%0 Journal Article
%T A Secure Algorithm for Inversion Modulo 2k
%A Carles Ferrer
%A Sadiel De la Fe
%J -
%D 2018
%R https://doi.org/10.3390/cryptography2030023
%X Abstract Modular inversions are widely employed in public key crypto-systems, and it is known that they imply a bottleneck due to the expensive computation. Recently, a new algorithm for inversions modulo p k was proposed, which may speed up the calculation of a modulus dependent quantity used in the Montgomery multiplication. The original algorithm lacks security countermeasures; thus, a straightforward implementation may expose the input. This is an issue if that input is a secret. In the RSA-CRT signature using Montgomery multiplication, the moduli are secrets (primes p and q). Therefore, the moduli dependent quantities related to p and q must be securely computed. This paper presents a security analysis of the novel method considering that it might be used to compute secrets. We demonstrate that a Side Channel Analysis leads to disclose the data being manipulated. In consequence, a secure variant for inversions modulo 2 k is proposed, through the application of two known countermeasures. In terms of performance, the secure variant is still comparable with the original one. View Full-Tex
%K modular inversion
%K montgomery multiplication
%K RSA
%K side channel attack
%U https://www.mdpi.com/2410-387X/2/3/23