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Information 2018, 9(9), 216; https://doi.org/10.3390/info9090216

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
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)
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Abstract

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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Fagin, B. Composite Numbers That Give Valid RSA Key Pairs for Any Coprime p. Information 2018, 9, 216.

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