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A simple and fast probabilistic algorithm for computing square roots modulo a prime number (Corresp.)

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A probabilistic polynomial-time algorithm for computing the square root of a numberx in {bf Z}/P{bf Z}, whereP = 2^{S}Q + 1(Qodd,s > 0)is a prime number, is described. In contrast to the Adleman, Manders, and Miller algorithm, this algorithm gets faster as s grows. As with the Berlekamp-Rabin algorithm, the expected running time of the algorithm is independent ofx. However, the algorithm presented here is considerably faster for values ofsgreater than2.

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Information Theory, IEEE Transactions on  (Volume:32 ,  Issue: 6 )