Analysis and design of stream ciphers
Analysis and design of stream ciphers
Multiplicative Difference Sets via Additive Characters
Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
Linear Codes in Constructing Resilient Functions with High Nonlinearity
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
Maximum Correlation Analysis of Nonlinear S-boxes in Stream Ciphers
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
The Filter-Combiner Model for Memoryless Synchronous Stream Ciphers
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Improved Construction of Nonlinear Resilient S-Boxes
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Decrypting a Class of Stream Ciphers Using Ciphertext Only
IEEE Transactions on Computers
The bit extraction problem or t-resilient functions
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
On the construction of highly nonlinear permutations
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
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
Binary m-sequences with three-valued crosscorrelation: a proof of Welch's conjecture
IEEE Transactions on Information Theory
Maximal recursive sequences with 3-valued recursive cross-correlation functions (Corresp.)
IEEE Transactions on Information Theory
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We investigate the security of n-bit to m-bit vectorial Boolean functions in stream ciphers. Such stream ciphers have higher throughput than those using single-bit output Boolean functions. However, as shown by Zhang and Chan at Crypto 2000, linear approximations based on composing the vector output with any Boolean functions have higher bias than those based on the usual correlation attack. In this paper, we introduce a new approach for analyzing vector Boolean functions called generalized correlation analysis. It is based on approximate equations which are linear in the input x but of free degree in the output z = F(x). Based on experimental results, we observe that the new generalized correlation attack gives linear approximation with much higher bias than the Zhang-Chan and usual correlation attacks. Thus it can be more effective than previous methods. First, the complexity for computing the generalized nonlinearity for this new attack is reduced from 22m×n+n to 22n. Second, we prove a theoretical upper bound for generalized nonlinearity which is much lower than the unrestricted nonlinearity (for Zhang-Chan's attack) or usual nonlinearity. This again proves that generalized correlation attack performs better than previous correlation attacks. Third, we introduce a generalized divide-and-conquer correlation attack and prove that the usual notion of resiliency is enough to protect against it. Finally, we deduce the generalized nonlinearity of some known secondary constructions for secure vector Boolean functions.