$\phi(n)$-evaluation algorithm: a novel approach for  an efficient retrieval of Euler's totient of an RSA Modulus

Jay Mehta; Hitarth Rana

Paper 2026/219

$\phi(n)$-evaluation algorithm: a novel approach for an efficient retrieval of Euler's totient of an RSA Modulus

Jay Mehta

, Department of Mathematics Sardar Patel University

Hitarth Rana

, Department of Mathematics Sardar Patel University

Abstract

In this paper, we propose an algorithm to efficiently retrieve the value of Euler's totient function of an RSA modulus, consequently voiding the RSA encryption. Furthermore, we show that the proposed algorithm is significantly faster and more effective when the prime factors of an RSA modulus are closer to each other. We conjecture a relation between the difference of two prime factors of the RSA modulus and the required number of steps for the algorithm.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: RSA cryptanalysis Euler's totient factorization prime gap bounds for phi(n)
Contact author(s): jay_mehta @ spuvvn edu
hitarth rana @ spuvvn edu
History: 2026-02-12: approved; 2026-02-10: received; See all versions
Short URL: https://ia.cr/2026/219
License: CC BY-NC-ND

BibTeX

@misc{cryptoeprint:2026/219,
      author = {Jay Mehta and Hitarth Rana},
      title = {$\phi(n)$-evaluation algorithm: a novel approach for  an efficient retrieval of Euler's totient of an {RSA} Modulus},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/219},
      year = {2026},
      url = {https://eprint.iacr.org/2026/219}
}