Advances in Cryptology - EUROCRYPT 2007: 26th Annual by Marc Stevens, Arjen Lenstra, Benne de Weger (auth.), Moni

By Marc Stevens, Arjen Lenstra, Benne de Weger (auth.), Moni Naor (eds.)

Those are the complaints of Eurocrypt 2007, the twenty sixth Annual IACR EurocryptConference. The convention used to be subsidized by means of the foreign organization forCryptologic study (IACR; see, this 12 months in cooperation withthe study workforce on arithmetic utilized to Cryptography at UPC and theResearch crew on details defense at UMA. The Eurocrypt 2007 ProgramCommittee (PC) consisted of 24 individuals whose names are indexed at the nextpage.The workstation selected a number of guidelines: 0 computer papers - no software Committeemember may well put up papers; non-compulsory anonymity - authors may well decide on toanonymize their papers or now not. nameless papers have been handled as ordinary, i.e.,the author’s id used to be now not printed to the computer. The submission software program usedwas “Web Submission and assessment software program” written and maintained via ShaiHalevi. there have been 173 papers submitted to the convention and the computer chose33 of them. every one paper used to be assigned to not less than 3 notebook contributors, who eitherhandled it themselves or assigned it to an exterior referee. After the experiences weresubmitted, the committee deliberated either on-line for a number of weeks and finallyin a face-to-face assembly held in Paris. as well as notification of the decisionof the committee, authors bought experiences. Our target used to be to supply meaningfulcomments to authors of all papers (both these chosen for this system andthose now not selected). The default for any document given to the committee was once thatit can be to be had to the authors besides.

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Details. Fix numbers n, q and an adversary A asking q queries to its oracle. We upper bound Pr[CollE (Q)] by exhibiting predicates Win0(Q), . , Win8(Q) such that CollE (Q) =⇒ Win0(Q) ∨ . . ∨ Win8(Q) and then by upper bounding separately the probabilities Pr[Win0(Q)], . , Pr[Win8(Q)]. Obviously Pr[CollE (Q)] ≤ Pr[Win0(Q)] + · · · + Pr[Win8(Q)]. (The event Win0(Q) happens if the adversary is lucky, whereas if the adversary is not lucky but makes a successful i-th query then one of the predicates Win1(Q), .

In order to show that a construction is a (k, )-robust combiner, one must provide an efficient procedure P which given two colliding inputs for the combiner, finds collisions for at least − k + 1 of the underlying Hi ’s. In this paper we only consider black-box combiners as defined in [7], this means that C and P are only given oracle access to the Hi ’s. The following definition of a (k, )-robust combiner is a generalization of the definition given in [2], where only the case k = 1 was considered. Definition 1.

We answer this question in the affirmative: any combiner for functions with range {0, 1}v must have output length at least (v − O(log(q))) bits3 , where q is the number of oracle calls made by the combiner. Stated in asymptotic terms, if q ∈ 2o(v) is subexponential, then the output length is in (1 − o(1))v , and if q is constant the output length is in v − O(1), this must be compared to v which is trivially achieved by concatenation. (k, )-Robust Combiner. In this paper we will consider the more general question whether secure and non-trivial (k, )-robust combiners for collision-resistant hash-functions exist.

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