Optimized Modular Multiplication for Supersingular Isogeny Diffie-Hellman

Maire O'Neill; Weiqiang Liu; Jian Ni; Zhe Liu; Chunyang Liu

doi:10.1109/TC.2019.2899847

Optimized Modular Multiplication for Supersingular Isogeny Diffie-Hellman

Maire O'Neill, Weiqiang Liu, Jian Ni, Zhe Liu, Chunyang Liu

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Abstract

Recent progress in quantum physics shows that quantum computers may be a reality in the not too distant future. Postquantum cryptography (PQC) refers to cryptographic schemes that are based on hard problems which are believed to be resistant to attacks from quantum computers. The supersingular isogeny Diffie-Hellman (SIDH) key exchange protocol shows promising security properties among various post-quantum cryptosystems that have been proposed. In this paper, we propose two efficient modular multiplication algorithms with special primes that can be used in SIDH key exchange protocol. Hardware architectures for the two proposed algorithms are also proposed. The hardware implementations are provided and compared with the original modular multiplication algorithm. The results show that the proposed finite field multiplier is over 6.79 times faster than the original multiplier in hardware. Moreover, the SIDH hardware/software codesign implementation using the proposed FFM2 hardware is over 31% faster than the best SIDH software implementation.

Original language	English
Pages (from-to)	1249
Journal	IEEE Transactions on Computers
Volume	68
Issue number	8
DOIs	https://doi.org/10.1109/TC.2019.2899847
Publication status	Published - 21 Feb 2019

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Optimized Modular Multiplication for Supersingular Isogeny Diffie-Hellman
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Maire O'Neill
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abstract = "Recent progress in quantum physics shows that quantum computers may be a reality in the not too distant future. Postquantum cryptography (PQC) refers to cryptographic schemes that are based on hard problems which are believed to be resistant to attacks from quantum computers. The supersingular isogeny Diffie-Hellman (SIDH) key exchange protocol shows promising security properties among various post-quantum cryptosystems that have been proposed. In this paper, we propose two efficient modular multiplication algorithms with special primes that can be used in SIDH key exchange protocol. Hardware architectures for the two proposed algorithms are also proposed. The hardware implementations are provided and compared with the original modular multiplication algorithm. The results show that the proposed finite field multiplier is over 6.79 times faster than the original multiplier in hardware. Moreover, the SIDH hardware/software codesign implementation using the proposed FFM2 hardware is over 31% faster than the best SIDH software implementation.",

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AU - O'Neill, Maire

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AU - Ni, Jian

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AU - Liu, Chunyang

PY - 2019/2/21

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Optimized Modular Multiplication for Supersingular Isogeny Diffie-Hellman

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