Seminario: "Advances in Non-Interactive Commitments from Cryptographic Group Actions" - Andrea Gangemi

Advances in Non-Interactive Commitments from Cryptographic Group Actions

Andrea Gangemi (Politecnico di Torino)
Mercoledì 24 Giugno 2025 - ore 15:00

Online seminars - Gruppo UMI Crittografia e Codici

Abstract: We present recent advances in non-interactive commitment schemes starting from group actions. D’Alconzo, Flamini, and Gangemi (ASIACRYPT 2023) initiate this line of work by proposing a commitment scheme based on non-transitive group actions, using tensor rank as an orbit invariant. Their construction achieves computational hiding, perfect binding, and introduces a novel linkability property. Later, Gilchrist et al. (CRYPTO 2024) demonstrate that this scheme is vulnerable: by exploiting low-rank structure in special orbits, they break the hiding property. They then repair the scheme by moving to the general Tensor Isomorphism Problem, which eliminates the exploitable structure and restores security. Building on these foundations, Jiang et al. (EUROCRYPT 2025) introduce a novel commitment framework called Re-randomize and Extract. They show how these techniques can significantly facilitate the construction of commitment schemes, providing a flexible framework for constructing either perfectly hiding or perfectly binding commitments, depending on the type of extractor involved. Their construction is then instantiated using lattice-based group actions. This framework not only generalizes prior tensor-based approaches but also supports more versatile commitment functionalities