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Computational Number Theory and Applications to Cryptography Wyoming Summer School, June 19–July 7, 2006

• Greatest common divisor (GCD) algorithms. We begin with Euclid’s algorithm, and the extended Euclidean algorithm [2, 12]. We will then discuss variations and improvements such as Lehmer’s algorithm [14], the binary algorithms [12], generalized binary algorithms [20], and FFT-based methods. We will also discuss how to adapt GCD algorithms to compute modular inverses and to compute the Jacobi and Legendre symbols [9].