Fast algorithm for finding a small root of a quadratic modular equation
The security of some cryptosystems is based on the difficulty of solving a quadratic modular equation. This paper shows a new algorithm for finding the small root of the quadratic modular equation. While previous algorithms for finding the small root of the modular equation are based on the LLL algorithm, the new algorithm is based on the continued fraction. Using the new algorithm, we can find the root less than n1/4, where n is the modulus. The new algorithm is more efficient than previous algorithms even if the modulus is large.
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