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%%Creator: dvips 5.519 Copyright 1986, 1993 Radical Eye Software
%%Title: jour.dvi
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403 y Fn(\))e Fh(\025)h Fi(n)728 410 y Ff(1)746 415 y
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466 y Fd(k)238 459 y Fn(b)q(e)g(a)g(collection)h(of)e(functions)i(suc)o
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Fd(k)1305 459 y Fn(,)g Fi(h)g Fn(:)37 b Fh(f)p Fn(0)p
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(olynomial)f(time)f(algorithm)f(\()p Fi(A)g Fn(is)h(a)f
Fm(c)n(ol)r(lision)75 572 y(adversary)p Fn(\))e(that)f(on)g(input)i
Fi(k)f Fn(outputs)g Fi(x)d Fh(2)28 b(f)p Fn(0)p Fi(;)8
b Fn(1)p Fh(g)994 554 y Fd(n)1015 559 y Fc(1)1030 567
y Fe(k)1066 572 y Fn(whic)o(h)16 b(w)o(e)e(call)i(an)e
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Fi(h)g Fh(2)g Fi(H)397 636 y Fd(k)432 629 y Fn(attempts)g(to)g(\014nd)i
Fi(y)f Fh(2)27 b(f)p Fn(0)p Fi(;)8 b Fn(1)p Fh(g)973
611 y Fd(n)994 616 y Fc(1)1009 624 y Fe(k)1045 629 y
Fn(suc)o(h)14 b(that)f Fi(h)p Fn(\()p Fi(x)p Fn(\))g(=)f
Fi(h)p Fn(\()p Fi(y)r Fn(\))i(but)g Fi(x)e Fh(6)p Fn(=)h
Fi(y)r Fn(.)20 b(In)14 b(other)75 685 y(w)o(ords,)g(after)h(getting)g
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b Fn(Suc)o(h)21 b(a)f Fi(U)26 b Fn(is)21 b(called)h(a)e
Fm(family)h(of)g(universal)g(one-way)g(hash)h(functions)40
b Fn(if)21 b(for)f(all)75 798 y(p)q(olynomials)15 b Fi(p)d
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j(large)e Fi(k)q Fn(.)131 948 y(1.)22 b(If)d Fi(x)f Fh(2)38
b(f)p Fn(0)p Fi(;)8 b Fn(1)p Fh(g)463 930 y Fd(n)484
935 y Fc(1)499 943 y Fe(k)540 948 y Fn(is)19 b Fi(A)p
Fn('s)g(initial)i(v)m(alue,)f(then)g Fi(P)6 b(r)q(ob)p
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1012 y Fd(k)1294 1005 y Fn(and)i(the)f(random)g(c)o(hoices)h(of)f
Fi(A)p Fn(.)131 1099 y(2.)22 b Fh(8)p Fi(h)15 b Fh(2)h
Fi(H)339 1106 y Fd(k)377 1099 y Fn(there)h(is)g(a)g(description)h(of)f
Fi(h)g Fn(of)f(length)i(p)q(olynomial)g(in)g Fi(n)1425
1106 y Ff(1)1443 1112 y Fe(k)1464 1099 y Fn(,)f(suc)o(h)g(that)f(giv)o
(en)h Fi(h)p Fn('s)189 1155 y(description)f(and)g Fi(x)p
Fn(,)e Fi(h)p Fn(\()p Fi(x)p Fn(\))h(is)h(computable)g(in)g(p)q
(olynomial)h(time.)131 1249 y(3.)22 b Fi(H)227 1256 y
Fd(k)269 1249 y Fn(is)h(accessible)g(:)33 b(there)22
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Fi(G)g Fn(on)h(input)h Fi(k)f Fn(generates)189 1305 y(uniformly)16
b(at)e(random)h(a)g(description)i(of)e Fi(h)d Fh(2)h
Fi(H)1060 1312 y Fd(k)1081 1305 y Fn(.)75 1399 y(W)l(e)i(note)f(that)g
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e(collision)i(adv)o(ersary)d Fi(A)h Fn(is)h(a)f(\(uniform\))f
(algorithm.)19 b(W)l(e)11 b(can)g(alternativ)o(ely)75
1569 y(de\014ne)16 b(UO)o(WHF)f(where)g Fi(A)g Fn(is)g(a)g(p)q
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(applications\))g(is)f(that)f(a)h(comp)q(osition)g(of)g(suc)o(h)g
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2002 y(Let)18 b Fi(H)268 2009 y Ff(1)287 2002 y Fi(;)8
b(H)346 2009 y Ff(2)365 2002 y Fi(;)g(:)g(:)g(:)d(H)484
2009 y Fd(l)515 2002 y Fn(b)q(e)18 b(families)i(of)e(functions)g(suc)o
(h)h(that)e Fh(8)p Fi(i)h Fn(and)g Fh(8)p Fi(h)1409 2009
y Fd(i)1441 2002 y Fh(2)g Fi(H)1527 2009 y Fd(i)1559
2002 y Fi(h)1585 2009 y Fd(i)1616 2002 y Fn(:)35 b Fh(f)p
Fn(0)p Fi(;)8 b Fn(1)p Fh(g)1777 1985 y Fd(n)1798 1990
y Fe(i)1830 2002 y Fh(7!)75 2058 y(f)p Fn(0)p Fi(;)g
Fn(1)p Fh(g)188 2042 y Fd(n)209 2047 y Fe(i)p Fl(\000)p
Fc(1)283 2058 y Fn(and)22 b Fi(n)405 2065 y Fd(i)442
2058 y Fi(<)h(n)527 2065 y Fd(i)p Ff(+1)586 2058 y Fn(.)39
b(W)l(e)21 b(call)h Fi(H)27 b Fn(=)c Fh(f)p Fi(h)p Fh(j)p
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b Fi(h)1225 2065 y Ff(2)1260 2058 y Fh(\016)g Fi(:)8
b(:)g(:)13 b Fh(\016)h Fi(h)1427 2065 y Fd(l)1440 2058
y Fh(g)21 b Fn(an)g Fi(l)q Fm(-c)n(omp)n(osition)f Fn(of)75
2115 y Fi(H)113 2122 y Ff(1)133 2115 y Fi(;)8 b(H)192
2122 y Ff(2)210 2115 y Fi(;)g(:)g(:)g(:)d(;)j(H)350 2122
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Fi(h)997 2122 y Fd(l)1023 2115 y Fn(=)k Fi(h)1096 2098
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(Schemes)e Fn(,)168 2246 y(Euro)q(crypt,)c(1987.)98 2340
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168 678 y(1988,)14 b(pp.)h(12-24.)75 770 y([12])21 b(S.)e(Goldreic)o
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883 y(Symp)q(osium)e(on)e(the)g(F)l(oundation)h(of)e(Computer)h
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1031 y(270-299.)75 1122 y([14])21 b(S.)g(Goldw)o(asser,)h(S.)e(Micali)j
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168 1828 y(Subset)g(Sum)p Fn(,)f(Pro)q(c.)g(of)g(the)g(30th)g(Symp.)g
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2032 y(mutations)p Fn(,)f(These)f(Pro)q(c.)75 2124 y([20])21
b(R.)g(Impagliazzo)h(and)e(M.)g(Y)l(ung,)i Fm(Dir)n(e)n(ct)f
(Minimum-Know)r(le)n(dge)g(Computations)h Fn(,)f(Pro)q(c.)f(of)168
2181 y(Crypto)15 b(87,)f(Springer)i(V)l(erlag.)75 2272
y([21])21 b(L.)14 b(Lamp)q(ort,)f Fm(Constructing)h(digital)h(signatur)
n(es)f(fr)n(om)h(one-way)h(functions)p Fn(,)c(SRI)j(in)o(tl.)f(CSL-98,)
168 2329 y(Octob)q(er)i(1979.)75 2420 y([22])21 b(L.)14
b(Levin,)h Fm(One-way)g(F)m(unctions)e(and)i(Pseudor)n(andom)h(Gener)n
(ators)p Fn(,)d(Pro)q(c.)g(17th)g(Ann)o(ual)i(Sym-)168
2477 y(p)q(osium)i(on)e(the)g(Theory)g(of)g(Computing,)g(1985,)e(pp.)j
(363-365.)75 2569 y([23])21 b(R.)f(Merkle,)g Fm(A)f(Digital)h(Signatur)
n(e)g(b)n(ase)n(d)f(on)g(Conventional)g(Encryption)g(F)m(unction)p
Fn(,)g(Crypto)168 2625 y(1987,)14 b(Springer)i(V)l(erlag.)952
2750 y(13)p eop
%%Page: 14 15
14 14 bop 75 121 a Fn([24])21 b(R.)13 b(Merkle,)g Fm(Se)n(cr)n(e)n(cy,)
g(A)o(uthentic)n(ation)g(and)h(Public)g(Key)f(Systems)p
Fn(,)f(Ph.D.)g(Thesis)h(\(1982\),)e(UMI)168 177 y(Researc)o(h)16
b(Press,)f(Ann)g(Arb)q(or,)g(Mic)o(higan.)75 271 y([25])21
b(R.)16 b(Merkle,)f Fm(A)h(Certi\014e)n(d)f(Digital)i(Signatur)n(e)p
Fn(,)d(Man)o(uscript)h(1979.)75 365 y([26])21 b(R.)16
b(Merkle)f(and)g(M.)f(Hellman,)j Fm(Hiding)e(Information)h(and)g
(Signatur)n(e)f(in)h(T)m(r)n(ap)n(do)n(or)g(Knapsack)p
Fn(,)168 421 y(IEEE)g(T)l(rans.)e(on)h(Information)h(Theory)l(,)e(v)o
(ol.)h(IT-24,)g(5)g(\(1978\),)e(pp.)i(525-530.)75 515
y([27])21 b(M.)15 b(Naor,)f Fm(Bit)i(c)n(ommitment)h(using)e(pseudo-r)n
(andomness)g Fn(Pro)q(c.)g(of)g(Crypto)f(89.)75 609 y([28])21
b(M.)16 b(O.)g(Rabin)i Fm(digitalize)n(d)e(signatur)n(es)g
Fn(,)h(in)g(F)l(oundation)f(of)g(Secure)h(Computation,)f(Academic)168
665 y(Press,)f(R.A.)g(DeMillo,)h(D.)e(Dobkin,)i(A.)f(Jones)g(and)h(R.)f
(Lipton,)h(eds.,)e(Academic)j(Press,)d(1977.)75 759 y([29])21
b(M.)16 b(O.)f(Rabin)j Fm(Fingerprinting)d(by)i(R)n(andom)g
(Polynomials)f Fn(,)g(Harv)m(ard)f(Univ)o(ersit)o(y)l(,)i(TR-15-81,)168
816 y(1981.)75 909 y([30])k(M.)14 b(O.)h(Rabin)h Fm(Digital)g(Signatur)
n(es)e(and)i(Public)f(Key)h(F)m(unctions)e(as)i(Intr)n(actable)f(as)g
(F)m(actoring)p Fn(,)168 966 y(T)l(ec)o(hnical)i(Memo)e(TM-212,)f(Lab.)
h(for)f(Computer)h(Science,)i(MIT,)e(1979.)75 1060 y([31])21
b(R.)16 b(Riv)o(est,)g(A.)g(Shamir)g(and)g(L.)f(Adleman,)i
Fm(A)f(Metho)n(d)h(for)g(Obtaining)f(Digital)h(Signatur)n(e)f(and)168
1116 y(Public)g(Key)g(Cryptosystems)p Fn(,)f(Comm.)f(of)g(A)o(CM,)h(21)
f(\(1978\),)f(pp.)i(120-126.)75 1210 y([32])21 b(J.)16
b(Romp)q(el,)g Fm(One-way)g(functions)g(ar)n(e)g(ne)n(c)n(essary)f(and)
h(su\016c)n(ent)f(for)i(se)n(cur)n(e)f(signatur)n(es)p
Fn(,)d(Pro)q(c.)168 1266 y(22nd)j(A)o(CM)e(Ann)o(ual)i(Symp)q(osium)g
(on)f(the)h(Theory)f(of)f(Computing,)h(1990,)f(pp.)h(387{394.)75
1360 y([33])21 b(A.)f(Shamir,)h Fm(On)e(the)i(Gener)n(ation)f(of)g
(Crypto)n(gr)n(aphic)n(al)r(ly)g(Str)n(ong)g(Pseudo-R)n(andom)h(Numb)n
(er)168 1417 y(Se)n(quenc)n(es)p Fn(,)13 b(A)o(CM)i(T)l(rans.)f
(Comput.)h(Sys.,)f(1)h(\(1983\),)e(pp.)i(38-44.)75 1510
y([34])21 b(M.)12 b(N.)g(W)l(egman)f(and)i(J.)f(L.)g(Carter,)f
Fm(New)j(Hash)f(F)m(unctions)f(and)i(Their)f(Use)g(in)f(A)o(uthentic)n
(ation)168 1567 y(and)17 b(Set)f(Equality)p Fn(,)e(Journal)i(of)f
(Computer)g(and)g(System)g(Sciences)i(22,)e(pp.)g(265-279)f(\(1981\).)
75 1661 y([35])21 b(A.)f(C.)e(Y)l(ao,)i Fm(The)n(ory)g(and)g(Applic)n
(ations)f(of)i(T)m(r)n(ap)n(do)n(or)e(functions)p Fn(,)h(Pro)q
(ceedings)g(of)f(the)h(23th)168 1717 y(Symp)q(osium)d(on)e(the)g(F)l
(oundation)h(of)e(Computer)h(Science,)i(1982,)d(pp.)h(80-91.)952
2750 y(14)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF
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