We study the rational Cherednik algebra Hc of type G(r, 1, n) by means of the Dunkl-Opdam operators introduced in [DuOp] and the generalized Jack polynomials introduced in [Gri]. Our main result is a characterization of the set of parameters c for which Hce+Hc 6= Hc, where e+ is the symmetrizing idempotent for G(r, 1, n). Such parameters are called aspherical. The proof is parallel to that in [...

The paper discusses the Feistel cipher with a block size of n = 2m, where the addition of a round key and a part of an incoming massage in each round is carried out modulo 2m. In order to evaluate the security of such a cipher against differential and linear cryptanalyses, the new parameters of cipher s-boxes are introduced. The upper bounds of maximum average differential and linear probabilit...

The Kupyna hash function was selected as the new Ukrainian standard DSTU 7564:2014 in 2015. It is designed to replace the old Independent States (CIS) standard GOST 34.311-95. The Kupyna hash function is an AES-based primitive, which uses Merkle-Damg̊ard compression function based on Even-Mansour design. In this paper, we show the first cryptanalytic attacks on the round-reduced Kupyna hash func...

One of the hardest practical problems in computer science is the problem of gate-efficient implementation. Such optimizations are particularly important in industrial hardware implementations of standard cryptographic algorithms. In this paper we focus on optimizing some small digital circuits such as S-boxes in some well-known ciphers. We consider the notion of Multiplicative Complexity which ...

In this paper, we propose related-key differential distinguishers based on the complementation property of Feistel ciphers. We show that with relaxed requirements on the complementation, i.e. the property does not have to hold for all keys and the complementation does not have to be on all bits, one can obtain a variety of distinguishers. We formulate criteria sufficient for attacks based on th...

– The NIST Secure Hash Algorithm (SHA) has been replaced with a new algorithm, SHA-1 [10]. The reason for this change is that NIST (or NSA) discovered an attack against the original SHA algorithm [11]. – This year’s measurements are based on a faster implementation of GOST 28147. – This year’s measurements were made with a different Sun workstation. The new machine is significantly slower; as a...