Fast correlation attacks on certain stream ciphers
Journal of Cryptology
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IEEE Transactions on Computers
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Primitive Polynomials over GF(2) - A Cryptologic Approach
ICICS '01 Proceedings of the Third International Conference on Information and Communications Security
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CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
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INDOCRYPT '00 Proceedings of the First International Conference on Progress in Cryptology
Improved fast correlation attacks using parity-check equations of weight 4 and 5
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Further Results on Multiples of Primitive Polynomials and Their Products over GF(2)
ICICS '02 Proceedings of the 4th International Conference on Information and Communications Security
Multiples of Primitive Polynomials and Their Products over GF(2)
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
Results on multiples of primitive polynomials and their products over GF(2)
Theoretical Computer Science
TCHo: a hardware-oriented trapdoor cipher
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
Divisibility of polynomials over finite fields and combinatorial applications
Designs, Codes and Cryptography
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In this paper we concentrate on finding out multiples of primitive polynomials over GF(2). Given any primitive polynomial f(x) of degree d, we denote the number of t-nomial multiples (t d - 1) with degree less than 2d - 1 as Nd,t. We show that (t - 1)Nd,t = (2d-2/t-2) - Nd,t-1 - t-1/t-2 (2d - t + 1)Nd,t-2, with the initial conditions Nd,2 = Nd,1 = 0. Moreover, we show that the sum of the degree of all the t-nomial multiples of any primitive polynomial is t-1/t (2d - 1)Nd,t. More interestingly we show that, given any primitive polynomial of degree d, the average degree t-1/t (2d - 1) of its t-nomial multiples with degree 驴 2d - 2 is equal to the average of maximum of all the distinct (t - 1) tuples from 1 to 2d - 2. In certain model of Linear Feedback Shift Register (LFSR) based cryptosystems, the security of the scheme is under threat if the connection polynomial corresponding to the LFSR has sparse multiples. We show here that given a primitive polynomial of degree d, it is almost guaranteed to get one t-nomial multiple with degree 驴 2 d/t-1 +log2(t-1)+1.