The implementation is optimized for clarity, not for speed. Pick a characteristic polynomial of some degree \(n\), where each monomial coefficient is either 0 or 1 (so the coefficients are drawn from \(\text\) modulo the characteristic polynomial equals \(x^0\).įor each \(k\) such that \(k < n\) and \(k\) is a factor of \(2^n - 1\), \(x^k\) modulo the characteristic polynomial does not equal \(x^0\).įast skipping in \(Î(\log k)\) time can be accomplished by exponentiation-by-squaring followed by a modulo after each square. Its setup and operation are quite simple: Here we will focus on the Galois LFSR form, not the Fibonacci LFSR form. A linear feedback shift register (LFSR) is a mathematical device that can be used to generate pseudorandom numbers.
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