(not)0
1388 4909 y(need)d(to)g(an)n(ticipate)g(or)f(otherwise)h(k)n(eep)f(trac)n(k)
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1392 (mathematically)g(or)g(b)n(y)h(simple)g(table)g(lo)r(okup.)43
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1394 (of)h(message)e(\015o)n(ws,)h(as)f(do)r(cumen)n(ted)i(in)g([4].)125
1395 5208 y(Unfortunately)-7 b(,)35 b(adding)e(the)h(transmission)e(of)h
1396 (the)h(group)e(parameters)g(has)h(lengthened)h(the)g(proto)r(col)e(b)n
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1404 %%Page: 4 4
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1417 b(alue)28 b Fh(A)p Fj(.)40 b(In)29 b(proto)r(cols)e(that)i(use)g(the)f
1418 (message)g Fh(B)k Fj(to)d(deriv)n(e)e(the)i(shared)f(v)-5
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1420 (to)f Fh(B)t Fj(,)h(since)f(rev)n(ealing)f Fh(B)33 b
1421 Fj(rev)n(eals)26 b Fh(u)i Fj(to)h(the)g(clien)n(t.)39
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1424 (sends)g(his)g(v)-5 b(alue)26 b Fh(A)h Fj(allo)n(ws)d(him)j(to)f(carry)
1425 e(out)j(an)e(attac)n(k.)36 b(More)25 b(sp)r(eci\014cally)-7
1426 b(,)26 b(an)0 1801 y(attac)n(k)n(er)20 b(who)h(kno)n(ws)f(the)i(serv)n
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1428 Fh(x)p Fj(\))g(can)f(p)r(ose)g(as)g(a)g(clien)n(t)g(and)g(send)h(the)g
1429 (v)-5 b(alue)21 b Fh(A)i Fj(=)g Fh(g)3722 1771 y Fg(a)3761
1430 1801 y Fh(v)3804 1771 y Fb(\000)p Fg(u)0 1900 y Fj(instead)i(of)g
1431 Fh(A)e Fj(=)g Fh(g)592 1870 y Fg(a)631 1900 y Fj(,)j(and)f(this)g(will)
1432 g(\\cancel)f(out")h(the)g Fh(v)1810 1870 y Fg(u)1879
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1439 (necessary)d(to)j(send)f Fh(u)h Fj(itself)g(after)f Fh(A)p
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1441 (to)f(send)h Fh(M)1417 2211 y Fe(1)1481 2199 y Fj(along)f(with)h
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1494 b Fj(=)-14 b Ff(\))23 b Fh(S)336 b(I)1497 4676 y(C)29
1495 b Ff(\()-14 b Fj(=)23 b Fh(S)192 b(N)t(;)14 b(g)s(;)g(s;)g(B)1497
1496 4776 y(C)29 b Fj(=)-14 b Ff(\))23 b Fh(S)249 b(A;)14
1497 b(M)2222 4788 y Fe(1)1497 4875 y Fh(C)29 b Ff(\()-14
1498 b Fj(=)23 b Fh(S)105 b(M)1979 4887 y Fe(2)2043 4875 y
1499 Fj(\(optional\))1094 5054 y(T)-7 b(able)27 b(4:)37 b(SRP)27
1500 b(with)h(optimized)g(message)e(ordering)1929 5656 y(4)p
1502 %%Page: 5 5
1503 5 4 bop 0 390 a Fk(4)135 b(Conclusion)0 572 y Fj(T)-7
1504 b(able)27 b(5)g(sho)n(ws)g(the)h(SRP)f(proto)r(col)g(incorp)r(orating)e
1505 (the)j(t)n(w)n(o)f(re\014nemen)n(ts)g(in)n(tro)r(duced)h(in)g(this)g
1506 (pap)r(er.)p 924 691 2052 4 v 922 791 4 100 v 1375 761
1507 a(Clien)n(t)880 b(Serv)n(er)p 2974 791 V 924 794 2052
1508 4 v 922 919 4 125 v 974 889 a(1.)2023 842 y Fg(I)1973
1509 889 y Ff(\000)-14 b(!)245 b Fj(\(lo)r(okup)27 b Fh(s)p
1510 Fj(,)h Fh(v)s Fj(\))p 2974 919 V 922 1029 4 111 v 974
1511 999 a(2.)186 b Fh(x)24 b Fj(=)f Fh(H)7 b Fj(\()p Fh(s;)14
1512 b(I)7 b(;)14 b(P)e Fj(\))2024 952 y Fg(s)1973 999 y Ff( )-14
1513 b(\000)p 2974 1029 V 922 1279 4 250 v 974 1175 a Fj(3.)1357
1514 1124 y Fh(A)23 b Fj(=)g Fh(g)1573 1094 y Fg(a)1252 1224
1515 y Fh(u)g Fj(=)g Fh(H)7 b Fj(\()p Fh(A;)14 b(B)t Fj(\))2015
1516 1077 y Fg(A)1973 1124 y Ff(\000)-14 b(!)2013 1202 y Fg(B)1973
1517 1249 y Ff( )g(\000)2367 1125 y Fh(B)27 b Fj(=)c(3)p Fh(v)e
1518 Fj(+)d Fh(g)2774 1095 y Fg(b)2354 1224 y Fh(u)23 b Fj(=)g
1519 Fh(H)7 b Fj(\()p Fh(A;)14 b(B)t Fj(\))p 2974 1279 V 922
1520 1380 4 101 v 974 1350 a(4.)99 b Fh(S)28 b Fj(=)23 b(\()p
1521 Fh(B)f Ff(\000)c Fj(3)p Fh(g)1590 1320 y Fg(x)1631 1350
1522 y Fj(\))1663 1320 y Fg(a)p Fe(+)p Fg(ux)2380 1350 y Fh(S)28
1523 b Fj(=)23 b(\()p Fh(Av)2684 1320 y Fg(u)2728 1350 y Fj(\))2760
1524 1320 y Fg(b)p 2974 1380 V 922 1506 4 126 v 974 1476 a
1525 Fj(5.)132 b Fh(M)1252 1488 y Fe(1)1312 1476 y Fj(=)23
1526 b Fh(H)7 b Fj(\()p Fh(A;)14 b(B)t(;)g(S)5 b Fj(\))1992
1527 1428 y Fg(M)2055 1436 y Fd(1)1973 1476 y Ff(\000)-14
1528 b(!)273 b Fj(\(v)n(erify)27 b Fh(M)2724 1488 y Fe(1)2761
1529 1476 y Fj(\))p 2974 1506 V 922 1631 V 974 1602 a(6.)239
1530 b(\(v)n(erify)27 b Fh(M)1622 1614 y Fe(2)1659 1602 y
1531 Fj(\))1992 1554 y Fg(M)2055 1562 y Fd(2)1973 1602 y Ff( )-14
1532 b(\000)141 b Fh(M)2329 1614 y Fe(2)2389 1602 y Fj(=)22
1533 b Fh(H)7 b Fj(\()p Fh(A;)14 b(M)2764 1614 y Fe(1)2801
1534 1602 y Fh(;)g(S)5 b Fj(\))p 2974 1631 V 922 1731 4 100
1535 v 974 1701 a(7.)254 b Fh(K)29 b Fj(=)22 b Fh(H)7 b Fj(\()p
1536 Fh(S)e Fj(\))719 b Fh(K)29 b Fj(=)22 b Fh(H)7 b Fj(\()p
1537 Fh(S)e Fj(\))p 2974 1731 V 924 1734 2052 4 v 1226 1888
1538 a(T)-7 b(able)27 b(5:)36 b(SRP)28 b(with)g(re\014nemen)n(ts)f
1539 (\(SRP-6\))125 2175 y(The)40 b(end)g(result)g(of)g(these)g(relativ)n
1540 (ely)f(small)h(re\014nemen)n(ts)g(is)g(a)g(strong)e(passw)n(ord)h
1541 (proto)r(col)g(that)h(holds)g(activ)n(e)0 2274 y(adv)n(ersaries)27
1542 b(to)j(the)h(desired)e(limit)i(of)f(one)g(passw)n(ord)e(guess)h(p)r(er)
1543 h(imp)r(ersonation)f(attac)n(k,)h(as)f(w)n(ell)h(as)f(a)h(proto)r(col)f
1544 (that)0 2374 y(o\013ers)18 b(more)g(\015exibilit)n(y)h(for)f(implemen)n
1545 (tors)g(b)n(y)h(allo)n(wing)e(the)j(ordering)d(of)h(the)i(clien)n(t)f
1546 (and)f(serv)n(er)f(k)n(ey)h(exc)n(hange)g(messages)0
1547 2474 y(to)j(v)-5 b(ary)e(.)34 b(This)22 b(is)f(particularly)f(useful)i
1548 (for)f(proto)r(cols)f(that)i(send)g(the)g(user's)e(group)h(parameters)f
1549 Fh(N)30 b Fj(and)21 b Fh(g)j Fj(in)e(the)g(serv)n(er's)0
1550 2573 y(\014rst)g(message)f(and)i(wish)f(to)g(sa)n(v)n(e)f(a)h(round)g
1551 (trip)h(b)n(y)f(including)g Fh(B)27 b Fj(in)c(this)g(message.)33
1552 b(One)22 b(example)g(of)h(suc)n(h)f(a)g(proto)r(col)f(is)0
1553 2673 y(SSL/TLS)k([1)o(],)h(whic)n(h)g(has)e(a)h(fairly)g(\014xed)g(set)
1554 g(of)g(message)f(\015o)n(ws;)h(in)n(tegration)f(with)i(SRP)f(is)g
1555 (considerably)f(easier)g(when)0 2773 y(the)i(serv)n(er)f(can)g(send)h
1556 (all)g(of)g(its)g(k)n(ey)g(exc)n(hange)e(messages)h(in)h(its)g
1557 Fa(ServerKeyExchang)o(e)20 b Fj(message,)25 b(whic)n(h)h(is)g
1558 (de\014ned)g(b)n(y)0 2872 y(the)i(proto)r(col)e(to)i(precede)f(the)h
1559 Fa(ClientKeyExchang)o(e)22 b Fj(message)k(from)h(the)h(clien)n(t.)125
1560 2972 y(The)37 b(impro)n(v)n(ed)g(proto)r(col)f(will)i(b)r(e)g(called)g
1561 (\\SRP-6")d(to)j(distinguish)g(it)g(from)f(previous)g(v)-5
1562 b(arian)n(ts)36 b(of)i(SRP)-7 b(,)38 b(b)r(oth)0 3071
1563 y(o\016cial)27 b(and)g(uno\016cial.)0 3346 y Fk(References)0
1564 3528 y Fj([1])41 b(T.)26 b(Dierks)f(and)h(C.)g(Allen.)34
1565 b Fi(The)29 b(TLS)f(pr)l(oto)l(c)l(ol)h(version)g(1.0)p
1566 Fj(.)35 b(Certicom,)26 b(Jan)n(uary)e(1999.)32 b(Request)25
1567 b(F)-7 b(or)25 b(Commen)n(ts)129 3627 y(\(RF)n(C\))j(2246.)0
1568 3794 y([2])41 b(P)-7 b(.)27 b(MacKenzie.)34 b(On)27 b(the)g(securit)n
1569 (y)f(of)g(the)i(SPEKE)d(passw)n(ord-authen)n(ticated)f(k)n(ey)i(exc)n
1570 (hange)f(proto)r(col.)35 b(T)-7 b(ec)n(hnical)129 3893
1571 y(Rep)r(ort)28 b(2001/057,)23 b(Lucen)n(t)28 b(T)-7 b(ec)n(hnologies,)
1572 26 b(2001.)0 4059 y([3])41 b(T.)f(W)-7 b(u.)74 b(The)40
1573 b(secure)f(remote)g(passw)n(ord)f(proto)r(col.)72 b(In)40
1574 b Fi(Pr)l(o)l(c)l(e)l(e)l(dings)i(of)g(the)f(Internet)f(So)l(ciety)h
1575 (Network)g(and)129 4159 y(Distribute)l(d)30 b(System)f(Se)l(curity)g
1576 (Symp)l(osium)p Fj(,)g(pages)d(97{111,)f(Marc)n(h)h(1998.)0
1577 4325 y([4])41 b(T.)e(W)-7 b(u.)72 b Fi(The)41 b(SRP)f(A)n(uthentic)l
1578 (ation)f(and)i(Key)g(Exchange)g(System)p Fj(.)70 b(Stanford)39
1579 b(Univ)n(ersit)n(y)-7 b(,)41 b(Septem)n(b)r(er)e(2000.)129
1580 4424 y(Request)28 b(F)-7 b(or)27 b(Commen)n(ts)g(\(RF)n(C\))h(2945.)
1581 1929 5656 y(5)p eop
1582 %%Trailer
1584 userdict /end-hook known{end-hook}if
1585 %%EOF