Rewriting Variables: The Complexity of Fast Algebraic Attacks on Stream Ciphers

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.

• Type: Conference
• Year: 2004
• Where: CRYPTO
• Authors: Philip Hawkes, Gregory G. Rose
• Keywords: CRYPTO 2004, Fast Algebraic Attack, Fast Fourier Transform, Process Complexity