Solving bivariate quadratic congruences in random polynomial time
Authors: Leonard M. Adleman, Dennis R. Estes and Kevin S. McCurley
Journal: Math. Comp. 48 (1987), 17-28
MSC: Primary 11Y16; Secondary 11A07, 11Y05
MathSciNet review: 866095
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Abstract: It has been known for some time that solving is as difficult as factoring n, at least in the sense that the two problems are random polynomial time equivalent. By contrast, solving a bivariate quadratic congruence can usually be done in random polynomial time even if the factorization of n is unknown. This was first proved by Pollard and Schnorr in 1985 under the assumption of the Piltz conjecture for Dirichlet L-functions. We now prove the result without assuming any unproved hypothesis.
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