Solving Bivariate Quadratic Congruences in Random Polynomial Time
نویسندگان
چکیده
It has been known for some time that solving x2 = a (modn) 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 x2 ky2 = m (mod n) 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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