Abstract
Elliptic Curve Cryptography is gaining popularity, and optimization opportunities exist on several different levels: algorithm, architecture, and/or implementation. To support a wide variety of curves and at the same time resist timing/power-based side-channel attacks, our scalar multiplication is implemented using the Co-Z ladder due to Hutter, Joye, and Sierra. We analyze the parallelism of the Co-Z ladder and show that a 12-core (though inefficient) system can complete a ladder step with the fastest speed. We also combine optimizations at every level in an efficient multi-core FPGA implementation. The size of the prime modulus can also be changed easily, for which we have implemented and tested up to 528-bits used in the NIST P-521 curve. Based on this building block, we have developed a multi-core architecture that supports multiple parallel modular additions, multiplications, and inverses.
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Peng, BY., Hsu, YC., Chen, YJ., Chueh, DC., Cheng, CM., Yang, BY. (2016). Multi-core FPGA Implementation of ECC with Homogeneous Co-Z Coordinate Representation. In: Foresti, S., Persiano, G. (eds) Cryptology and Network Security. CANS 2016. Lecture Notes in Computer Science(), vol 10052. Springer, Cham. https://doi.org/10.1007/978-3-319-48965-0_42
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DOI: https://doi.org/10.1007/978-3-319-48965-0_42
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