Article

Improved Cryptanalysis of the Multi-Power RSA Cryptosystem Variant

Authors:

Abderrahmane Nitaj,

Maher BoudabraAuthors Info & Claims

Progress in Cryptology - AFRICACRYPT 2023: 14th International Conference on Cryptology in Africa, Sousse, Tunisia, July 19–21, 2023, Proceedings

Pages 252 - 269

https://doi.org/10.1007/978-3-031-37679-5_11

Published: 19 July 2023 Publication History

Abstract

The multi-power RSA cryptosystem is a variant of RSA where the modulus is in the form

N = p^{r} q^{s}

with

max (r, s) \geq 2

. In the multi-power RSA variant, the decryption phase is much faster than the standard RSA. While RSA has been intensively studied, the security of the multi-power RSA variant needs to be deeply investigated.

In this paper, we consider a multi-power RSA cryptosystem with a modulus

N = p^{r} q^{s}

, and propose a method to solve the modular polynomial equations of the form

F (x) \equiv 0 (mod W p^{u} q^{v})

where F(x) is a polynomial with integer coefficients, W is a positive integer, and u, v are integers satisfying

0 \leq u \leq r

,

0 \leq v \leq s

, and

s u - r v \neq 0

. Our method is based on Coppersmith’s method and lattice reduction techniques.

We show that the new results retrieve or supersede the former results. Moreover, we apply the new method to study various instances of the multi-power RSA cryptosystem, especially when the private exponent is small, when the prime factors have a specific form, and when the least significant or the most significant bits of the private exponent are known.

References

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Information & Contributors

Information

Published In

cover image Guide Proceedings

Progress in Cryptology - AFRICACRYPT 2023: 14th International Conference on Cryptology in Africa, Sousse, Tunisia, July 19–21, 2023, Proceedings

Jul 2023

517 pages

ISBN:978-3-031-37678-8

DOI:10.1007/978-3-031-37679-5

Editors:
Nadia El Mrabet
EMSE, Saint-Étienne, France
,
Luca De Feo
IBM Research Europe, Rüschlikon, Switzerland
,
Sylvain Duquesne
Université de Rennes 1, Rennes Cedex, France

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 19 July 2023

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