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- W2143460029 abstract "The algorithm of Tonelli and Shanks for computing square roots modulo a prime number is the most used, and probably the fastest among the known algorithms when averaged over all prime numbers. However, for some particular prime numbers, there are other algorithms which are considerably faster. In this paper we compare the algorithm of Tonelli and Shanks with an algorithm based in quadratic field extensions due to Cipolla, and give an explicit condition on a prime number to decide which algorithm is faster. Finally, we show that there exists an infinite sequence of prime numbers for which the algorithm of Tonelli and Shanks is asymptotically worse." @default.
- W2143460029 created "2016-06-24" @default.
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- W2143460029 date "2002-01-01" @default.
- W2143460029 modified "2023-10-12" @default.
- W2143460029 title "Square Roots Modulo p" @default.
- W2143460029 cites W2078645706 @default.
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- W2143460029 doi "https://doi.org/10.1007/3-540-45995-2_38" @default.
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