Abstract
This chapter extends Chap. 3 by giving a complete description of the solutions of systems of two or more simultaneous linear congruences. One solution method, for pairwise coprime moduli, uses Bezout’s Identity and yields the Chinese Remainder Theorem. An immediate application of this case is to speed up the decryption of messages in an RSA cryptosystem. For the general case of systems of congruences to non-coprime moduli, we show how to decide if solutions exist, and if so, how to find all of the solutions.
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Childs, L.N. (2019). Solving Systems of Congruences. In: Cryptology and Error Correction. Springer Undergraduate Texts in Mathematics and Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-15453-0_11
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DOI: https://doi.org/10.1007/978-3-030-15453-0_11
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-15451-6
Online ISBN: 978-3-030-15453-0
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