Abstract. Let L1 be the set of all mappings f: Zp → Zp of the space of all p-adic integers Zp into itself that satisfy Lipschitz condition with a constant 1. We prove that the mapping f ∈ L1 is ergodic with respect to the normalized Haar measure on Zp if and only if f induces a single cycle permutation on each residue ring Z/p k Z modulo p k, for all k = 1,2,3,.... The multivariate case, as well as measure-preserving mappings, are considered also. Results of the paper in a combination with earlier results of the author give explicit description of ergodic mappings from L1. This characterization is complete for p = 2. As an application we obtain a characterization of polynomials (and certain locally analytic functions) that induce ergodic transformations of p-adic spheres. The latter result implies a solution of a problem (posed by A. Khrennikov) about the ergodicity of a perturbed monomial mapping on a sphere. 1.

ABC is a synchronous stream cipher submitted to ECRYPT Stream Cipher Project [2]. The changes proposed in this paper increase ABC keystream period to 2 1) words and the size of ABC internal state to 1287 bits while keeping all the guaranteed properties of the keystream without a considerable overhead.

Abstract. ABC is a synchronous stream cipher submitted to eSTREAM. Here we describe ABC v.2 – a tweaked version of ABC. The tweaks made ABC v.2 resistant to certain attacks, including the ones presented by Berbain and Gilbert and by Khazaei. We give a design rationale and a brief security analysis of ABC v.2. Also it is shown that the distinguishing attacks against ABC v.2 like the one suggested by Khazaei and Kiaei are totally impractical. ABC v.2 is extremely fast in software often heading the eSTREAM benchmark list. Further we define informal requirements for an industrial software stream cipher and show that ABC v.2 meets them. Moreover, we demonstrate that ABC v.2 is also suitable for embedded security applications demanding high performance. Keywords: cryptography, stream cipher, ABC, eSTREAM, ECRYPT, distinguishing attack, stream cipher performance

Abstract — In this paper we present the design of a new encryption scheme. The scheme we propose is a very flexible encryption and authentication primitive. We build this scheme on two relatively new design principles: t-functions and fast pseudo hadamard transforms. We recapitulate the theory behind these principles and analyze their security properties and efficiency. In more detail we propose a stream cipher which outputs a message authentication tag along with the encrypted data stream with only little overhead. Moreover we propose security-speed tradeoffs. Our scheme is faster than other comparable t-function based designs while offering the same security level.

Abstract. The paper develops techniques in order to construct computer programs, pseudorandom number generators (PRNG), that produce uniformly distributed sequences. The paper exploits an approach that treats standard processor instructions (arithmetic and bitwise logical ones) as continuous functions on the space of 2-adic integers. Within this approach, a PRNG is considered as a dynamical system and is studied by means of the non-Archimedean ergodic theory. 1.