## Cryptology ePrint Archive: Report 2016/672

Post-Quantum Cryptography on FPGA Based on Isogenies on Elliptic Curves

Brian Koziel, Reza Azarderakhsh, Mehran Mozaffari Kermani, David Jao

Abstract: To the best of our knowledge, we present the first hardware implementation of isogeny-based cryptography available in the literature. Particularly, we present the first implementation of the supersingular isogeny Diffie-Hellman (SIDH) key exchange, which features quantum-resistance. We optimize this design for speed by creating a high throughput multiplier unit, taking advantage of parallelization of arithmetic in $\mathbb{F}_{p^{2}}$, and minimizing pipeline stalls with optimal scheduling. Consequently, our results are also faster than software libraries running affine SIDH even on Intel Haswell processors. For our implementation at 85-bit quantum security and 128-bit classical security, we generate ephemeral public keys in 1.655 million cycles for Alice and 1.490 million cycles for Bob. We generate the shared secret in an additional 1.510 million cycles for Alice and 1.312 million cycles for Bob. On a Virtex-7, these results are approximately 1.5 times faster than known software implementations running the same 512-bit SIDH. Our results and observations show that the isogeny-based schemes can be implemented with high efficiency on reconfigurable hardware.

Category / Keywords: Post-quantum cryptography, elliptic curve cryptography (ECC), isogeny-based cryptography, Field Programmable Gate Array (FPGA)

Original Publication (with minor differences): IEEE Transactions on Circuits and Systems (TCAS-I)

Date: received 4 Jul 2016, last revised 17 Sep 2016, withdrawn 3 Nov 2016

Contact author: azarderakhsh at gmail com

Available format(s): (-- withdrawn --)

Short URL: ia.cr/2016/672

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