Multi-core FPGA Implementation of ECC with Homogeneous Co-Z Coordinate Representation

Peng, Bo-Yuan; Hsu, Yuan-Che; Chen, Yu-Jia; Chueh, Di-Chia; Cheng, Chen-Mou; Yang, Bo‐Yin

doi:10.1007/978-3-319-48965-0_42

Cited by 2 publications

(1 citation statement)

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“…Bos [3] introduced a low-latency 7-way GPU implementation of an (X, Z)-only Co-Z ladder for the NIST curve P-224. Peng et al [22] presented an optimized multi-core FPGA implementation of the X-only Co-Z ladder from [13] for a set of Weierstrass curves, whereby they combined a number of Montgomery modular multipliers to work in parallel. They concluded that a 3-core implementation achieves the best throughput-resource ratio.…”

Section: Overview Of Related Work and Motivation For Our Workmentioning

confidence: 99%

Parallel Implementation of SM2 Elliptic Curve Cryptography on Intel Processors with AVX2

Huang

Liu

et al. 2020

Information Security and Privacy

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This paper presents an efficient and secure implementation of SM2, the Chinese elliptic curve cryptography standard that has been adopted by the International Organization of Standardization (ISO) as ISO/IEC 14888-3:2018. Our SM2 implementation uses Intel's Advanced Vector Extensions version 2.0 (AVX2), a family of three-operand SIMD instructions operating on vectors of 8, 16, 32, or 64-bit data elements in 256-bit registers, and is resistant against timing attacks. To exploit the parallel processing capabilities of AVX2, we studied the execution flows of Co-Z Jacobian point arithmetic operations and introduce a parallel 2-way Co-Z addition, Co-Z conjugate addition, and Co-Z ladder algorithm, which allow for fast Co-Z scalar multiplication. Furthermore, we developed an efficient 2-way prime-field arithmetic library using AVX2 to support our Co-Z Jacobian point operations. Both the field and the point operations utilize branch-free (i.e. constant-time) implementation techniques, which increase their ability to resist Simple Power Analysis (SPA) and timing attacks. Our software for scalar multiplication on the SM2 curve is, to our knowledge, the first constant-time implementation of the Co-Z based ladder that leverages the parallelism of AVX2.

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Section: Overview Of Related Work and Motivation For Our Workmentioning

confidence: 99%