Bibliographic Information: Chung, K.-M., Hsieh, Y.-C., Huang, M.-Y., Huang, Y.-H., Lange, T., & Yang, B.-Y. (2024, November 19). Isogeny-based Group Signatures and Accountable Ring Signatures in QROM. arXiv. arXiv:2110.04795v4 [cs.CR]
Research Objective: This paper aims to construct the first provably secure group signatures (GS) and accountable ring signatures (ARS) based on isogeny-based assumptions in the quantum random oracle model (QROM).
Methodology: The authors introduce an intermediate primitive called the "openable sigma protocol" and demonstrate that any such protocol, when combined with the Fiat-Shamir transformation, yields secure GS and ARS schemes. They then construct a specific openable sigma protocol based on the decisional CSIDH assumption (D-CSIDH) and prove its security in the QROM, leveraging techniques like measure-and-reprogram and adaptive reprogramming.
Key Findings: The authors successfully construct the first provably QROM-secure ARS scheme from isogeny-based assumptions. They also achieve the first provably QROM-secure group signature and ring signature schemes, as ARS can be easily transformed into these primitives while preserving QROM security.
Main Conclusions: This work demonstrates the feasibility of constructing advanced cryptographic primitives like GS and ARS with group-action-based assumptions, even with their limited expressiveness compared to group-based assumptions. The proposed isogeny-based schemes offer a viable post-quantum alternative to existing lattice-based solutions, enhancing the resilience of cryptographic systems against quantum threats.
Significance: This research significantly advances the field of post-quantum cryptography by providing new constructions for essential cryptographic primitives based on the promising area of isogeny-based cryptography. It addresses the limitations of previous isogeny-based GS and ARS schemes that were only secure in the classical random oracle model (CROM) and were potentially vulnerable to quantum attacks.
Limitations and Future Research: The paper acknowledges the larger payload size of the proposed schemes as a trade-off for achieving QROM security. Future research could explore more efficient constructions or investigate the applicability of these techniques to other cryptographic primitives.
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