Efficient Solution of Large Sparse Linear Equations
نویسنده
چکیده
Algebraic attacks is a powerful type of attacks against LFSR-based stream ciphers. Solving large sparse linear equations Ax = b is needed for this attack. The traditional Gaussian elimination is not efficient for such matrix equations because of its cube run time complexity. Quadratic run time algorithms like Lanczos or Wiedemann Methods are the better for such large sparse matrices. We implemented efficiently the Wiedemann algorithm and its application for Algebraic Attacks on Stream Ciphers. Our implementation works for matrices of sizes up to 10 with average sparsity 20. A little modification of Wiedemann algorithm is proposed which is very efficient compare to the Wiedemann method if the period of the matrix is O(n), where n is the size of the system matrix. Periodicity of any matrix A ∈ GF2(n) is being studied. Also the relations between its characteristic polynomial and periodicity are shown.
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