Resisting HODPA attacks in modular exponentiation using inner product with differential evolution

Abstract

This paper presents a secured computation of modular exponentiation to resist higher-order differential power analysis (HODPA) attacks in asymmetric cryptosystems like RSA. HODPA attacks can be resisted by segmenting secret sensitive data and its intermediate values into multiple shares. In modular exponentiation-based cryptosystems, the exponent plays a significant part in the secret key. We have used inner product with differential evolution algorithm to segment the exponent into multiple shares. Using entropy-based nearest neighbor algorithm, we have randomly computed independent modular exponentiation to resist SPA and DPA attacks. Analysis was done on 1024, 1536 and 2048 bit RSA. With a pre-computation complexity, the proposed approach can provide significant resistance to SPA, DPA and HODPA attacks against modular exponentiation-based cryptosystems.