[Resource Topic] 2022/880: Efficient supersingularity testing over $\mathbb{F}_p$ and CSIDH key validation

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Efficient supersingularity testing over \mathbb{F}_p and CSIDH key validation

Authors: Gustavo Banegas, Valerie Gilchrist, and Benjamin Smith


Many public-key cryptographic protocols, notably non-interactive key exchange (NIKE), require incoming public keys to be validated to mitigate some adaptive attacks. In CSIDH, an isogeny-based post-quantum NIKE, a key is deemed legitimate if the given Montgomery coefficient specifies a supersingular elliptic curve over the prime field. In this work, we survey the current supersingularity tests used for CSIDH key validation, and implement and measure two new alternative algorithms. Our implementation shows that we can determine supersingularity substantially faster, and using less memory, than the state-of-the-art.

ePrint: https://eprint.iacr.org/2022/880

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Talk by V.Gilchrist at the isogeny days in Leuven.

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