Abstract
The isogeny-based protocols SIDH and SIKE have received much attention for being post-quantum key agreement candidates that retain relatively small keys. A recent line of work has proposed and further improved compression of public keys, leading to the inclusion of public-key compression in the SIKE proposal for Round 2 of the NIST Post-Quantum Cryptography Standardization effort. We show how to employ the dual isogeny to significantly increase performance of compression techniques, reducing their overhead from 160–182% to 77–86% for Alice’s key generation and from 98–104% to 59–61% for Bob’s across different SIDH parameter sets. For SIKE, we reduce the overhead of (1) key generation from 140–153% to 61–74%, (2) key encapsulation from 67–90% to 38–57%, and (3) decapsulation from 59–65% to 34–39%. This is mostly achieved by speeding up the pairing computations, which has until now been the main bottleneck, but we also improve (deterministic) basis generation.
J. Renes—Partially supported by the Technology Foundation STW (project 13499 – TYPHOON & ASPASIA), from the Dutch government.
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- 1.
The implementation is available as part of the SIDH Library v3.2, https://github.com/microsoft/PQCrypto-SIDH.
- 2.
Note that when considering \(\phi _{\ell }\) of degree \(\ell ^{e_\ell }\), we generate a basis of the \(m^{e_m}\)-torsion.
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Acknowledgements
We thank the anonymous reviewers for their detailed remarks and Paulo S.L.M. Barreto for valuable feedback to improve the paper.
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Naehrig, M., Renes, J. (2019). Dual Isogenies and Their Application to Public-Key Compression for Isogeny-Based Cryptography. In: Galbraith, S., Moriai, S. (eds) Advances in Cryptology – ASIACRYPT 2019. ASIACRYPT 2019. Lecture Notes in Computer Science(), vol 11922. Springer, Cham. https://doi.org/10.1007/978-3-030-34621-8_9
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