GCD calculation in the search task of pseudoprime and strong pseudoprime numbers

Abstract

© 2016, Pleiades Publishing, Ltd.Integer n is called pseudoprime (psp) relative to base a if n is composite, (a, n) = 1, and an−1 mod n = 1. Integer n is called strong pseudoprime (spsp) relative to base a if n is composite, (a, n) = 1, and, ad mod n = 1, or, ad2i mod n = −1, where n −1 = 2s * d, d is odd, 0 ≤ i < s. Pseudoprime and strong pseudoprime numbers are used in public-key cryptography in probabilistic tests. We use recurrent sequences in the task of search pseudoprime and strong pseudoprime numbers. This article describes acceleration of GCD calculation.