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

DOI:
https://doi.org/10.1090/S0025-5718-1987-0866095-8

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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DOI:
https://doi.org/10.1090/S0025-5718-1987-0866095-8

Article copyright:
© Copyright 1987
American Mathematical Society