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Composite Numbers That Give Valid RSA Key Pairs for Any Coprime p

Department of Computer Science, US Air Force Academy, Colorado Springs, CO 80840, USA
Information 2018, 9(9), 216; https://doi.org/10.3390/info9090216
Received: 13 August 2018 / Revised: 23 August 2018 / Accepted: 25 August 2018 / Published: 28 August 2018
(This article belongs to the Section Information Theory and Methodology)
RSA key pairs are normally generated from two large primes p and q. We consider what happens if they are generated from two integers s and r, where r is prime, but unbeknownst to the user, s is not. Under most circumstances, the correctness of encryption and decryption depends on the choice of the public and private exponents e and d. In some cases, specific ( s , r ) pairs can be found for which encryption and decryption will be correct for any ( e , d ) exponent pair. Certain s exist, however, for which encryption and decryption are correct for any odd prime r s . We give necessary and sufficient conditions for s with this property. View Full-Text
Keywords: cryptography; abstract algebra; RSA; computer science education; cryptography education cryptography; abstract algebra; RSA; computer science education; cryptography education
MDPI and ACS Style

Fagin, B. Composite Numbers That Give Valid RSA Key Pairs for Any Coprime p. Information 2018, 9, 216.

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