Introduction to finite fields and their applications
Introduction to finite fields and their applications
Fast correlation attacks on certain stream ciphers
Journal of Cryptology
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Shift Register Sequences
Primitive Polynomials over GF(2) - A Cryptologic Approach
ICICS '01 Proceedings of the Third International Conference on Information and Communications Security
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
A Generalized Birthday Problem
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Multiples of Primitive Polynomials over GF(2)
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
Proceedings of the Third International Workshop on Fast Software Encryption
Computation of Low-Weight Parity Checks for Correlation Attacks on Stream Ciphers
Proceedings of the 5th IMA Conference on Cryptography and Coding
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
TCHo: a hardware-oriented trapdoor cipher
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
WSEAS Transactions on Computers
Fast correlation attacks: methods and countermeasures
FSE'11 Proceedings of the 18th international conference on Fast software encryption
A new mode of encryption providing a tweakable strong pseudo-random permutation
FSE'06 Proceedings of the 13th international conference on Fast Software Encryption
Divisibility of polynomials over finite fields and combinatorial applications
Designs, Codes and Cryptography
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Linear feedback shift registers (LFSR) are important building blocks in stream cipher cryptosysterns. To be cryptographically secure, the connection polynomials of the LFSRs need to be primitive over GF(2). Moreover, the polynomials should have high weight and they should not have sparse multiples at low or moderate degree. Here we provide results on t-nomial multiples of primitive polynomials and their products. We present results for counting t-nomial multiples and also analyse the statistical distribution of their degrees. The results in this paper helps in deciding what kind of primitive polynomial should be chosen and which should be discarded in terms of cryptographic applications. Further the results involve important theoretical identities in terms of t-nomial multiples which were not known earlier.