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Square and Cube Root Algorithms in Finite Field and Their Applications
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 Title & Authors
Square and Cube Root Algorithms in Finite Field and Their Applications
Cho, Gook Hwa; Ha, Eunhye; Koo, Namhun; Kwon, Soonhak;
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We study an algorithm that can efficiently find square roots and cube roots by modifying Tonelli-Shanks algorithm, which has an application in Number Field Sieve (NFS). The Number Field Sieve, the fastest known factoring algorithm, is a powerful tool for factoring very large integer. NFS first chooses two polynomials having common root modulo N, and it consists of the following four major steps; 1. Polynomial Selection 2. Sieving 3. Matrix 4. Square Root. The last step of NFS needs the process of square root computation in Number Field, which can be computed via square root algorithm over finite field.
NFS;Tonelli-Shanks algorithm;CRT;Finite Field;
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