Re-randomize and Extract: A Novel Commitment Construction Framework Based on Group Actions

Abstract. Cryptographic group actions have attracted growing attention as a useful tool for constructing cryptographic schemes. Among their applications, commitment schemes are particularly interesting as fundamental primitives, playing a crucial role in protocols such as zero-knowledge proofs, multi-party computation, and more. In this paper, we introduce a novel framework to construct commitment schemes based on cryptographic group actions. Specifically, we propose two key techniques for general group actions: re-randomization and randomness extraction. Roughly speaking, a re-randomization algorithm introduces randomness within an orbit for any input element, while a randomness extractor maps this randomness to uniformity over the message space. We demonstrate that 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. Moreover, we extend our framework to support the construction of commitments with additional desirable properties beyond hiding and binding, such as dual-mode commitments and enhanced linkable commitments. These extensions are achieved by further adapting the extractor to satisfy trapdoor or homomorphic properties. Finally, we instantiate all our proposed commitment schemes using lattices, specifically leveraging the lattice isomorphism problem (LIP) and the lattice automorphism problem (LAP) as underlying cryptographic assumptions. To the best of our knowledge, this is the first commitment scheme construction based on LIP/LAP. Additionally, we use LIP to provide a repair and improvement to the tensor isomorphism-based non-interactive commitment scheme proposed by D’Alconzo, Flamini, and Gangemi (ASIACRYPT 2023), which was recently shown to be insecure by an attack from Gilchrist, Marco, Petit, and Tang (CRYPTO 2024).

Recommended citation: K. Jiang, A. Wang, H. Luo, G. Liu, G. Tang, Y. Pan and X. Wang. Re-randomize and Extract: A Novel Commitment Construction Framework Based on Group Actions. In: Fehr, S., Fouque, PA. (eds) Advances in Cryptology – EUROCRYPT 2025. EUROCRYPT 2025. Lecture Notes in Computer Science, vol 15602. Springer, Cham. https://doi.org/10.1007/978-3-031-91124-8_5
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