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Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Open Access Research Article

Cryptanalysis of RSA with smooth prime sum

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pp. 2183–2203Vol. 26Issue 8December 2023DOI: 10.1080/09720529.2021.2000152 Crossmark XML
Received:
01 Apr 2021
Accepted:
01 Jul 2021
Published Online:
18 Aug 2022
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1461
Pages:
2183–2203

Abstract

Let N = pq be an RSA modulus with balanced prime factors, that is q < p < 2q. There exist infinitely many integers x, y and z such that ex - ϕ (N ) y = ( p + q -1)z. We show that if the prime sum p + q -1 has only small prime factors and e satisfies an equation of the form ex - ϕ (N ) y = ( p + q -1)z with suitably small integers x, y and Z, then one can factor the RSA modulus in polynomial time. In addition we show that the number of such RSA moduli, as well as the number of exponents that are vulnerable to our attack is non-negligible.

Keywords

Subject Classifications

94A60

References

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