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Ergodic Transformations in the Space of pAdic Integers
 In book: padic Mathematical Physics, AIP Conference Proceedings
, 2006
"... Abstract. Let L1 be the set of all mappings f: Zp → Zp of the space of all padic 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 permutat ..."
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Abstract. Let L1 be the set of all mappings f: Zp → Zp of the space of all padic 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 measurepreserving 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 padic 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.
NONARCHIMEDEAN ERGODIC THEORY AND PSEUDORANDOM GENERATORS
, 710
"... 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 functio ..."
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Cited by 5 (3 self)
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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 2adic integers. Within this approach, a PRNG is considered as a dynamical system and is studied by means of the nonArchimedean ergodic theory. 1.
Increasing the ABC stream cipher period
 eSTREAM, ECRYPT Stream Cipher Project, Report 2005/050
"... ..."
ABC – a New Fast Flexible Stream Cipher Specification, Version 3
"... ABC is a synchronous stream cipher optimized for software applications. Its key length is 128 bits. It accommodates a 128bit initial vector. Here a version of ABC with a 128bit key and 32bit internal variables is presented. A new approach to the design of stream ciphers has been used which result ..."
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Cited by 1 (1 self)
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ABC is a synchronous stream cipher optimized for software applications. Its key length is 128 bits. It accommodates a 128bit initial vector. Here a version of ABC with a 128bit key and 32bit internal variables is presented. A new approach to the design of stream ciphers has been used which results
Security and Implementation Properties of ABC v.2
"... 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 o ..."
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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
The Single Cycle Tfunctions
"... Abstract In this paper the single cycle Tfunctions are studied. Making use of the explicit formulas of sum and product of 2adic integers, we present the necessary and sufficient conditions on the generalized polynomial ˜ p(x) = a0 + ⊕a1x + ⊕·· · + ⊕adx d (mod2 n) being a single cycle Tfunction. F ..."
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Abstract In this paper the single cycle Tfunctions are studied. Making use of the explicit formulas of sum and product of 2adic integers, we present the necessary and sufficient conditions on the generalized polynomial ˜ p(x) = a0 + ⊕a1x + ⊕·· · + ⊕adx d (mod2 n) being a single cycle Tfunction. Furthermore, for any given generalized polynomial, we can deduce some expressions about its coefficients by which we can determine whether it is single cycle or not. Key words Tfunction, single cycle, generalized polynomial 1
ASC – A Stream Cipher with Built–In MAC Functionality
"... 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: tfunctions and fast pseudo hadamard transforms. We recapitulate the theory behin ..."
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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: tfunctions 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 securityspeed tradeoffs. Our scheme is faster than other comparable tfunction based designs while offering the same security level.
ASC – A Stream Cipher with Built–In MAC Functionality
"... 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: tfunctions and fast pseudo hadamard transforms. We recapitulate the theory behin ..."
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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: tfunctions 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 securityspeed tradeoffs. Our scheme is faster than other comparable tfunction based designs while offering the same security level.
doi:10.1093/comjnl/bxm100 Computational Aspects of Monomial Dynamical Systems
, 2007
"... We consider the dynamics of x 7! x n, where n 2 is an integer, over the multiplicative group modulo p k, where k is a positive integer and p an odd prime. This paper is a review of earlier results by the author, but new results are also contained. Possible applications to pseudorandom number generat ..."
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We consider the dynamics of x 7! x n, where n 2 is an integer, over the multiplicative group modulo p k, where k is a positive integer and p an odd prime. This paper is a review of earlier results by the author, but new results are also contained. Possible applications to pseudorandom number generation will be discussed. The main results are a description of the preperiodic points and an algorithm to find the longest possible cycle. The preperiodic points form trees, all isomorphic as graphs to the preperiodic points of the fixed point 1. When n is a prime, different from p, we can describe the tree structure completely. A formula for the length of the longest cycle is presented. We can find one of the longest cycles of the monomial system using a primitive root modulo p k as an initial value.
ASC – A Stream Cipher with Built–In MAC Functionality
"... 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: tfunctions and fast pseudo hadamard transforms. We recapitulate the theory behin ..."
Abstract
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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: tfunctions 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 securityspeed tradeoffs. Our scheme is faster than other comparable tfunction based designs while offering the same security level.