Fast correlation attacks on certain stream ciphers
Journal of Cryptology
An Architecture for Computing Zech's Logarithms in GF(2m)
IEEE Transactions on Computers
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Shift Register Sequences
Nonlinearity Bounds and Constructions of Resilient Boolean Functions
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Fast Correlation Attacks through Reconstruction of Linear Polynomials
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
On Choice of Connection-Polynominals for LFSR-Based Stream Ciphers
INDOCRYPT '00 Proceedings of the First International Conference on Progress in Cryptology
Decrypting a Class of Stream Ciphers Using Ciphertext Only
IEEE Transactions on Computers
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
Multiples of Primitive Polynomials over GF(2)
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
Results on multiples of primitive polynomials and their products over GF(2)
Theoretical Computer Science
A simple stream cipher with proven properties
Cryptography and Communications
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Linear Feedback Shift Registers (LFSR) are important building blocks in stream cipher systems. The connection polynomials of the LFSRs need to be primitive over GF(2). Also the polynomial should have high weight and it should not have sparse multiples of moderate degree. Here we provide results which have immediate application in synthesis of connection polynomials for stream cipher systems. We show that, given any primitive polynomial f(x) of degree d there exists 2d-1 - 1 many distinct trinomial multiples of degree less than 2d - 1. Among these trinomial multiples, it is known that a trinomial of the form x2/3(2d-1) +x1/3 (2d-1) + 1 contains all the degree d (d even) primitive polynomials as its factors. We extend this result by showing that, if d1 (even) divides d (even) and 2d-1/3 驴 0 mod (2d1 - 1), then the trinomial x2/3(2d-1) + x1/3(2d-1) + 1 contains all the primitive polynomials of degree d1 as its factor. We also discuss algorithmic issues in getting trinomial multiples of low degree. Next we present some results on t-nomial multiples of primitive polynomials which help us in choosing primitive polynomials that do not have sparse multiples.