Introduction to finite fields and their applications
Introduction to finite fields and their applications
Fast correlation attacks on certain stream ciphers
Journal of Cryptology
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
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
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
Results on multiples of primitive polynomials and their products over GF(2)
Theoretical Computer Science
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A standard model of nonlinear combiner generator for stream cipher system combines the outputs of several independent Linear Feed-back Shift Register (LFSR) sequences using a nonlinear Boolean function to produce the key stream. Given such a model, cryptanalytic attacks have been proposed by finding the sparse multiples of the connection polynomials corresponding to the LFSRs. In this direction recently a few works are published on t-nomial multiples of primitive polynomials. We here provide further results on degree distribution of the t-nomial multiples. However, getting the sparse multiples of just a single primitive polynomial does not suffice. The exact cryptanalysis of the nonlinear combiner model depends on finding sparse multiples of the products of primitive polynomials. We here make a detailed analysis on t-nomial multiples of products of primitive polynomials. We present new enumeration results for these multiples and provide some estimation on their degree distribution.