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Discrete Logarithms in Finite Fields and Their Cryptographic Significance
, 1984
"... Given a primitive element g of a finite field GF(q), the discrete logarithm of a nonzero element u GF(q) is that integer k, 1 k q  1, for which u = g k . The wellknown problem of computing discrete logarithms in finite fields has acquired additional importance in recent years due to its appl ..."
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Cited by 87 (6 self)
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Given a primitive element g of a finite field GF(q), the discrete logarithm of a nonzero element u GF(q) is that integer k, 1 k q  1, for which u = g k . The wellknown problem of computing discrete logarithms in finite fields has acquired additional importance in recent years due to its applicability in cryptography. Several cryptographic systems would become insecure if an efficient discrete logarithm algorithm were discovered. This paper surveys and analyzes known algorithms in this area, with special attention devoted to algorithms for the fields GF(2 n ). It appears that in order to be safe from attacks using these algorithms, the value of n for which GF(2 n ) is used in a cryptosystem has to be very large and carefully chosen. Due in large part to recent discoveries, discrete logarithms in fields GF(2 n ) are much easier to compute than in fields GF(p) with p prime. Hence the fields GF(2 n ) ought to be avoided in all cryptographic applications. On the other hand, ...
Shiftregister synthesis (modulo m)
 SIAM J. Computing
, 1985
"... The BerlekampMassey algorithm takes a sequence of elements from a field and finds the shortest linear recurrence (or linear feedback shift register) that can generate the sequence. In this paper we extend the algorithm to the case when the elements of the sequence are integers modulo m, where m is ..."
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Cited by 15 (0 self)
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The BerlekampMassey algorithm takes a sequence of elements from a field and finds the shortest linear recurrence (or linear feedback shift register) that can generate the sequence. In this paper we extend the algorithm to the case when the elements of the sequence are integers modulo m, where m is an arbitrary integer with known prime decomposition.
GENETIC ALGORITHM FOR DECODING LINEAR CODES OVER AWGN AND FADING CHANNELS 1
"... This paper introduces a decoder for binary linear codes based on Genetic Algorithm (GA) over the Gaussian and Rayleigh flat fading channel. The performances and compututional complexity of our decoder applied to BCH and convolutional codes are good compared to Chase2 and Viterbi algorithm respectiv ..."
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This paper introduces a decoder for binary linear codes based on Genetic Algorithm (GA) over the Gaussian and Rayleigh flat fading channel. The performances and compututional complexity of our decoder applied to BCH and convolutional codes are good compared to Chase2 and Viterbi algorithm respectively. It show that our algorithm is less complex for linear block codes of large block length; furthermore it's performances can be improved by tuning the decoder's parameters, in particular the number of individuals by population and the number of generations