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On the Optimality of the Binary Algorithm for the Jacobi Symbol
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On the Optimality of the Binary Algorithm for the Jacobi Symbol
Fundamenta Informaticae
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We present a new algorithm to compute the Jacobi symbol, based on Stein's binary algorithm for the greatest common divisor, and we determine the worst-case behavior of this algorithm. Our implementation of the algorithm runs approximately 7--25% faster than traditional methods on inputs of size 100--1000 decimal digits.