Abstract
The best known algorithm to compute the Jacobi symbol of two n-bit integers runs in time O(M(n)logn), using Schönhage’s fast continued fraction algorithm combined with an identity due to Gauss. We give a different O(M(n)logn) algorithm based on the binary recursive gcd algorithm of Stehlé and Zimmermann. Our implementation — which to our knowledge is the first to run in time O(M(n)logn) — is faster than GMP’s quadratic implementation for inputs larger than about 10000 decimal digits.
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Brent, R.P., Zimmermann, P. (2010). An O(M(n) logn) Algorithm for the Jacobi Symbol. In: Hanrot, G., Morain, F., Thomé, E. (eds) Algorithmic Number Theory. ANTS 2010. Lecture Notes in Computer Science, vol 6197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14518-6_10
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DOI: https://doi.org/10.1007/978-3-642-14518-6_10
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