Recently proposed algebraic attacks [2,6] and fast algebraic attacks [1,5] have provided the best analyses against some deployed LFSR-based ciphers. The process complexity is exponential in the degree of the equations. Fast algebraic attacks were introduced [5] as a way of reducing run-time complexity by reducing the degree of the system of equations. Previous reports on fast algebraic attacks [1,5] have underestimated the complexity of substituting the keystream into the system of equations, which in some cases dominates the attack. We also show how the Fast Fourier Transform (FFT) [4] can be applied to decrease the complexity of the substitution step. Finally, it is shown that all functions of degree d satisfy a common, function-independent linear combination that may be used in the pre-computation step of the fast algebraic attack. An explicit factorization of the corresponding characteristic polynomial yields the fastest known method for performing the pre-computation step. © International Association for Cryptologic Research 2004.
CITATION STYLE
Hawkes, P., & Rose, G. G. (2004). Rewriting variables: The complexity of fast algebraic attacks on stream ciphers. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3152, 390–406. https://doi.org/10.1007/978-3-540-28628-8_24
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