## Cryptology ePrint Archive: Report 2021/1031

Commitment Schemes from Supersingular Elliptic Curve Isogeny Graphs

Bruno Sterner

Abstract: In this work we present two commitment schemes based on hardness assumptions arising from supersingular elliptic curve isogeny graphs, which possess strong security properties. The first is based on the CGL hash function while the second is based on the SIDH framework, both of which require a trusted third party for the setup phrase. The proofs of security of these protocols depend on properties of non-backtracking random walks on regular graphs. The optimal efficiency of these protocols depends on the size of a certain constant, defined in the paper, related to relevant isogeny graphs, which we give conjectural upper bounds for.

Category / Keywords: public-key cryptography / post-quantum cryptography, public-key cryptography, commitment schemes, isogeny-based cryptography, isogeny graphs

Original Publication (with minor differences): MathCrypt 2021