A Randomized Montgomery Powering Ladder Exponentiation for Side-Channel Attack Resilient RSA and Leakage Assessment

Abstract

This paper presents a randomized Montgomery Powering Ladder Modular Exponentiation (RMPLME) scheme for side channel attacks (SCA) resistant Rivest-Shamir-Adleman (RSA) and its leakage resilience analysis. This method randomizes the computation time of square-and-multiply operations for each exponent bit of the Montgomery Powering Ladder (MPL) based RSA exponentiation using various radices (Radix – 2, 22, and 24) based Montgomery Modular multipliers (MMM) randomly. The randomized computations of RMPLME generates non-uniform timing channels information and power traces thus protecting against SCA. In this work, we have developed and implemented a) an unmasked right-to-left Montgomery Modular Exponentiation (R-L MME), b) MPL exponentiation and c) the proposed RMPLME schemes for RSA decryption. All the three realizations have been assessed for side channel leakage using Welch’s t-test and analyzed for secured realizations based on degree of side channel information leakage. RMPLME scheme shows the least side-channel leakage and resilient against SPA, DPA, C-Safe Error, CPA and Timing Attacks.