Cryptography

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

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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 was once backed by means of the foreign organization forCryptologic study (IACR; see www.iacr.org), this yr in cooperation withthe study crew on arithmetic utilized to Cryptography at UPC and theResearch team on info safeguard at UMA. The Eurocrypt 2007 ProgramCommittee (PC) consisted of 24 participants whose names are indexed at the nextpage.The laptop selected a number of guidelines: 0 notebook papers - no application Committeemember may perhaps publish papers; not obligatory anonymity - authors may possibly decide upon toanonymize their papers or now not. nameless papers have been handled as traditional, i.e.,the author’s identification used to be no longer published to the computer. The submission software program usedwas “Web Submission and evaluation software program” written and maintained by way of ShaiHalevi. there have been 173 papers submitted to the convention and the computer chose33 of them. every one paper used to be assigned to no less than 3 workstation 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 stories. Our target used to be to supply meaningfulcomments to authors of all papers (both these chosen for this system andthose no longer selected). The default for any record given to the committee used to be thatit can be on hand to the authors besides.

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Additional info for Advances in Cryptology - EUROCRYPT 2007: 26th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Barcelona, Spain, May 20-24, 2007. Proceedings

Example text

H ˆ ), (M, M )] ≤ (qP + qC ) + k . AdvPk [(H 2v relative to Proof. Let J ⊆ {1, . . e. ∀j ∈ J : |Vj (M ) ∪ Vj (M )| = |Wj (M ) ∪ Wj (M )|. ,H 10 Our Lemma 1 is basically Theorem 2 from [2], the only difference is that we consider (k, )-robust combiners whereas [2] were only interested in the case k = 1. 30 K. Pietrzak on inputs M, M , let Q denote all those inputs together with the corresponding outputs. {Vi (M ), Wi (M ), Vi (M ), Wi (M )} Q= i=1 Let P be the oracle PPTM which makes at most qP oracle calls and maximizes the probability α defined below.

Let C : {0, 1}m → {0, 1}n be as in the previous lemma. Then whenever n < (v − 2 log(2qC ))( − k + 1) − − 1 and m > n there exist functions H1 , . . ,H (M ). – |Vj (M )∪Vj (M )| = |Wj (M )∪Wj (M )| for at least k different j ∈ {1, . . , }. For the special case where k = 1 and C queries each Hi exactly once (which are the constructions considered in [2]) the bounds on n can be improved to nn or n n. Proof. Consider the following random experiment. 13 Then M, M ∈ {0, 1}m are sampled uniformly at random.

I, the two words would be the same), so we can assume either (ii) or (iii). Say first the collision is of type (ii), namely that the collision has one word with m ≥ 2 blocks, which is wlog word 1, and one word of with one block, which is word 2. Note first that when word 1 is hashed via MDC-2 there can never be a round where the same query appears both on the left and right-hand sides unless ExistsFit1 (Q) holds (to see this, take the earliest such round; since the constant keys A1 , B1 are different this is not the first round and the two queries from the round before are different but have the same XOR output, so ExistsFit1 (Q)).

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