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
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
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
Multiples of Primitive Polynomials over GF(2)
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
Decrypting a Class of Stream Ciphers Using Ciphertext Only
IEEE Transactions on Computers
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
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
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Recently the problem of analysing the multiples of primitive polynomials and their products has received a lot of attention. These primitive polynomials are basically the connection polynomials of the LFSRs (Linear Feedback Shift Registers) used in the stream cipher system. Analysis of sparse multiples of a primitive polynomial or product of primitive polynomials helps in identifying the robustness of the stream ciphers based on nonlinear combiner model. In this paper we first prove some important results related to the degree of the multiples. Earlier these results were only observed for small examples. Proving these results clearly identify the statistical behavior related to the degree of multiples of primitive polynomials or their products. Further we discuss a randomized algorithm for finding sparse multiples of primitive polynomials and their products. Our results clearly identify the time memory trade off for finding such multiples.