Advances in Cryptology — EUROCRYPT 2003: International - download pdf or read online

By Antoine Joux (auth.), Eli Biham (eds.)

This ebook constitutes the refereed court cases of the overseas convention at the idea and purposes of Cryptographic recommendations, EUROCRYPT 2003, held in Warsaw, Poland in may perhaps 2003.

The 37 revised complete papers provided including invited papers have been rigorously reviewed and chosen from 156 submissions. The papers are geared up in topical sections on cryptanalysis, safe multi-party communique, zero-knowledge protocols, foundations and complexity-theoretic safeguard, public key encryption, new primitives, elliptic curve cryptography, electronic signatures, information-theoretic cryptography, and staff signatures.

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On the Optimality of Linear, Differential, and Sequential Distinguishers 23 Generally, the Chernoff information cannot be expressed explicitely, because one has to solve a transcendental equation. 2 ; unfortunately, even if it captures the asymptotic exponential shape of the best advantage curve, it is not practically useful for “interesting” values of n; for which concerns the upper bound, it is useful for all n but it is not tight: one may give a tighter lower bound using Bernstein’s inequality (see Theorem 4 and [11] for a proof).

N} : u ≥ n · log(2m − 2) − log(2m − 2 − ) log((2m − 2)(1 + )) − log(2m − 2 − ) (14) where u is defined in Algorithm 3. For small , (14) may be approximated by (n) Aopt ≈ u ∈ {0, . . , n} : u ≥ n · 1 2m−1 − 1 + · 2m − 1 (2m − 2)(2m − 1) (15) Thus, we have Corollary 1. δdiff is an optimal differential distinguisher submitting n queries to the oracle if and only if (14) is satisfied for all u ∈ N with 1 < u ≤ n and for all 0 < ≤ 2m − 2. It is not difficult to build artificially a situation where Algorithm 2 is not optimal: it is sufficient to take a characteristic (a, b) with DPC (a, b) having a very high probability.

Be random variables observed sequentially. A sequential decision procedure consists in: 1. a stopping rule σn which specifies whether a decision must be taken without taking any further observation. If at least one observation is taken, this rule specifies for every set of observed values (x1 , . . , xn ), with n ≥ 1, whether to stop sampling and take a decision out of D or to take another observation xn+1 . 2. a decision rule δn which specifies the decision to be taken. If n ≥ 1 observations have been taken, then one takes an action δn (x1 , .

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