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New constructions for resilient and highly nonlinear boolean functions
- Lecture Notes in Computer Science 2727
, 2003
"... Abstract. We explore three applications of geometric sequences in constructing cryptographic Boolean functions. First, we construct 1-resilient functions of n Boolean variables with nonlinearity 2 n−1 −2 (n−1)/2, n odd. The Hadamard transform of these functions is 3-valued, which limits the efficien ..."
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Cited by 6 (2 self)
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Abstract. We explore three applications of geometric sequences in constructing cryptographic Boolean functions. First, we construct 1-resilient functions of n Boolean variables with nonlinearity 2 n−1 −2 (n−1)/2, n odd. The Hadamard transform of these functions is 3-valued, which limits the efficiency of certain stream cipher attacks. From the case for n odd, we construct highly nonlinear 1-resilient functions which disprove a conjecture of Pasalic and Johansson for n even. Our constructions do not have a potential weakness shared by resilient functions which are formed from concatenation of linear functions. Second, we give a new construction for balanced Boolean functions with high nonlinearity, exceeding 2 n−1 −2 (n−1)/2, which is not based on the direct sum construction. Moreover, these functions have high algebraic degree and large linear span. Third, we construct balanced vectorial Boolean functions with nonlinearity 2 n−1 − 2 (n−1)/2 and low maximum correlation. They can be used as nonlinear combiners for stream cipher systems with high throughput. 1
Relationship Between Propagation Characteristics and Nonlinearity of Cryptographic Functions
- Journal of Universal Computer Science
, 1995
"... Abstract: The connections among the various nonlinearity criteria is currently an important topic in the area of designing and analyzing cryptographic functions. In this paper we show a quantitative relationship between propagation characteristics and nonlinearity, two critical indicators of the cry ..."
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Abstract: The connections among the various nonlinearity criteria is currently an important topic in the area of designing and analyzing cryptographic functions. In this paper we show a quantitative relationship between propagation characteristics and nonlinearity, two critical indicators of the cryptographic strength of a Boolean function. We also present a tight lower bound on the nonlinearity of a cryptographic function that has propagation characteristics.
Cryptographic hash functions based on ALife
"... Abstract. There is a long history of cryptographic hash functions, i.e. functions mapping variable-length strings to fixed-length strings, and such functions are also expected to enjoy certain security properties. Hash functions can be effected via modular arithmetic, permutationbased schemes, chaot ..."
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Abstract. There is a long history of cryptographic hash functions, i.e. functions mapping variable-length strings to fixed-length strings, and such functions are also expected to enjoy certain security properties. Hash functions can be effected via modular arithmetic, permutationbased schemes, chaotic mixing, and so on. Herein we introduce the notion of an artificial-life (ALife) hash function (ALHF), whereby the requisite mixing action of a good hash function is accomplished via ALife rules that give rise to complex evolution of a given system. Various security tests have been run, and the results reported for examples of ALHFs. 1 Brief history of hash function design A hash function H maps arbitrary messages (bitstrings) called keys or pre-images into fixed-length bitstrings called hash values (the definitive treatment of hash functions is [Knuth 1998]). By the nomenclature H(κ) = ν
unknown title
, 2004
"... Abstract. There is a long history of cryptographic hash functions, i.e. functions mapping variable-length strings to fixed-length strings, with such functions also expected to enjoy certain security properties. Hash functions can be effected via modular arithmetic, recursive permutation-based scheme ..."
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Abstract. There is a long history of cryptographic hash functions, i.e. functions mapping variable-length strings to fixed-length strings, with such functions also expected to enjoy certain security properties. Hash functions can be effected via modular arithmetic, recursive permutation-based schemes, chaotic mixing, and so on. Herein we introduce the notion of an Artificial Life (or ALife) hash function (ALHF), whereby the requisite mixing action of a good hash function is accomplished via typical ALife rules that give rise to complex system evolution. Various security tests have been run, and the results reported herein, for exemplary ALHFs.
