%!PS-Adobe-2.0 %%Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %%Title: bcrypt.dvi %%Pages: 12 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentPaperSizes: A4 %%EndComments %DVIPSCommandLine: dvips -o bcrypt.ps bcrypt %DVIPSParameters: dpi=600, comments removed %DVIPSSource: TeX output 1999.04.28:0601 %%BeginProcSet: tex.pro /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if} forall round exch round exch]setmatrix}N /@landscape{/isls true N}B /@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 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b(y)n(et,)48 b(ssh)43 b(uses)g(simple)g(3-DES)g(to)0 5364 y(encrypt)37 b(priv)-5 b(ate)37 b(k)n(eys,)i(making)d(the)i(cost)f (of)g(guessing)0 5464 y(ssh)26 b(passw)n(ords)f(comparable)g(to)h(the)h (cost)g(of)f(computing)0 5564 y Fp(crypt)p Fq(.)62 b(Nonetheless,)38 b(b)r(ecause)d(of)h(its)g(\015exibilit)n(y)-7 b(,)39 b(ssh's)0 5663 y(RSA)33 b(authen)n(tication)f(is)g(a)g(generally)f(b)r (etter)i(approac)n(h)2010 383 y(than)i(sc)n(hemes)f(more)g(closely)f (tied)i(to)g(passw)n(ords.)56 b(F)-7 b(or)2010 483 y(example,)28 b(without)g(mo)r(difying)g(the)g(core)f(proto)r(cols,)f(ssh)2010 582 y(could)32 b(easily)g(emplo)n(y)g(the)h Fp(eksblow\014sh)41 b Fq(algorithm)31 b(pro-)2010 682 y(p)r(osed)22 b(in)g(this)g(pap)r(er) f(to)h(impro)n(v)n(e)e(the)i(securit)n(y)f(of)h(stored)2010 782 y(secret)27 b(k)n(eys.)2010 1097 y Fr(3)112 b(Design)142 b(criteria)d(for)j(passw)m(ord)2178 1213 y(sc)m(hemes)2010 1462 y Fq(An)n(y)23 b(algorithm)f(that)h(tak)n(es)f(a)h(user-c)n(hosen) e(passw)n(ord)g(as)2010 1562 y(input)35 b(should)f(b)r(e)h(hardened)e (against)g(passw)n(ord)f(guess-)2010 1662 y(ing.)69 b(That)38 b(means)g(an)n(y)g(public)h(or)f(long-liv)n(ed)f(output)2010 1761 y(should)22 b(b)r(e)h(of)f(minimal)g(use)g(in)h(reconstructing)e (the)h(pass-)2010 1861 y(w)n(ord.)49 b(Sev)n(eral)31 b(design)h(criteria)f(can)h(help)g(ac)n(hiev)n(e)f(this)2010 1960 y(goal.)2010 2160 y(Ideally)-7 b(,)40 b(one)e(w)n(ould)g(lik)n(e)f (an)n(y)h(passw)n(ord)e(handling)i(al-)2010 2259 y(gorithm)46 b(to)g(b)r(e)i(a)e(strong)f(one-w)n(a)n(y)g(function)i(of)g(the)2010 2359 y(passw)n(ord|that)19 b(is,)j(giv)n(en)e(the)h(algorithm's)e (output)i(and)2010 2459 y(other)32 b(inputs,)i(an)e(attac)n(k)n(er)e (should)j(ha)n(v)n(e)e(little)i(c)n(hance)2010 2558 y(of)i(learning)g (ev)n(en)g(partial)g(information)f(she)i(could)f(not)2010 2658 y(already)24 b(ha)n(v)n(e)h(guessed)f(ab)r(out)i(the)g(passw)n (ord.)34 b(Unfortu-)2010 2757 y(nately)-7 b(,)21 b(one-w)n(a)n(y)c 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Fq(\))25 b(of)f(the)g(distribution)h(to)f(b)r(e)h(the)2010 4053 y(highest)34 b(probabilit)n(y)g(Pr)o(\()p Fo(s)p Fq(\))h(of)g(an)n(y)e(single)h(passw)n(ord)f Fo(s)2010 4152 y Fq(in)28 b Fo(D)r Fq(:)38 b Fo(R)q Fq(\()p Fo(D)r Fq(\))24 b(=)f(max)2705 4164 y Fn(s)p Fm(2)p Fn(D)2855 4152 y Fq(Pr)o(\()p Fo(s)p Fq(\).)39 b(A)28 b(function)h(of)f(a)f (pass-)2010 4252 y(w)n(ord)19 b(is)i(secure)e(if)i(an)g(attac)n(k)n (er's)d(probabilit)n(y)i(of)g(learning)2010 4351 y(an)n(y)29 b(partial)g(information)g(ab)r(out)h(the)g(passw)n(ord)e(is)h(pro-)2010 4451 y(p)r(ortional)22 b(to)h(the)g(pro)r(duct)g(of)g(the)g(w)n(ork)e (she)i(in)n(v)n(ests)f(and)2010 4551 y(the)28 b(predictabilit)n(y)f(of) h(the)g(passw)n(ord)d(distribution.)2010 4750 y(What)30 b(do)r(es)g(it)h(mean)f(for)f(an)h(attac)n(k)n(er)f(to)h(learn)f (partial)2010 4850 y(information)19 b(ab)r(out)g(a)g(passw)n(ord?)33 b(W)-7 b(e)20 b(de\014ne)f(partial)g(in-)2010 4949 y(formation)j(to)h (b)r(e)g(the)h(v)-5 b(alue)23 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b(b)r(e)g(a)f(function.)43 b(The)30 b(argu-)0 782 y(men)n(t)37 b Fo(s)f Fq(represen)n(ts)f(a)h(user's)g(secret)f(passw)n(ord,)i(whic)n (h)0 881 y(will)42 b(b)r(e)h(dra)n(wn)e(from)h(a)g(probabilit)n(y)f (distribution)h Fo(D)r Fq(.)0 981 y(The)19 b(argumen)n(t)g Fo(t)g Fq(represen)n(ts)f(an)n(y)h(additional)f(non-secret)0 1080 y(inputs)31 b Fo(F)43 b Fq(migh)n(t)30 b(tak)n(e.)45 b(Let)31 b(the)g(v)-5 b(alues)30 b(of)h Fo(t)f Fq(b)r(e)h(dra)n(wn)0 1180 y(from)26 b(a)g(probabilit)n(y)f(distribution)i Fo(T)12 b Fq(.)35 b(W)-7 b(e)27 b(mo)r(del)f(an)h(at-)0 1280 y(tac)n(k)n(er)39 b(as)i(a)g(randomized)f(b)r(o)r(olean)g(circuit) 1473 1250 y Fl(1)1510 1280 y Fq(,)45 b Fo(A)p Fq(,)g(that)0 1379 y(tries)k(to)g(guess)f(a)h(predicate)g Fo(P)61 b Fq(ab)r(out)49 b(a)g(passw)n(ord.)0 1479 y(The)d(cost)e(of)i(an)f (attac)n(k|or)f(the)h(w)n(ork)f(in)n(v)n(ested)h(b)n(y)0 1579 y(an)k(attac)n(k)n(er|is)e(the)j(n)n(um)n(b)r(er)f(of)g(gates)f (in)h(the)h(cir-)0 1678 y(cuit,)45 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y(b)g Fk( )g Fo(A)p Fq(\()p Fo(t)831 3583 y Fl(1)869 3571 y Fo(;)14 b(F)e Fq(\()p Fo(s;)i(t)1109 3583 y Fl(1)1146 3571 y Fq(\))p Fo(;)g(:)g(:)g(:)28 b(;)14 b(t)1407 3583 y Fn(c)1441 3571 y Fo(;)g(F)e Fq(\()p Fo(s;)i(t)1681 3583 y Fn(c)1714 3571 y Fq(\)\);)542 3696 y Fo(b)23 b Fq(=)g Fo(P)12 b Fq(\()p Fo(s)p Fq(\))857 3628 y Fj(\003)335 3828 y Fk(\000)18 b Fq(Pr)507 3761 y Fj(\002)541 3828 y Fo(t)571 3840 y Fl(1)632 3828 y Fk( )23 b Fo(T)7 b(;)32 b(:)14 b(:)g(:)27 b(;)33 b(t)1059 3840 y Fn(c)1115 3828 y Fk( )23 b Fo(T)7 b(;)32 b(s)23 b Fk( )g Fo(D)r(;)542 3953 y(b)g Fk( )g Fo(A)p Fq(\()p Fo(t)831 3965 y Fl(1)869 3953 y Fo(;)14 b(F)e Fq(\()p Fo(s;)i(t)1109 3965 y Fl(1)1146 3953 y Fq(\))p Fo(;)g(:)g(:)g(:)28 b(;)14 b(t)1407 3965 y Fn(c)1441 3953 y Fo(;)g(F)e Fq(\()p Fo(s;)i(t)1681 3965 y Fn(c)1714 3953 y Fq(\)\))p Fo(;)542 4078 y(s)581 4043 y Fm(0)628 4078 y Fk( )23 b Fo(D)r Fq(;)32 b Fo(b)23 b Fq(=)f Fo(P)12 b Fq(\()p Fo(s)1142 4043 y Fm(0)1166 4078 y Fq(\))1198 4010 y Fj(\003)1233 4007 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b(Eac)n(h)29 b(gate)i(computes)e(a)h(b)r(o)r(olean)g (function)g(of)e(0,)j(1)e(or)g(2)0 5252 y(single-bit)c(inputs.)37 b(A)25 b(randomized)g(b)r(o)r(olean)i(circuit)e(tak)n(es)i(a)e(cer-)0 5331 y(tain)i(n)n(um)n(b)r(er)f(of)h(random)f(input)h(bits)g(in)g (addition)g(to)h(its)e(regular)0 5410 y(inputs.)2176 383 y Fq(bits:)2385 566 y Fk(8)p Fo(D)r(;)32 b Fk(8)p Fo(A;)2468 690 y Fq(Pr)2557 623 y Fj(\002)2592 690 y Fo(t)23 b Fk( )g Fo(T)7 b(;)32 b(s)23 b Fk( )g Fo(D)r(;)32 b(s)3195 656 y Fm(0)3242 690 y Fk( )23 b Fo(A)p Fq(\()p Fo(s;)14 b(t)p Fq(\);)2717 823 y Fo(s)23 b Fk(6)p Fq(=)g Fo(s)2906 789 y Fm(0)2948 823 y Fk(^)c Fo(F)12 b Fq(\()p Fo(s;)i(t)p Fq(\))23 b(=)g Fo(F)12 b Fq(\()p Fo(s)3504 789 y Fm(0)3527 823 y Fo(;)i(t)p Fq(\))3626 756 y Fj(\003)2551 948 y Fo(<)23 b(\017)18 b Fk(\001)h(j)p Fo(A)p Fk(j)g(\001)f Fo(R)q Fq(\()p Fo(D)r Fq(\))2010 1213 y(W)-7 b(e)41 b(should)g(\014rst) g(note)g(that)g(this)g(de\014nition)h(matc)n(hes)2010 1313 y(our)20 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b(high)g(probabilit)n(y)-7 b(,)42 b(an)e(adv)n(ersary)d(should)i(need)2010 2608 y(to)i(exp)r(end)g(a)g(large)f(amoun)n(t)g(of)h(e\013ort)g(\(as)g (measured)2010 2708 y(in)e(circuit)g(gates\))g(to)g(disco)n(v)n(er)e (an)n(y)h(non-trivial)g(infor-)2010 2807 y(mation)30 b(ab)r(out)h(a)f(passw)n(ord.)44 b(Finally)-7 b(,)31 b(w)n(e)f(also)g(wish)g(to)2010 2907 y(prev)n(en)n(t)f(an)g(attac)n(k)n (er)f(from)i(\014nding)g(other)f(strings)g(that)2010 3007 y(hash)g(to)g(the)h(same)f(v)-5 b(alue)30 b(as)e(a)h(passw)n(ord;) g(suc)n(h)g(strings)2010 3106 y(ma)n(y)j(pro)n(v)n(e)f(equiv)-5 b(alen)n(t)32 b(to)g(passw)n(ords)e(during)i(authen-)2010 3206 y(tication.)65 b(The)37 b(requiremen)n(t)g(of)g(second)f(preimage) g(re-)2010 3305 y(sistance)27 b(guaran)n(tees)f(suc)n(h)i(collisions)f (are)f(hard)i(to)g(\014nd,)2010 3405 y(ev)n(en)37 b(with)h(kno)n (wledge)e(of)i(the)g(original)e(passw)n(ord.)65 b(It)2010 3505 y(also)31 b(ensures)g(that)h Fo(F)44 b Fq(do)r(es)32 b(not)g(ignore)f(an)n(y)g(bits)h(of)g(its)2010 3604 y(passw)n(ord)26 b(input.)2010 3804 y(The)i(de\014nition)f(implies)h(that)g(a)f(secure)f (passw)n(ord)g(func-)2010 3903 y(tion)i Fo(F)12 b Fq(\()p Fo(s;)i(t)p Fq(\))28 b(m)n(ust)g(mak)n(e)f(non-trivial)f(use)i(of)g (its)g(second)2010 4003 y(argumen)n(t,)g Fo(t)p Fq(.)41 b(T)-7 b(o)29 b(see)f(this,)i(consider)d(that)j(the)f(\014rst)g(bit) 2010 4102 y(of)19 b Fo(F)12 b Fq(\()p Fo(s;)i Fq(0\))19 b(is)g(a)g(p)r(erfectly)g(v)-5 b(alid)19 b(predicate)f(on)h(passw)n (ords.)2010 4202 y(An)g(attac)n(k)n(er)e(could)i(easily)f(guess)g(this) h(predicate)f(if)h(either)2010 4302 y Fo(F)46 b Fq(ignored)33 b(its)h(second)g(argumen)n(t)f(or)g(the)h(string)g(0)g(o)r(c-)2010 4401 y(curred)25 b(in)h Fo(T)36 b Fq(with)26 b(high)g(probabilit)n(y)-7 b(.)35 b(This)26 b(p)r(oin)n(t)g(is)f(not)2010 4501 y(merely)34 b(an)h(academic)f(one.)57 b(A)35 b(single-input)g(passw)n(ord)2010 4601 y(hashing)c(function)h Fo(F)12 b Fq(\()p Fo(s)p Fq(\))32 b(can)g(b)r(e)g(in)n(v)n(erted)f(b)n(y)g(a)g(circuit)2010 4700 y(large)18 b(enough)h(to)h(enco)r(de)f(a)g(lo)r(okup)h(table)f (mapping)h Fo(F)12 b Fq(\()p Fo(s)p Fq(\))2010 4800 y(\(or)27 b(su\016cien)n(tly)h(man)n(y)g(bits)g(of)g Fo(F)12 b Fq(\()p Fo(s)p Fq(\)\))29 b(to)e Fo(s)p Fq(.)38 b(The)28 b(size)g(of)2010 4899 y(suc)n(h)j(a)g(circuit)g(dep)r(ends)h(only)f(on) g(the)g(probabilit)n(y)f(dis-)2010 4999 y(tribution)36 b(of)h(the)f(passw)n(ords,)h(not)f(on)g(the)h(particulars)2010 5099 y(of)28 b Fo(F)12 b Fq(.)2010 5298 y(As)24 b(prop)r(osed)g(b)n(y)g (Morris)f(and)h(Thompson)f([9],)i(ho)n(w)n(ev)n(er,)2010 5398 y(lo)r(okup)31 b(tables)h(can)g(b)r(e)g(th)n(w)n(arted)f(with)i (the)f(second)f(in-)2010 5497 y(put)j(to)f Fo(F)12 b Fq(,)34 b(whic)n(h)f(they)h(call)e(a)h Fp(salt)p Fq(.)54 b(If)33 b(a)g(random)f(salt)2010 5597 y(is)i(c)n(hosen)f(whenev)n(er)g (users)g(establish)g(new)h(passw)n(ords,)2010 5696 y(and)23 b(if)g(the)g(salt)f(space)g(is)h(large)e(enough)h(to)g(ensure)h(a)f (neg-)p eop %%Page: 5 5 5 4 bop 0 383 a Fq(ligible)27 b(probabilit)n(y)g(of)g(recurrence,)f(lo) r(okup)h(tables)h(o\013er)0 483 y(an)23 b(adv)n(ersary)e(no)i(adv)-5 b(an)n(tage;)23 b(he)h(ma)n(y)e(as)h(w)n(ell)g(compute)0 582 y Fo(F)42 b Fq(at)29 b(the)h(time)g(of)f(attac)n(k.)42 b(If,)31 b(on)e(the)h(other)f(hand,)h(the)0 682 y(salt)25 b(space)g(is)g(to)r(o)g(small,)g(the)h(output)g(bits)g(of)f Fo(F)37 b Fq(b)r(ecome)0 782 y(useful)31 b(predicates)f(on)g(passw)n (ords,)f(a)h(fact)h(exploited)f(b)n(y)0 881 y(the)e(QCrac)n(k)e([12)o (])h(program)f(describ)r(ed)h(in)h(Section)g(6.)0 1080 y(While)j(salted)e(passw)n(ords)f(defeat)i(lo)r(okup)g(tables,)g(giv)n (en)0 1180 y(a)38 b(particular)g(salt)h(and)f(hash,)k(an)c(adv)n (ersary)e(can)j(still)0 1280 y(moun)n(t)26 b(a)g(brute)g(force)g(attac) n(k)f(b)n(y)h(ev)-5 b(aluating)26 b Fo(F)12 b Fq(\()p Fo(s;)i(t)p Fq(\))26 b(on)0 1379 y(ev)n(ery)d(p)r(ossible)h(passw)n (ord.)34 b(It)25 b(follo)n(ws)e(that)i(the)g(b)r(est)g(se-)0 1479 y(curit)n(y)f(one)h(can)g(ac)n(hiev)n(e)e(is)i Fo(\017)e Fk(\031)g Fq(1)p Fo(=)p Fk(j)p Fo(F)12 b Fk(j)p Fq(,)24 b(where)h Fk(j)p Fo(F)12 b Fk(j)25 b Fq(is)g(the)0 1579 y(cost)j(in)h(gates)e(of)i(implemen)n(ting)g Fo(F)12 b Fq(.)39 b(Usabilit)n(y)28 b(require-)0 1678 y(men)n(ts)j(therefore)e (e\013ect)i(a)g(lo)n(w)n(er)e(limit)i(on)f Fo(\017)p Fq(|if)h(p)r(eople)0 1778 y(can)37 b(only)h(tolerate)e(a)i(one)f (second)g(dela)n(y)g(for)g(c)n(hec)n(king)0 1877 y(passw)n(ords,)29 b Fo(F)42 b Fq(can)30 b(tak)n(e)g(at)g(most)h(one)f(second)f(to)i(ev)-5 b(al-)0 1977 y(uate.)39 b Fo(F)i Fq(should)28 b(not)h(tak)n(e)e (signi\014can)n(tly)h(less,)g(ho)n(w)n(ev)n(er,)0 2077 y(as)f(this)h(w)n(ould)f(unnecessarily)f(w)n(eak)n(en)g(securit)n(y)-7 b(.)0 2276 y(The)26 b(n)n(um)n(b)r(er)f(of)g(gates)g Fk(j)p Fo(A)p Fk(j)h Fq(that)f(an)h(adv)n(ersary)c(can)j(rea-)0 2376 y(sonably)37 b(m)n(uster)h(for)g(an)g(attac)n(k)g(increases)f (constan)n(tly)0 2475 y(as)44 b(hardw)n(are)f(impro)n(v)n(es.)87 b(F)-7 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y(pro)n(v)n(es)h(and)h(users)g(will)h(tolerate.)48 b(Compromised)30 b(pass-)0 3671 y(w)n(ord)j(databases)g(will)i(then)g (enjo)n(y)f(maxim)n(um)g(securit)n(y)0 3770 y(against)26 b(o\013-line)i(attac)n(ks.)0 3970 y(In)37 b(summary)-7 b(,)37 b(a)f(go)r(o)r(d)g(passw)n(ord)e(function)j(mak)n(es)f(ex-)0 4069 y(tracting)41 b(an)n(y)g(partial)g(information)g(ab)r(out)g(passw) n(ords)0 4169 y(as)34 b(di\016cult)i(as)f(guessing)e(passw)n(ords.)57 b(A)36 b(concrete)e(pa-)0 4268 y(rameter,)40 b Fo(\017)p Fq(,)h(should)d(c)n(haracterize)f(this)h(di\016cult)n(y)-7 b(.)70 b(T)-7 b(o)0 4368 y(ac)n(hiev)n(e)34 b(lo)n(w)h(v)-5 b(alues)35 b(of)g Fo(\017)p Fq(,)j(a)d(passw)n(ord)e(function)j(m)n (ust)0 4468 y(tak)n(e)31 b(a)h(second)g(input,)i(the)e(salt,)h(that)g (prev)n(en)n(ts)e(adv)n(er-)0 4567 y(saries)21 b(from)g(b)r (ene\014ting)i(from)e(large)g(lo)r(okup)g(tables.)35 b(The)0 4667 y(b)r(est)30 b(v)-5 b(alue)30 b(of)g Fo(\017)f Fq(is)h(in)n(v)n(ersely)e(prop)r(ortional)h(to)g(the)i(cost)0 4767 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b(The)42 b(arra)n(ys)c(act)0 5050 y(as)28 b(substitution)i(b)r(o)n(xes)e(or)g Fp(S-b)l(oxes)p Fq(,)h(replacing)f (an)g(8-bit)0 5150 y(input)35 b(with)g(a)f(32-bit)f(output.)58 b Fo(F)46 b Fq(splits)34 b(its)h(32-bit)e(in-)0 5249 y(put)d(in)n(to)g(four)f(8-bit)h(b)n(ytes,)g Fo(a)p Fq(,)g Fo(b)p Fq(,)g Fo(c)p Fq(,)g(and)g Fo(d)p Fq(,)h(with)f Fo(a)g Fq(the)0 5349 y(most)h(signi\014can)n(t)g(b)n(yte.)48 b(It)32 b(replaces)e(eac)n(h)h(b)n(yte)h(b)n(y)f(the)0 5449 y(con)n(ten)n(ts)k(of)g(an)h(S-b)r(o)n(x,)h(and)e(com)n(bines)g (the)h(results)f(as)0 5548 y(follo)n(ws:)h(Letting)28 b Fg(\001)f Fq(signify)g(addition)h(mo)r(dulo)f(2)1619 5518 y Fl(32)1689 5548 y Fq(:)93 5700 y Fo(F)12 b Fq(\()p Fo(a;)i(b;)g(c;)g(d)p Fq(\))23 b(=)603 5633 y Fj(\000)641 5700 y Fq(\()p Fo(S)724 5712 y Fl(1)761 5700 y Fq([)p Fo(a)p Fq(])c Fg(\001)f Fo(S)1004 5712 y Fl(2)1041 5700 y Fq([)p Fo(b)p Fq(]\))g Fk(\010)g Fo(S)1307 5712 y Fl(3)1345 5700 y Fq([)p Fo(c)p Fq(])1427 5633 y Fj(\001)1483 5700 y Fg(\001)g Fo(S)1617 5712 y Fl(4)1654 5700 y Fq([)p Fo(d)p Fq(])p Fo(:)2218 453 y Fq(EksBlo)n(w\014shSetup)26 b(\()p Fp(c)l(ost)p Fq(,)i Fp(salt)p Fq(,)g Fp(key)7 b Fq(\))2301 552 y Fp(state)34 b Fk( )27 b Fq(InitState)i(\(\))2301 652 y Fp(state)34 b Fk( )27 b Fq(ExpandKey)g(\()p Fp(state)p Fq(,)g Fp(salt)p Fq(,)h Fp(key)7 b Fq(\))2301 752 y Ff(rep)s(eat)28 b Fq(\(2)2669 722 y Fe(c)m(ost)2793 752 y Fq(\))2384 851 y Fp(state)34 b Fk( )27 b Fq(ExpandKey)g(\()p Fp(state)p Fq(,)g(0,)h Fp(salt)8 b Fq(\))2384 951 y Fp(state)34 b Fk( )27 b Fq(ExpandKey)g(\()p Fp(state)p Fq(,)g(0,)h Fp(key)7 b Fq(\))2301 1051 y Ff(return)28 b Fp(state)2010 1446 y Fq(Figure)21 b(2:)34 b(Eksblo)n(w\014sh,)21 b(exp)r(ensiv)n(e)g (k)n(ey)h(sc)n(hedule)f(blo)n(w-)2010 1545 y(\014sh,)33 b(is)g(a)e(cost)h(parameterizable)e(and)i(salted)g(v)-5 b(ariation)2010 1645 y(of)28 b(the)g(blo)n(w\014sh)f(blo)r(c)n(k)g (cipher.)2010 1910 y(Eksblo)n(w\014sh)35 b(encrypts)g(iden)n(tically)h (to)g(Blo)n(w\014sh.)61 b(The)2010 2010 y(t)n(w)n(o)23 b(di\013er)h(in)g(the)h(functions)f(they)g(use)g(to)g(transform)e(en-) 2010 2109 y(cryption)35 b(k)n(eys)g(in)n(to)g(subk)n(eys)f(and)i(S-b)r (o)n(xes.)60 b(Figure)34 b(2)2010 2209 y(sk)n(etc)n(hes)k Fp(EksBlow\014shSetup)p Fq(,)44 b(the)39 b(algorithm)f(used)h(b)n(y) 2010 2309 y(eksblo)n(w\014sh.)51 b Fp(EksBlow\014shSetup)39 b Fq(has)32 b(three)g(input)i(pa-)2010 2408 y(rameters:)k(a)29 b(cost,)g(a)f(salt,)i(and)e(the)i(encryption)e(k)n(ey)-7 b(.)41 b(It)2010 2508 y(returns)25 b(a)g(set)g(of)h(subk)n(eys)e(and)i (S-b)r(o)n(xes,)f(also)f(kno)n(wn)h(as)2010 2608 y(a)i Fp(key)k(sche)l(dule)p Fq(.)2010 2807 y(The)c(cost)g(parameter)f(con)n (trols)f(ho)n(w)i(exp)r(ensiv)n(e)f(the)i(k)n(ey)2010 2906 y(sc)n(hedule)i(is)g(to)g(compute.)44 b(The)30 b(salt)g(is)g(a)f (128-bit)g(v)-5 b(alue)2010 3006 y(that)25 b(mo)r(di\014es)g(the)h(k)n (ey)e(sc)n(hedule)g(so)h(that)g(the)g(same)g(k)n(ey)2010 3106 y(need)32 b(not)g(alw)n(a)n(ys)e(pro)r(duce)i(the)g(same)f (result,)i(as)e(moti-)2010 3205 y(v)-5 b(ated)31 b(b)n(y)g(Section)g (3.)48 b(Finally)-7 b(,)32 b(the)g(k)n(ey)e(argumen)n(t)g(is)h(a)2010 3305 y(secret)k(encryption)g(k)n(ey)-7 b(,)37 b(whic)n(h)f(can)g(b)r(e) g(a)f(user-c)n(hosen)2010 3405 y(passw)n(ord)22 b(of)i(up)g(to)g(56)g (b)n(ytes)f(\(including)i(a)e(terminating)2010 3504 y(zero)j(b)n(yte)i (when)g(the)g(k)n(ey)f(is)g(an)g(ASCI)r(I)i(string\).)2010 3703 y Fp(EksBlow\014shSetup)c Fq(b)r(egins)19 b(b)n(y)f(calling)g Fp(InitState)p Fq(,)i(a)e(func-)2010 3803 y(tion)24 b(that)h(copies)e (the)i(digits)f(of)g(the)g(n)n(um)n(b)r(er)g Fo(\031)j Fq(\014rst)d(in)n(to)2010 3903 y(the)k(subk)n(eys,)f(then)h(in)n(to)f (the)h(S-b)r(o)n(xes.)2010 4102 y Fp(Exp)l(andKey\(state,)46 b(salt,)f(key\))g Fq(mo)r(di\014es)40 b(the)h(P-Arra)n(y)2010 4202 y(and)32 b(S-b)r(o)n(xes)g(based)g(on)g(the)h(v)-5 b(alue)32 b(of)g(the)h(128-bit)e(salt)2010 4301 y(and)h(the)h(v)-5 b(ariable)31 b(length)i(k)n(ey)-7 b(.)51 b(First)32 b(it)h(X)n(ORs)f (all)g(the)2010 4401 y(subk)n(eys)20 b(in)g(the)h(P-arra)n(y)c(with)k (the)g(encryption)f(k)n(ey)-7 b(.)34 b(The)2010 4500 y(\014rst)24 b(32)f(bits)h(of)g(the)h(k)n(ey)e(are)g(X)n(ORed)h(with)g Fo(P)3486 4512 y Fl(1)3524 4500 y Fq(,)g(the)h(next)2010 4600 y(32)34 b(bits)h(with)g Fo(P)2546 4612 y Fl(2)2584 4600 y Fq(,)i(and)d(so)g(on.)59 b(The)35 b(k)n(ey)f(is)g(view)n(ed)h (as)2010 4700 y(b)r(eing)i(cyclic;)42 b(when)37 b(the)g(pro)r(cess)f (reac)n(hes)f(the)j(end)f(of)2010 4799 y(the)27 b(k)n(ey)-7 b(,)27 b(it)g(starts)f(reusing)g(bits)h(from)g(the)g(b)r(eginning)g(to) 2010 4899 y(X)n(OR)g(with)h(subk)n(eys.)2010 5098 y(Subsequen)n(tly)-7 b(,)76 b Fp(Exp)l(andKey)e Fq(blo)n(w\014sh-encrypts)65 b(the)2010 5198 y(\014rst)34 b(64)e(bits)i(of)g(its)g(salt)g(argumen)n (t)e(using)i(the)g(curren)n(t)2010 5297 y(state)c(of)h(the)g(k)n(ey)f (sc)n(hedule.)45 b(The)31 b(resulting)f(ciphertext)2010 5397 y(replaces)18 b(subk)n(eys)h Fo(P)2669 5409 y Fl(1)2726 5397 y Fq(and)h Fo(P)2933 5409 y Fl(2)2970 5397 y Fq(.)35 b(That)19 b(same)h(ciphertext)f(is)2010 5497 y(also)k(X)n(ORed)i(with)g (the)g(second)e(64-bits)h(of)g(salt,)h(and)g(the)2010 5596 y(result)19 b(encrypted)g(with)h(the)g(new)f(state)g(of)g(the)h(k) n(ey)f(sc)n(hed-)2010 5696 y(ule.)52 b(The)33 b(output)g(of)g(the)g (second)f(encryption)g(replaces)p eop %%Page: 7 7 7 6 bop 0 383 a Fq(subk)n(eys)27 b Fo(P)361 395 y Fl(3)428 383 y Fq(and)h Fo(P)643 395 y Fl(4)680 383 y Fq(.)40 b(It)29 b(is)f(also)f(X)n(ORed)i(with)f(the)h(\014rst)0 483 y(64-bits)f(of)h(salt)g(and)f(encrypted)h(to)g(replace)f Fo(P)1517 495 y Fl(5)1584 483 y Fq(and)g Fo(P)1799 495 y Fl(6)1837 483 y Fq(.)0 582 y(The)c(pro)r(cess)f(con)n(tin)n(ues,)h (alternating)g(b)r(et)n(w)n(een)g(the)g(\014rst)0 682 y(and)30 b(second)f(64)g(bits)h(salt.)44 b(When)30 b Fp(Exp)l(andKey)38 b Fq(\014nishes)0 782 y(replacing)26 b(en)n(tries)h(in)h(the)g(P-Arra)n(y)-7 b(,)26 b(it)i(con)n(tin)n(ues)f (on)g(re-)0 881 y(placing)d(S-b)r(o)n(x)h(en)n(tries)f(t)n(w)n(o)h(at)g (a)f(time.)37 b(After)25 b(replacing)0 981 y(the)35 b(last)g(t)n(w)n(o) e(en)n(tries)i(of)f(the)h(last)g(S-b)r(o)n(x,)h Fo(S)1484 993 y Fl(4)1521 981 y Fq([254])d(and)0 1080 y Fo(S)51 1092 y Fl(4)88 1080 y Fq([255],)27 b Fp(Exp)l(andKey)35 b Fq(returns)27 b(the)h(new)g(k)n(ey)f(sc)n(hedule.)0 1280 y(In)k(computing)g Fp(Exp)l(andKey\(state,)k(0,)f(key\))p Fq(,)f(a)e(blo)r(c)n(k)f(of)0 1379 y(128)c(0)h(bits)g(is)g(used)g (instead)g(of)g(the)h(salt.)36 b(This)28 b(is)f(equiv-)0 1479 y(alen)n(t)32 b(to)g(a)g(single)g(iteration)g(of)g(the)h(standard) f(blo)n(w\014sh)0 1579 y(k)n(ey)27 b(sc)n(hedule.)37 b(The)28 b(call)f(to)g Fp(Exp)l(andKey\(state,)k(0,)g(salt\))0 1678 y Fq(simply)d(treats)f(the)h(salt)f(as)g(a)g(16-b)n(yte)f(k)n(ey) -7 b(.)0 1877 y(After)20 b(calling)f Fp(InitState)25 b Fq(to)20 b(\014ll)g(a)f(new)h(k)n(ey)f(sc)n(hedule)h(with)0 1977 y(the)35 b(digits)f(of)g Fo(\031)s Fq(,)j Fp(EksBlow\014shSetup)j Fq(calls)34 b Fp(Exp)l(andKey)0 2077 y Fq(with)k(the)f(salt)g(and)g(k)n (ey)-7 b(.)65 b(This)37 b(ensures)f(that)h(all)g(sub-)0 2176 y(sequen)n(t)h(state)h(dep)r(ends)g(on)g(b)r(oth,)j(and)c(that)h (no)g(part)0 2276 y(of)28 b(the)g(algorithm)f(can)h(b)r(e)g (precomputed)g(without)h(b)r(oth)0 2376 y(salt)h(and)h(k)n(ey)-7 b(.)46 b(Thereafter,)31 b Fp(Exp)l(andKey)g Fq(is)g(alternately)0 2475 y(called)22 b(with)g(the)g(salt)g(and)g(then)g(k)n(ey)g(for)f(2) 1349 2445 y Fe(c)m(ost)1495 2475 y Fq(iterations.)0 2575 y(F)-7 b(or)34 b(all)h(but)g(the)h(\014rst)e(in)n(v)n(o)r(cation)g(of)h Fp(Exp)l(andKey)p Fq(,)j(the)0 2674 y(second)24 b(argumen)n(t)f(is)h(a) g(blo)r(c)n(k)g(of)g(128)f(0)h(bits.)36 b(This)24 b(more)0 2774 y(closely)g(resem)n(bles)f(the)i(original)e(blo)n(w\014sh)h(k)n (ey)g(sc)n(hedule,)0 2874 y(and)18 b(also)g(allo)n(ws)f Fp(EksBlow\014shSetup)25 b Fq(to)19 b(b)r(e)f(implemen)n(ted)0 2973 y(more)25 b(e\016cien)n(tly)h(on)f(CPU)h(arc)n(hitectures)e(with)i (few)g(reg-)0 3073 y(isters.)0 3272 y(W)-7 b(e)29 b(hop)r(e)h(that)f (the)g(unpredictable)g(and)g(c)n(hanging)f(con-)0 3372 y(ten)n(t)f(of)h(the)f(P-arra)n(y)d(and)j(S-Bo)n(xes)e(will)j(reduce)e (the)i(ap-)0 3471 y(plicabilit)n(y)c(of)h(y)n(et)f(unkno)n(wn)g (optimizations.)36 b(Addition-)0 3571 y(ally)g(the)i Fp(eksblow\014sh)44 b Fq(S-Bo)n(xes)35 b(require)h(4)h(KB)f(of)h(con-)0 3671 y(stan)n(tly)d(accessed)g(and)h(mo)r(di\014ed)g(memory)-7 b(.)57 b(Th)n(us,)37 b(the)0 3770 y(S-Bo)n(xes)j(cannot)h(b)r(e)h (shared)f(across)f(k)n(ey)h(sc)n(hedules|)0 3870 y(separate)26 b(S-Bo)n(xes)h(m)n(ust)g(exist)h(for)f(ev)n(ery)g(sim)n(ultaneous)0 3970 y(execution.)51 b(This)32 b(v)-5 b(astly)32 b(limits)h(the)f (usefulness)h(of)f(an)n(y)0 4069 y(attempts)40 b(to)g(pip)r(eline)h (the)f(F)-7 b(eistel)40 b(net)n(w)n(ork)f(in)h(hard-)0 4169 y(w)n(are.)0 4469 y Fr(5)112 b(Bcrypt)37 b(Algorithm)0 4704 y Fq(The)46 b(problems)g(presen)n(t)f(in)i(traditional)e(UNIX)i (pass-)0 4803 y(w)n(ord)19 b(hashes)h(led)h(naturally)e(to)i(a)f(new)g (passw)n(ord)f(sc)n(heme)0 4903 y(whic)n(h)34 b(w)n(e)g(call)g Fp(b)l(crypt)p Fq(,)j(referring)c(to)h(the)h(Blo)n(w\014sh)e(en-)0 5003 y(cryption)d(algorithm.)43 b(Bcrypt)30 b(uses)g(a)f(128-bit)g (salt)h(and)0 5102 y(encrypts)f(a)h(192-bit)f(magic)g(v)-5 b(alue.)43 b(It)31 b(tak)n(es)e(adv)-5 b(an)n(tage)0 5202 y(of)28 b(the)g(exp)r(ensiv)n(e)f(k)n(ey)f(setup)i(in)g Fp(eksblow\014sh)p Fq(.)0 5401 y(The)j Fp(b)l(crypt)40 b Fq(algorithm)29 b(runs)i(in)g(t)n(w)n(o)g(phases,)g(sk)n(etc)n(hed)0 5501 y(in)39 b(Figure)e(3.)69 b(In)38 b(the)h(\014rst)f(phase,)j Fp(EksBlow\014shSetup)0 5600 y Fq(is)31 b(called)g(with)g(the)h(cost,)f (the)h(salt,)g(and)f(the)g(passw)n(ord,)0 5700 y(to)41 b(initialize)f Fp(eksblow\014sh)6 b Fq('s)43 b(state.)76 b(Most)40 b(of)h(b)r(crypt's)2128 453 y(b)r(crypt)27 b(\()p Fp(c)l(ost)p Fq(,)h Fp(salt)p Fq(,)g Fp(pwd)9 b Fq(\))2211 552 y Fp(state)33 b Fk( )28 b Fq(EksBlo)n(w\014shSetup)e (\()p Fp(c)l(ost)p Fq(,)i Fp(salt)p Fq(,)g Fp(key)7 b Fq(\))2211 652 y Fp(ctext)34 b Fk( )28 b Fq (\\OrpheanBeholderScryDoubt")2211 752 y Ff(rep)s(eat)f Fq(\(64\))2294 851 y Fp(ctext)34 b Fk( )28 b Fq(EncryptECB)e(\()p Fp(state)p Fq(,)i Fp(ctext)8 b Fq(\))2211 951 y Ff(return)28 b Fq(Concatenate)f(\()p Fp(c)l(ost)p Fq(,)g Fp(salt)p Fq(,)h Fp(ctext)8 b Fq(\))2010 1346 y(Figure)31 b(3:)44 b(The)32 b(b)r(crypt)f(algorithm)g(for)f(hashing)h(UNIX)2010 1446 y(passw)n(ords,)25 b(based)i(on)h(eksblo)n(w\014sh.)2010 1711 y(time)d(is)f(sp)r(en)n(t)h(in)g(the)g(exp)r(ensiv)n(e)f(k)n(ey)g (sc)n(hedule.)35 b(F)-7 b(ollo)n(w-)2010 1811 y(ing)30 b(that,)i(the)f(192-bit)e(v)-5 b(alue)31 b(\\OrpheanBeholderScry-)2010 1910 y(Doubt")k(is)f(encrypted)h(64)e(times)i(using)f Fp(eksblow\014sh)43 b Fq(in)2010 2010 y(ECB)27 b(mo)r(de)h(with)g(the)h (state)e(from)h(the)g(previous)f(phase.)2010 2109 y(The)21 b(output)g(is)f(the)h(cost)g(and)f(128-bit)g(salt)g(concatenated)2010 2209 y(with)28 b(the)g(result)f(of)h(the)g(encryption)f(lo)r(op.)2010 2408 y(In)49 b(Section)f(3,)54 b(w)n(e)48 b(deriv)n(ed)g(that)h(an)f Fo(\017)p Fq(-secure)f(pass-)2010 2508 y(w)n(ord)38 b(function)h (should)f(ful\014ll)i(sev)n(eral)d(imp)r(ortan)n(t)h(cri-)2010 2608 y(teria:)d(second)24 b(preimage-resistance,)e(a)i(salt)h(space)e (large)2010 2707 y(enough)38 b(to)g(defeat)h(precomputation)e(attac)n (ks,)j(and)e(an)2010 2807 y(adaptable)25 b(cost.)36 b(W)-7 b(e)27 b(b)r(eliev)n(e)f(that)g Fp(Bcrypt)35 b Fq(ac)n(hiev)n(es)24 b(all)2010 2906 y(three)36 b(prop)r(erties,)i(and)e(that)g(it)h(can)f (b)r(e)h Fo(\017)p Fq(-secure)e(with)2010 3006 y(useful)23 b(v)-5 b(alues)21 b(of)i Fo(\017)f Fq(for)f(y)n(ears)g(to)h(come.)34 b(Though)22 b(w)n(e)g(can-)2010 3106 y(not)32 b(formally)e(pro)n(v)n(e) g Fp(b)l(crypt)40 b Fo(\017)p Fq(-secure,)32 b(an)n(y)f(\015a)n(w)g(w)n (ould)2010 3205 y(lik)n(ely)f(deal)h(a)g(serious)e(blo)n(w)i(to)g(the)g (w)n(ell-studied)g(blo)n(w-)2010 3305 y(\014sh)d(encryption)f (algorithm.)2010 3521 y Fd(5.1)105 b(Implemen)m(tation)2010 3737 y Fq(W)-7 b(e)20 b(ha)n(v)n(e)f(implemen)n(ted)i Fp(b)l(crypt)28 b Fq(and)20 b(deplo)n(y)n(ed)f(it)h(as)g(part)2010 3836 y(of)h(the)g(Op)r(enBSD)g(op)r(erating)f(system.)35 b Fp(Bcrypt)29 b Fq(has)21 b(b)r(een)2010 3936 y(the)28 b(default)g(passw)n(ord)e(sc)n(heme)h(since)g(Op)r(enBSD)h(2.1.)2010 4135 y(An)e(imp)r(ortan)n(t)f(requiremen)n(t)g(of)g(an)n(y)g Fp(b)l(crypt)34 b Fq(implemen-)2010 4235 y(tation)f(is)g(that)h(it)f (exploit)g(the)h(full)g(128-bit)e(salt)h(space.)2010 4334 y(Op)r(enBSD)26 b(generates)e(the)h(128-bit)g Fp(b)l(crypt)33 b Fq(salt)25 b(from)g(an)2010 4434 y(arcfour)40 b(\()p Fp(ar)l(c4r)l(andom\(3\))s Fq(\))k(k)n(ey)d(stream,)j(seeded)e(with) 2010 4534 y(random)19 b(data)h(the)h(k)n(ernel)e(collects)h(from)g (device)g(timings.)2010 4733 y(Op)r(enBSD)55 b(lets)f(administrators)f (select)h(a)g(passw)n(ord)2010 4833 y(hashing)24 b(sc)n(heme)h(through) g(a)f(sp)r(ecial)h(con\014guration)f(\014le,)2010 4932 y Fp(p)l(asswd.c)l(onf\(5\))p Fq(.)39 b Fp(p)l(asswd.c)l(onf)44 b Fq(allo)n(ws)24 b(detailed)h(con)n(trol)2010 5032 y(o)n(v)n(er)h (whic)n(h)h(t)n(yp)r(e)h(of)f(passw)n(ord)f(to)h(use)g(for)g(a)g(giv)n (en)g(user)2010 5131 y(or)20 b(group.)33 b(It)21 b(also)f(p)r(ermits)g (di\013eren)n(t)h(passw)n(ord)e(sc)n(hemes)2010 5231 y(for)h(lo)r(cal)h(and)f(YP)h(passw)n(ords.)32 b(F)-7 b(or)20 b Fp(b)l(crypt)p Fq(,)j(one)e(can)f(also)2010 5331 y(sp)r(ecify)34 b(the)g(cost.)54 b(This)33 b(lets)h(p)r(eople)f (adjust)h(passw)n(ord)2010 5430 y(v)n(eri\014cation)27 b(time)j(for)e(increasing)f(pro)r(cessor)g(sp)r(eed.)41 b(A)n(t)2010 5530 y(the)34 b(time)g(of)g(publication,)h(the)f(default)g (cost)g(is)f(6)g(for)g(a)2010 5630 y(normal)40 b(user)f(and)i(8)f(for)g (the)h(sup)r(eruser.)75 b(Of)40 b(course,)p eop %%Page: 8 8 8 7 bop 0 383 a Fq(whatev)n(er)30 b(cost)g(p)r(eople)h(c)n(ho)r(ose)f (should)h(b)r(e)g(reev)-5 b(aluated)0 483 y(from)27 b(time)h(to)g (time.)0 682 y(T)-7 b(o)36 b(di\013eren)n(tiate)f(b)r(et)n(w)n(een)h (passw)n(ords)e(hashed)h(b)n(y)h(dif-)0 782 y(feren)n(t)46 b(algorithms,)k(ev)n(ery)45 b(passw)n(ord)f(function)j(other)0 881 y(than)38 b(the)g(original)f Fp(crypt)46 b Fq(pre\014xes)37 b(its)i(output)f(with)g(a)0 981 y(v)n(ersion)c(iden)n(ti\014er.)60 b(Th)n(us)35 b(a)g(single)g(passw)n(ord)e(\014le)i(can)0 1080 y(con)n(tain)49 b(sev)n(eral)f(t)n(yp)r(es)i(of)f(passw)n(ord.)102 b(In)50 b(the)g(cur-)0 1180 y(ren)n(t)42 b(Op)r(enBSD)h(implemen)n (tation,)j Fp(b)l(crypt)k Fq(passw)n(ords)0 1280 y(start)23 b(with)i(\\$2a$",)d(while)i(MD5)g Fp(crypt)32 b Fq(passw)n(ords)22 b(with)0 1379 y(\\$1$.")34 b(Because)23 b(the)j(result)e(of)h (traditional)f Fp(crypt)33 b Fq(nev)n(er)0 1479 y(b)r(egins)27 b(with)i(a)e(\\$",)f(there)h(is)h(nev)n(er)f(an)n(y)f(am)n(biguit)n(y) -7 b(.)0 1785 y Fr(6)112 b(Bcrypt)37 b(Ev)-6 b(aluation)0 2024 y Fq(Because)56 b Fp(b)l(crypt)65 b Fq(has)56 b(adjustable)g (cost,)63 b(w)n(e)57 b(cannot)0 2124 y(meaningfully)29 b(ev)-5 b(aluate)29 b(the)h(p)r(erformance)e(of)h(the)h(algo-)0 2223 y(rithm)35 b(on)g(its)g(o)n(wn.)58 b(Instead,)37 b(w)n(e)d(will)i(place)e(it)h(in)h(the)0 2323 y(con)n(text)25 b(of)h(t)n(w)n(o)f(p)r(opular)h(passw)n(ord)e(hashing)h(functions.)0 2423 y(W)-7 b(e)22 b(describ)r(e)e(v)-5 b(arious)20 b(attac)n(ks)g(and) h(optimizations)g(these)0 2522 y(functions)31 b(ha)n(v)n(e)e (undergone,)h(and)g(discuss)g(the)h(applica-)0 2622 y(bilit)n(y)d(of)f (the)h(same)f(tec)n(hniques)h(to)f Fp(b)l(crypt)p Fq(.)0 2833 y Fd(6.1)105 b(Comparison)0 3044 y Fq(In)41 b(the)g(follo)n(wing,) i(w)n(e)d(giv)n(e)g(a)g(brief)h(o)n(v)n(erview)d(of)j(t)n(w)n(o)0 3143 y(passw)n(ord)17 b(hashing)h(functions)h(in)g(widespread)f(use)h (to)r(da)n(y)-7 b(,)0 3243 y(and)27 b(state)h(their)f(main)h (di\013erences)f(from)g Fp(b)l(crypt)p Fq(.)0 3554 y Ff(6.1.1)94 b(T)-8 b(raditional)32 b(crypt)0 3807 y Fq(T)-7 b(raditional)21 b Fp(crypt\(3\))p Fq('s)i(design)e(rationale)g(dates)g (bac)n(k)g(to)0 3907 y(1976)e([9)o(].)35 b(It)21 b(uses)g(a)f(passw)n (ord)f(of)h(up)h(to)g(eigh)n(t)f(c)n(haracters)0 4006 y(as)h(a)g(k)n(ey)h(for)f(DES)h([10)o(].)35 b(The)22 b(56-bit)f(DES)h(k)n(ey)f(is)g(formed)0 4106 y(b)n(y)26 b(com)n(bining)f(the)i(lo)n(w-order)d(7)h(bits)i(of)f(eac)n(h)f(c)n (haracter)0 4206 y(in)32 b(the)g(passw)n(ord.)47 b(If)32 b(the)g(passw)n(ord)d(is)j(shorter)e(than)h(8)0 4305 y(c)n(haracters,)25 b(it)j(is)g(padded)f(with)i(zero)d(bits)i(on)f(the) h(righ)n(t.)0 4504 y(A)e(12-bit)g(salt)f(is)h(used)g(to)g(p)r(erturb)g (the)g(DES)g(algorithm,)0 4604 y(so)38 b(that)h(the)g(same)f(passw)n (ord)f(plain)n(text)h(can)g(pro)r(duce)0 4704 y(4,096)e(p)r(ossible)h (passw)n(ord)f(encryptions.)66 b(A)38 b(mo)r(di\014ca-)0 4803 y(tion)19 b(to)h(the)f(DES)h(algorithm,)g(sw)n(apping)e(bits)i Fo(i)f Fq(and)g Fo(i)r Fq(+)r(24)0 4903 y(in)35 b(the)f(DES)h(E-Bo)n(x) d(output)j(when)f(bit)h Fo(i)f Fq(is)g(set)g(in)h(the)0 5003 y(salt,)20 b(ac)n(hiev)n(es)e(this)h(while)g(also)f(making)h(DES)g (encryption)0 5102 y(hardw)n(are)26 b(useless)g(for)h(passw)n(ord)f (guessing.)0 5301 y(The)i(64-bit)e(constan)n(t)h(\\0")f(is)i(encrypted) f(25)g(times)h(with)0 5401 y(the)39 b(DES)g(k)n(ey)-7 b(.)71 b(The)39 b(\014nal)g(output)g(is)g(the)g(12-bit)f(salt)0 5501 y(concatenated)28 b(with)h(the)h(encrypted)e(64-bit)g(v)-5 b(alue.)41 b(The)0 5600 y(resulting)c(76-bit)g(v)-5 b(alue)37 b(is)g(reco)r(ded)g(in)n(to)g(13)g(prin)n(table)0 5700 y(ASCI)r(I)28 b(c)n(haracters.)2010 383 y(A)n(t)h(the)g(time)g (traditional)e Fp(crypt)37 b Fq(w)n(as)27 b(conceiv)n(ed,)h(it)h(w)n (as)2010 483 y(fast)42 b(enough)f(for)h(authen)n(tication)g(but)g(to)r (o)g(costly)g(for)2010 582 y(passw)n(ord)34 b(guessing)i(to)g(b)r(e)h (practical.)62 b(T)-7 b(o)r(da)n(y)g(,)38 b(w)n(e)e(are)2010 682 y(a)n(w)n(are)26 b(that)i(it)g(exhibits)g(three)f(serious)g (limitations:)37 b(the)2010 782 y(restricted)25 b(passw)n(ord)g(space,) g(the)i(small)f(salt)f(space,)h(and)2010 881 y(the)k(constan)n(t)e (execution)h(cost.)41 b(In)29 b(con)n(trast,)f Fp(b)l(crypt)38 b Fq(al-)2010 981 y(lo)n(ws)h(for)g(longer)f(passw)n(ords,)i(has)g (salts)f(large)f(enough)2010 1080 y(to)29 b(b)r(e)g(unique)g(o)n(v)n (er)e(all)i(time,)g(and)g(has)f(adaptable)g(cost.)2010 1180 y(These)f(limitiations)h(therefore)e(do)h(not)h(apply)f(to)g Fp(b)l(crypt)p Fq(.)2010 1495 y Ff(6.1.2)94 b(MD5)31 b(crypt)2010 1748 y Fq(MD5)c Fp(crypt)36 b Fq(w)n(as)26 b(written)h(b)n(y)f(P)n(oul-Henning)g(Kamp)h(for)2010 1848 y(F)-7 b(reeBSD.)53 b(The)33 b(main)g(reason)f(for)g(using)h(MD5)g (w)n(as)f(to)2010 1948 y(a)n(v)n(oid)f(problems)g(with)h(American)g (exp)r(ort)g(prohibitions)2010 2047 y(on)21 b(cryptographic)f(pro)r (ducts,)j(and)e(to)h(allo)n(w)e(for)h(a)g(longer)2010 2147 y(passw)n(ord)i(length)h(than)h(the)g(8)f(c)n(haracters)e(used)j (b)n(y)f(DES)2010 2246 y Fp(crypt)p Fq(.)74 b(The)40 b(passw)n(ord)e(length)i(is)g(restricted)f(only)g(b)n(y)2010 2346 y(MD5's)28 b(maxim)n(um)g(message)e(size)i(of)f(2)3276 2316 y Fl(64)3374 2346 y Fq(bits.)38 b(The)28 b(salt)2010 2446 y(can)f(v)-5 b(ary)27 b(from)g(12)g(to)g(48)g(bits.)2010 2645 y(MD5)g Fp(crypt)36 b Fq(hashes)26 b(the)h(passw)n(ord)f(and)g (salt)h(in)h(a)e(n)n(um-)2010 2745 y(b)r(er)e(of)g(di\013eren)n(t)g (com)n(binations)f(to)h(slo)n(w)g(do)n(wn)f(the)i(ev)-5 b(al-)2010 2844 y(uation)29 b(sp)r(eed.)43 b(Some)30 b(steps)f(in)h(the)g(algorithm)f(mak)n(e)g(it)2010 2944 y(doubtful)c(that)f(the)g(sc)n(heme)f(w)n(as)g(designed)g(from)h(a)f (cryp-)2010 3043 y(tographic)40 b(p)r(oin)n(t)h(of)f(view|for)h (instance,)j(the)d(binary)2010 3143 y(represen)n(tation)21 b(of)i(the)h(passw)n(ord)d(length)i(at)g(some)g(p)r(oin)n(t)2010 3243 y(determines)28 b(whic)n(h)g(data)g(is)g(hashed,)h(for)e(ev)n(ery) g(zero)h(bit)2010 3342 y(the)j(\014rst)f(b)n(yte)g(of)g(the)g(passw)n (ord)f(and)h(for)f(ev)n(ery)g(set)i(bit)2010 3442 y(the)d(\014rst)f(b)n (yte)h(of)f(a)h(previous)e(hash)h(computation.)2010 3641 y(The)c(output)g(is)g(the)g(concatenation)e(of)i(the)g(v)n(ersion)e (iden-)2010 3741 y(ti\014er)29 b(\\$1$",)e(the)i(salt,)g(a)g(\\$")f (separator,)f(and)h(the)i(128-)2010 3840 y(bit)e(hash)f(output.)2010 4040 y(MD5)46 b Fp(crypt)55 b Fq(places)46 b(virtually)f(no)h(limit)h (on)f(the)g(size)2010 4139 y(of)56 b(passw)n(ords,)62 b(while)57 b Fp(b)l(crypt)65 b Fq(has)56 b(a)g(maxim)n(um)g(of)2010 4239 y(55)38 b(b)n(ytes.)70 b(W)-7 b(e)39 b(do)g(not)f(consider)g(this) h(a)g(serious)e(lim-)2010 4339 y(itation)d(of)g Fp(b)l(crypt)p Fq(,)i(ho)n(w)n(ev)n(er.)54 b(Not)34 b(only)g(are)f(users)g(un-)2010 4438 y(lik)n(ely)20 b(to)h(c)n(ho)r(ose)f(suc)n(h)g(long)h(passw)n (ords,)f(but)h(if)h(they)f(did,)2010 4538 y(MD5)29 b Fp(crypt)8 b Fq('s)30 b(128-bit)e(output)h(size)g(w)n(ould)g(b)r(ecome) g(the)2010 4637 y(limiting)36 b(factor)g(in)g(securit)n(y)-7 b(.)61 b(A)37 b(brute)f(force)f(attac)n(k)n(er)2010 4737 y(could)c(more)g(easily)g(\014nd)h(short)f(strings)g(hashing)g(to)h (the)2010 4837 y(same)d(v)-5 b(alue)29 b(as)g(a)g(user's)f(passw)n(ord) f(than)j(guess)e(the)i(ac-)2010 4936 y(tual)h(passw)n(ord.)43 b(Finally)-7 b(,)31 b(lik)n(e)f(DES)h Fp(crypt)p Fq(,)h(MD5)e Fp(crypt)2010 5036 y Fq(has)d(\014xed)h(cost.)2010 5252 y Fd(6.2)105 b(A)m(ttac)m(ks)35 b(and)g(V)-9 b(ulnerabilities)2010 5468 y Fq(Once)38 b(an)h(attac)n(k)n(er)e(has)h(obtained)g(a)g(list)h (of)g(passw)n(ord)2010 5567 y(hashes,)24 b(passw)n(ords)f(can)h(b)r(e)h (guessed)e(b)n(y)i(comparing)e(the)2010 5667 y(target)e(list)h(to)g(a)g (list)g(of)g(hashes)f(of)h(candidate)f(passw)n(ords.)p eop %%Page: 9 9 9 8 bop 146 303 3579 4 v 144 403 4 100 v 290 403 V 307 403 V 539 373 a Fq(10)p 852 403 V 462 w(26)p 1398 403 V 482 w(36)p 1985 403 V 483 w(52)p 2530 403 V 482 w(62)p 3117 403 V 512 w(95)p 3723 403 V 144 503 V 195 473 a(n)p 290 503 V 307 503 V 241 w(digits)p 852 503 V 277 w(lo)n(w)n(ercase)p 1398 503 V 226 w(lo)n(w)n(ercase)p 1985 503 V 198 w(mixed)27 b(case)p 2530 503 V 171 w(mixed)h(case)p 3117 503 V 231 w(k)n(eyb)r(oard)p 3723 503 V 144 602 V 290 602 V 307 602 V 852 602 V 1398 602 V 1450 572 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781 l 1982 780 l 1984 779 l 1986 779 l 1987 778 l 1989 777 l 1991 776 l 1993 775 l 1994 775 l 1996 774 l 1998 773 l 2000 772 l 2001 771 l 2003 771 l 2005 770 l 2006 769 l 2008 768 l 2010 767 l 2012 767 l 2013 766 l 2015 765 l 2017 764 l 2019 764 l 2020 763 l 2022 762 l 2024 761 l 2025 761 l 2027 760 l 2029 759 l 2031 758 l 2032 757 l 2034 757 l 2036 756 l 2038 755 l 2039 754 l 2041 754 l 2043 753 l 2044 752 l 2046 752 l 2048 751 l 2050 750 l 2051 749 l 2053 749 l 2055 748 l 2057 747 l 2058 746 l 2060 746 l 2062 745 l 2063 744 l 2065 743 l 2067 743 l 2069 742 l 2070 741 l 2072 741 l 2074 740 l 2076 739 l 2077 738 l 2079 738 l 2081 737 l 2082 736 l 2084 736 l 2086 735 l 2088 734 l 2089 734 l 2091 733 l 2093 732 l 2095 731 l 2096 731 l 2098 730 l 2100 729 l 2101 729 l 2103 728 l 2105 727 l 2107 727 l 2108 726 l 2110 725 l 2112 725 l 2114 724 l 2115 723 l 2117 723 l 2119 722 l 2120 721 l 2122 721 l 2124 720 l 2126 719 l 2127 719 l 2129 718 l 2131 717 l 2133 717 l 2134 716 l 2136 715 l 2138 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619 l 2454 619 l 2456 618 l 2457 618 l 2459 617 l 2461 617 l 2463 617 l 2464 616 l 2466 616 l 2468 615 l 2469 615 l 2471 614 l 2473 614 l 2475 614 l 2476 613 l 2478 613 l 2480 612 l 2482 612 l 2483 612 l 2485 611 l 2487 611 l 2488 610 l 2490 610 l 2492 610 l 2494 609 l 2495 609 l 2497 608 l 2499 608 l 2501 608 l 2502 607 l 2504 607 l 2506 607 l 2507 606 l 2509 606 l 2511 605 l 2513 605 l 2514 605 l 2516 604 l 2518 604 l 2520 603 l 2521 603 l 2523 603 l 2525 602 l 2526 602 l 2528 602 l 2530 601 l 2532 601 l 2533 600 l 2535 600 l 2537 600 l 2539 599 l 2540 599 l 2542 599 l 2544 598 l 2545 598 l 2547 598 l 2549 597 l 2551 597 l 2552 596 l 2554 596 l 2556 596 l 2558 595 l 2559 595 l 2561 595 l 2563 594 l 2564 594 l 2566 594 l 2568 593 l 2570 593 l 2571 592 l 2573 592 l 2575 592 l 2577 591 l 2578 591 l 2580 591 l 2582 590 l 2583 590 l 2585 590 l 2587 589 l 2589 589 l 2590 589 l 2592 588 l gs col-1 s gr % Polyline n 2592 588 m 2594 588 l 2596 588 l 2597 587 l 2599 587 l 2601 587 l 2602 586 l 2604 586 l 2606 586 l 2608 585 l 2609 585 l 2611 585 l 2613 584 l 2615 584 l 2616 584 l 2618 583 l 2620 583 l 2621 583 l 2623 582 l 2625 582 l 2627 582 l 2628 581 l 2630 581 l 2632 581 l 2634 580 l 2635 580 l 2637 580 l 2639 579 l 2640 579 l 2642 579 l 2644 578 l 2646 578 l 2647 578 l 2649 577 l 2651 577 l 2653 577 l 2654 576 l 2656 576 l 2658 576 l 2659 576 l 2661 575 l 2663 575 l 2665 575 l 2666 574 l 2668 574 l 2670 574 l 2672 573 l 2673 573 l 2675 573 l 2677 572 l 2678 572 l 2680 572 l 2682 572 l 2684 571 l 2685 571 l 2687 571 l 2689 570 l 2691 570 l 2692 570 l 2694 569 l 2696 569 l 2697 569 l 2699 569 l 2701 568 l 2703 568 l 2704 568 l 2706 567 l 2708 567 l 2710 567 l 2711 567 l 2713 566 l 2715 566 l 2716 566 l 2718 565 l 2720 565 l 2722 565 l 2723 565 l 2725 564 l 2727 564 l 2729 564 l 2730 563 l 2732 563 l 2734 563 l 2735 563 l 2737 562 l 2739 562 l 2741 562 l 2742 561 l 2744 561 l 2746 561 l 2748 561 l 2749 560 l 2751 560 l 2753 560 l 2754 560 l 2756 559 l 2758 559 l 2760 559 l 2761 558 l 2763 558 l 2765 558 l 2767 558 l 2768 557 l 2770 557 l 2772 557 l 2773 557 l 2775 556 l 2777 556 l 2779 556 l 2780 556 l 2782 555 l 2784 555 l 2786 555 l 2787 554 l 2789 554 l 2791 554 l 2792 554 l 2794 553 l 2796 553 l 2798 553 l 2799 553 l 2801 552 l 2803 552 l 2805 552 l 2806 552 l 2808 551 l 2810 551 l 2811 551 l 2813 551 l 2815 550 l 2817 550 l 2818 550 l 2820 550 l 2822 549 l 2824 549 l 2825 549 l 2827 549 l 2829 548 l 2830 548 l 2832 548 l 2834 548 l 2836 547 l 2837 547 l 2839 547 l 2841 547 l 2843 546 l 2844 546 l 2846 546 l 2848 546 l 2849 546 l 2851 545 l 2853 545 l 2855 545 l 2856 545 l 2858 544 l 2860 544 l 2862 544 l 2863 544 l 2865 543 l 2867 543 l 2868 543 l 2870 543 l 2872 542 l 2874 542 l 2875 542 l 2877 542 l 2879 542 l 2881 541 l 2882 541 l 2884 541 l 2886 541 l 2887 540 l 2889 540 l 2891 540 l 2893 540 l 2894 540 l 2896 539 l 2898 539 l 2900 539 l 2901 539 l 2903 538 l 2905 538 l 2906 538 l 2908 538 l 2910 538 l 2912 537 l 2913 537 l 2915 537 l 2917 537 l 2919 536 l 2920 536 l 2922 536 l 2924 536 l 2925 536 l 2927 535 l 2929 535 l 2931 535 l 2932 535 l 2934 535 l 2936 534 l 2938 534 l 2939 534 l 2941 534 l 2943 533 l 2944 533 l 2946 533 l 2948 533 l 2950 533 l 2951 532 l 2953 532 l 2955 532 l 2957 532 l 2958 532 l 2960 531 l 2962 531 l 2963 531 l 2965 531 l 2967 531 l 2969 530 l 2970 530 l 2972 530 l 2974 530 l 2976 530 l 2977 529 l 2979 529 l 2981 529 l 2982 529 l 2984 529 l 2986 528 l 2988 528 l 2989 528 l 2991 528 l 2993 528 l 2995 527 l 2996 527 l 2998 527 l 3000 527 l 3001 527 l 3003 526 l 3005 526 l 3007 526 l 3008 526 l 3010 526 l 3012 526 l 3014 525 l 3015 525 l 3017 525 l 3019 525 l 3020 525 l 3022 524 l 3024 524 l 3026 524 l 3027 524 l 3029 524 l 3031 523 l 3033 523 l 3034 523 l 3036 523 l 3038 523 l 3039 523 l 3041 522 l 3043 522 l 3045 522 l 3046 522 l 3048 522 l 3050 521 l 3052 521 l 3053 521 l 3055 521 l 3057 521 l 3058 521 l 3060 520 l 3062 520 l 3064 520 l 3065 520 l 3067 520 l 3069 520 l 3071 519 l 3072 519 l 3074 519 l 3076 519 l 3077 519 l 3079 518 l 3081 518 l 3083 518 l 3084 518 l 3086 518 l 3088 518 l 3090 517 l 3091 517 l 3093 517 l 3095 517 l 3096 517 l 3098 517 l 3100 516 l 3102 516 l 3103 516 l 3105 516 l 3107 516 l 3109 516 l 3110 515 l 3112 515 l 3114 515 l 3115 515 l 3117 515 l 3119 515 l 3121 514 l 3122 514 l 3124 514 l 3126 514 l 3128 514 l 3129 514 l 3131 513 l 3133 513 l 3134 513 l 3136 513 l 3138 513 l 3140 513 l 3141 513 l 3143 512 l 3145 512 l 3147 512 l 3148 512 l 3150 512 l 3152 512 l 3153 511 l 3155 511 l 3157 511 l 3159 511 l 3160 511 l 3162 511 l 3164 511 l 3166 510 l 3167 510 l 3169 510 l 3171 510 l 3172 510 l 3174 510 l 3176 509 l 3178 509 l 3179 509 l 3181 509 l 3183 509 l 3185 509 l 3186 509 l 3188 508 l 3190 508 l 3191 508 l 3193 508 l 3195 508 l 3197 508 l 3198 508 l 3200 507 l 3202 507 l 3204 507 l 3205 507 l 3207 507 l 3209 507 l 3210 507 l 3212 506 l 3214 506 l 3216 506 l 3217 506 l 3219 506 l 3221 506 l 3223 506 l 3224 505 l 3226 505 l 3228 505 l 3229 505 l 3231 505 l 3233 505 l 3235 505 l 3236 504 l 3238 504 l 3240 504 l 3242 504 l 3243 504 l 3245 504 l 3247 504 l 3248 503 l 3250 503 l 3252 503 l 3254 503 l 3255 503 l 3257 503 l 3259 503 l 3261 503 l 3262 502 l 3264 502 l 3266 502 l 3267 502 l 3269 502 l 3271 502 l 3273 502 l 3274 501 l 3276 501 l 3278 501 l 3280 501 l 3281 501 l 3283 501 l 3285 501 l 3286 501 l 3288 500 l 3290 500 l 3292 500 l 3293 500 l 3295 500 l 3297 500 l 3299 500 l 3300 500 l 3302 499 l 3304 499 l 3305 499 l 3307 499 l 3309 499 l 3311 499 l 3312 499 l 3314 499 l 3316 498 l 3318 498 l 3319 498 l 3321 498 l 3323 498 l 3324 498 l 3326 498 l 3328 498 l 3330 497 l 3331 497 l 3333 497 l 3335 497 l 3337 497 l 3338 497 l 3340 497 l 3342 497 l 3343 497 l 3345 496 l 3347 496 l 3349 496 l 3350 496 l 3352 496 l 3354 496 l 3356 496 l 3357 496 l 3359 495 l 3361 495 l 3362 495 l 3364 495 l 3366 495 l 3368 495 l 3369 495 l 3371 495 l 3373 495 l 3375 494 l 3376 494 l 3378 494 l 3380 494 l 3381 494 l 3383 494 l 3385 494 l 3387 494 l 3388 494 l 3390 493 l 3392 493 l 3394 493 l 3395 493 l 3397 493 l 3399 493 l 3400 493 l 3402 493 l 3404 493 l 3406 492 l 3407 492 l 3409 492 l 3411 492 l 3413 492 l 3414 492 l 3416 492 l 3418 492 l 3419 492 l 3421 491 l 3423 491 l 3425 491 l 3426 491 l 3428 491 l 3430 491 l 3432 491 l 3433 491 l 3435 491 l 3437 491 l 3438 490 l 3440 490 l 3442 490 l 3444 490 l 3445 490 l 3447 490 l 3449 490 l 3451 490 l 3452 490 l 3454 489 l 3456 489 l 3457 489 l gs col-1 s gr % Polyline [15 45] 45 sd n 868 2053 m 868 2053 l 894 1994 l 920 1934 l 947 1875 l 973 1816 l 999 1756 l 1025 1697 l 1051 1637 l 1077 1578 l 1104 1519 l 1130 1459 l 1156 1400 l 1182 1341 l 1208 1281 l 1234 1222 l 1261 1162 l 1287 1103 l 1313 1044 l 1339 984 l 1365 925 l 1391 866 l 1418 806 l 1444 747 l 1470 687 l 1496 628 l 1522 569 l 1548 509 l 1575 450 l 1576 448 l gs col-1 s gr [] 0 sd /Times-Roman ff 105.00 scf sf 1498 665 m gs 1 -1 sc (> 2^41) dup sw pop neg 0 rm col-1 sh gr /Times-Roman ff 150.00 scf sf 794 1723 m gs 1 -1 sc (1000) dup sw pop neg 0 rm col-1 sh gr /Times-Roman ff 150.00 scf sf 794 1331 m gs 1 -1 sc (2000) dup sw pop neg 0 rm col-1 sh gr /Times-Roman ff 150.00 scf sf 794 939 m gs 1 -1 sc (3000) dup sw pop neg 0 rm col-1 sh gr /Times-Roman ff 150.00 scf sf 794 548 m gs 1 -1 sc (4000) dup sw pop neg 0 rm col-1 sh gr /Times-Roman ff 150.00 scf sf 868 2239 m gs 1 -1 sc (0) dup sw pop 2 div neg 0 rm col-1 sh gr /Times-Roman ff 150.00 scf sf 1559 2239 m gs 1 -1 sc (4000) dup sw pop 2 div neg 0 rm col-1 sh gr /Times-Roman ff 150.00 scf sf 2250 2239 m gs 1 -1 sc (8000) dup sw pop 2 div neg 0 rm col-1 sh gr /Times-Roman ff 150.00 scf sf 2941 2239 m gs 1 -1 sc (12000) dup sw pop 2 div neg 0 rm col-1 sh gr /Times-Roman ff 150.00 scf sf 300 1313 m gs 1 -1 sc 90.0 rot (Number of different salts) dup sw pop 2 div neg 0 rm col-1 sh gr /Times-Roman ff 150.00 scf sf 2163 2363 m gs 1 -1 sc (Number of password file entries) dup sw pop 2 div neg 0 rm col-1 sh gr /Times-Roman ff 105.00 scf sf 2941 665 m gs 1 -1 sc (2^12) col-1 sh gr /Times-Roman ff 150.00 scf sf 794 2115 m gs 1 -1 sc (0) dup sw pop neg 0 rm col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 0 1516 a Fq(Figure)41 b(4:)64 b(Distribution)41 b(of)h(exp)r(ected)f(di\013eren)n(t)h(salts)0 1616 y(dep)r(ending)31 b(on)g(the)g(salt)f(space)g(against)g(the)h(n)n(um)n(b)r(er)f(of)0 1715 y(en)n(tries)d(in)h(a)f(passw)n(ord)f(\014le.)0 1981 y Fp(crypt)p Fq(,)39 b(the)d(result)g(of)f(hashing)h(ev)n(ery)e (dictionary)h(w)n(ord)0 2080 y(under)23 b(ev)n(ery)f(p)r(ossible)h (12-bit)f(salt)h(w)n(ould)f(\014t)i(on)f(a)g(single)0 2180 y(9)k(GB)h(hard)f(disk.)0 2379 y(One)22 b(can)f(do)h(b)r(etter,)h (ho)n(w)n(ev)n(er,)e(b)n(y)h(storing)e(less)i(than)g(the)0 2479 y(full)k(output)g(of)f Fp(crypt)33 b Fq(in)26 b(a)f(database.)34 b(The)26 b(QCrac)n(k)d([12)o(])0 2578 y(passw)n(ord)36 b(crac)n(king)h(program)g(tak)n(es)g(exactly)h(this)h(ap-)0 2678 y(proac)n(h.)32 b(QCrac)n(k)17 b(precomputes)i(a)f(database)g(of)h (common)0 2778 y(passw)n(ords)38 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setgray ef gr gs col0 s gr /Times-Roman-iso ff 150.00 scf sf 6375 2025 m gs 1 -1 sc (850) dup sw pop 2 div neg 0 rm col0 sh gr /Times-Roman-iso ff 150.00 scf sf 6675 3075 m gs 1 -1 sc (62.5) dup sw pop 2 div neg 0 rm col0 sh gr /Times-Roman-iso ff 150.00 scf sf 3300 3075 m gs 1 -1 sc (69) dup sw pop 2 div neg 0 rm col0 sh gr /Times-Roman-iso ff 180.00 scf sf 1725 4725 m gs 1 -1 sc (VAX-11/780*) col0 sh gr /Times-Roman-iso ff 180.00 scf sf 1725 4950 m gs 1 -1 sc (1977) col0 sh gr /Times-Roman-iso ff 150.00 scf sf 5025 3375 m gs 1 -1 sc (22.5) dup sw pop 2 div neg 0 rm col0 sh gr $F2psEnd rs %%EndDocument @endspecial 624 2202 a Fq(Figure)27 b(5:)36 b(Impact)28 b(of)g(Algorithm)f(Optimization)g(and)h(Adv)-5 b(ance)27 b(in)h(Pro)r(cessors)0 2467 y(able)39 b(n)n(um)n(b)r(er)f(of)h(rounds.) 70 b(With)40 b(increasing)e(pro)r(cess-)0 2567 y(ing)24 b(p)r(o)n(w)n(er,)f(these)h(functions)h(b)r(ecome)f(steadily)f(easier)g (to)0 2667 y(compute.)75 b(In)40 b(con)n(trast,)i Fp(b)l(crypt)49 b 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