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Improved Constant-Time Modular Inversion
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DOI：10.1007/978-981-95-2961-2_25.png)
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Abstract
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Constant-time modular inversion (CTMI) is a critical operation in secure elliptic curve cryptosystems. Existing CTMI algorithms include those by Bos, Bernstein and Yang, and Jin and Miyaji, denoted as BOS, BY, and JM. While BOS is constant-time, it incurs redundant computations in its iteration function. BY reduces iteration cost but increases the number of iterations, whereas JM balances both by incorporating a table-lookup function. We propose two new CTMI algorithms, KM1 and KM2, that improve upon JM by reducing table lookups and lowering iteration count. We prove that their iteration count is reduced by two compared to JM, and we implement both algorithms for practical evaluation. Experiments over NIST prime fields (P192, P224, P256, P384, P512) show that KM1 and KM2 achieve fewer average clock cycles than existing CTMI algorithms. These results demonstrate that the proposed algorithms are efficient and secure choices for modular inversion in side-channel-resistant elliptic curve cryptography.
Keywords:
Timing side-channel attack
Constant time modular inversion
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