How Mathematics Keeps Our Data Safe: The RSA Cryptosystem for Regular Numbers

Modern Internet applications, such as online banking, private chats and blockchains, rely on secure cryptographic techniques that require profound mathematical knowledge, particularly in modular arithmetic—a subfield of number theory. This article, aimed at non-experts, promotes a basic understanding of modular arithmetic by examining the RSA cryptosystem and its recent multi-prime multi-power generalization for moduli n > 1 and messages which are regular modulo n. While, at first glance, this generalization appears to restrict the message space, it is shown that this restriction is negligible in practice, since under reasonable assumptions almost all messages are regular modulo n. The article can be read without deep mathematical prerequisites. Key concepts, such as modular arithmetic, are introduced where necessary and illustrated with examples.