How Secure is Exponent-blinded RSA–CRT with Sliding Window Exponentiation?
Keywords:Cache attack, Simple power analysis, Partial key exposure attack, Exponent blinding, Sliding window exponentiation, Side-channel attack, RSA–CRT
This paper presents the first security evaluation of exponent-blinded RSA–CRT implementation with sliding window exponentiation against cache attacks. Our main contributions are threefold. (1) We demonstrate an improved cache attack using Flush+Reload on RSA–CRT to estimate the squaring–multiplication operational sequence. The proposed method can estimate a correct squaring–multiplication sequence from one Flush+Reload trace, while the existing Flush+Reload attacks always contain errors in the sequence estimation. This is mandatory for the subsequent steps in the proposed attack. (2) We present a new and first partial key exposure attack on exponent-blinded RSA–CRT with a random-bit leak. The proposed attack first estimates a random mask for blinding exponent using a modification of the Schindler–Wiemers continued fraction attack, and then recovers the secret key using an extension of the Heninger–Shacham branch-and-prune attack. We experimentally show that the proposed attack on RSA–CRT using a practical window size of 5 with 16-, 32-, and 64-bit masks is carried out with complexity of 225.6, 267.7, and 2161, respectively. (3) We then investigate the tradeoffs between mask bit length and implementation performance. The computational cost of exponent-blinded RSA–CRT using a sliding window with a 32- and 64-bit mask are 15% and 10% faster than that with a 128-bit mask, respectively, as we confirmed that 32- and 64-bit masks are sufficient to defeat the proposed attack. Our source code used in the experiment is publicly available.
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Copyright (c) 2023 Rei Ueno, Naofumi Homma
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