By Mitsuri Matsui
This e-book constitutes the refereed court cases of the fifteenth overseas convention at the concept and alertness of Cryptology and data safeguard, ASIACRYPT 2009, held in Tokyo, Japan, in December 2009.
The forty-one revised complete papers awarded have been rigorously reviewed and chosen from 298 submissions. The papers are prepared in topical sections on block ciphers, quantum and post-quantum, hash capabilities I, encryption schemes, multi social gathering computation, cryptographic protocols, hash funtions II, versions and frameworks I, cryptoanalysis: sq. and quadratic, types and framework II, hash capabilities III, lattice-based, and aspect channels.
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S). For a finite set S, we denote by |S| the number of its elements. A k-tuple is denoted as Cascade Encryption Revisited 39 uk = (u1 , . . , uk ), and the set of all k-tuples of elements of U is denoted as U k . , f ◦ g denotes the mapping g(f (·)). The set of all permutations of {0, 1}n is denoted by Perm(n) and id represents the identity mapping, if the domain is implicitly given. , xn = x(x − 1) · · · (x − n + 1). , that they are not all distinct. It is well-known that pcoll (n, k) < k 2 /2n.
First, it is easy to see that ∆q (C2 (E), Cd2 (E)) ≤ pcoll (2k , l) < l2 /2k+1 and hence we have ∆q (C1 (E, P), C2 (E)) ≤ ∆q (C1 (E, P), Cd2 (E)) + l2 /2k+1 . However, note that Cd2 (E) ≡ C3 (E, P); this is because in both systems the permutations EK1 , . . , EKl , P are chosen randomly with the only restriction that EK1 ◦ · · · ◦ EKl = P is satisfied. Now we can use Lemma 3 to substitute the random permutation P in both C1 (E, P) and C3 (E, P) for a fixed one. Let S denote the permutation guaranteed by Lemma 3.
Kr ) is an K (r + 1)-tuple (x0 , K1 , . . , Kr ) for which there exist x1 , . . , xr such that x0 →1 K K x1 →2 · · · →r xr holds. Similarly, if a fixed permutation S is given and 1 ≤ i < r, then an i-disconnected r-chain for keys (K1 , . . , Kr ) with respect to S is an (r+1)tuple (x0 , K1 , . . , Kr ) for which there exist x1 , . . , xr such that we have both 1 w(E) was denoted as KeysE in [4]. Cascade Encryption Revisited Kr−i+1 Kr−i+2 K K K 43 Kr−i x0 → x1 → · · · →r xi and S −1 (xi ) →1 xi+1 →2 · · · → xr .