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

Those are the lawsuits of Eurocrypt 2007, the twenty sixth Annual IACR EurocryptConference. The convention used to be backed through the foreign organization forCryptologic study (IACR; see www.iacr.org), this yr in cooperation withthe study staff on arithmetic utilized to Cryptography at UPC and theResearch workforce on details defense at UMA. The Eurocrypt 2007 ProgramCommittee (PC) consisted of 24 contributors whose names are indexed at the nextpage.The workstation selected numerous guidelines: 0 notebook papers - no application Committeemember might post papers; not obligatory anonymity - authors may possibly decide on toanonymize their papers or now not. nameless papers have been taken care of as traditional, i.e.,the author’s identification was once now not printed to the computer. The submission software program usedwas “Web Submission and overview software program” written and maintained through ShaiHalevi. there have been 173 papers submitted to the convention and the computer chose33 of them. every one paper was once assigned to not less than 3 laptop contributors, who eitherhandled it themselves or assigned it to an exterior referee. After the studies 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 obtained reports. Our objective was once to supply meaningfulcomments to authors of all papers (both these chosen for this system andthose no longer selected). The default for any document given to the committee was once thatit will be to be had to the authors in addition.

**Read or Download Advances in Cryptology - EUROCRYPT 2007: 26th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Barcelona, Spain, May 20-24, 2007. Proceedings PDF**

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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**

**Sample text**

J| > − k where ∀j ∈ J : |Vj (M ) ∪ Vj (M )| = |Wj (M ) ∪ Wj (M )| We will show that Pr[E1 ] > Pr[E2 ], which then implies Pr[E1 ∧ ¬E2 ] > 0. This will prove the lemma as it shows that random H1 , . . , H and M, M have the property as claimed by the lemma with non-zero probability, and thus H1 , . . , H and M, M with this property exist. ,H (M )] ≥ 2−n and m > n we get Pr[E1 ] ≥ 2−n − 2−m ≥ 2−n−1 . (6) Let qi denote the number of Hi oracle gates in C, note that i=1 qi = qC . 14 As the Hi ’s are all independent random functions, the best A can do is to query it i’th oracle on 2qi distinct inputs (which ones is 13 14 One can’t simply sample a Hi as this would need inﬁnite randomness, but one can use lazy sampling here, this means that Hi (X) is only assigned a (random) value when Hi is actually invoked on input X.

5 . Figure 2 shows our upper bound as function of q for the case n = 128. 9 80 90 Fig. 2. Our upper bound on AdvMDC2 (q) as a function of q (solid line) compared to 128 the previous best upper bound of q(q + 1)/2128 (dotted line) 2 Preliminaries n n n Let Bloc(n) be the set of functions E: {0, 1} × {0, 1} → {0, 1} such that n E(K, ·) = EK (·) is a permutation on {0, 1} . Given a blockcipher E ∈ Bloc(n) n 2n we deﬁne MDC2E : ({0, 1} )+ → {0, 1} by the algorithm of Fig. 1. The hash of a word X where |X| is a multiple of n by MDC2E is denoted by MDC2E (X).

Take for example the conﬁguration 1a of Fig. 5. i are diﬀerent. These are the only constraints; unmarked strings may or may not be equal, and other queries in the diagram may or may not be equal. Since the bottom left and bottom right queries are distinct ﬁtting the diagram means using two distinct queries Qi = (Xi , Ki , Yi ) and Qi = (Xi , Ki , Yi ) from Q for these two positions. We say that four queries Qi = (Xi , Ki , Yi ), Qi = (Xi , Yi , Yi ), Qj = (Xj , Kj , Yj ), Qk = (Xk , Kk , Yk ) in Q “ﬁt” conﬁguration 1a if i = i and if Qi , Qi , Qj , Qk can be placed in respectively the bottom left, bottom right, top left and top right positions of conﬁguration 1a such that the wiring constraints of the diagram are respected and such that the two strings marked A are equal.