Identity-Based Threshold Signatures from Isogenies

Shahla Atapoor

Paper 2023/1459

Identity-Based Threshold Signatures from Isogenies

Shahla Atapoor

, COSIC, KU Leuven, Leuven, Belgium

Abstract

The identity-based signature, initially introduced by Shamir [Sha84], plays a fundamental role in the domain of identity-based cryptography. It offers the capability to generate a signature on a message, allowing any user to verify the authenticity of the signature using the signer's identifier information (e.g., an email address), instead of relying on a public key stored in a digital certificate. Another significant concept in practical applications is the threshold signature, which serves as a valuable tool for distributing the signing authority. The notion of an identity-based threshold signature scheme pertains to the distribution of a secret key associated with a specific identity among multiple entities, rather than depending on a master secret key generated by a public key generator. This approach enables a qualified group of participants to jointly engage in the signing process. In this paper, we present two identity-based threshold signature schemes based on isogenies, each of which addresses a different aspect of security. The first scheme prioritizes efficiency but offers security with abort, while the second scheme focuses on robustness. Both schemes ensure active security in the quantum random oracle model. To build these identity-based threshold signatures, we begin by modifying the identity-based signature scheme proposed by Shaw and Dutta [SD21], to accommodate the CSI-SharK signature scheme. Subsequently, we leverage the resulting identity-based signature and build two threshold schemes within the CSIDH (Commutative Supersingular Isogeny Diffie-Hellman) framework. Our proposed identity-based threshold signatures are designed based on CSI-SharK and can be easily adapted with minimal adjustments to function with CSI-FiSh.

Note: This is the full version of the IMACC'23 paper.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Published elsewhere. Major revision. IMACC 2023 - 19th IMA Conference on Cryptography and Coding Theory
Keywords: Identity-based signature Identity-based threshold signature Isogeny-based cryptography CSI-SharK CSI-FiSh CSIDH
Contact author(s): sh_atapoor @ yahoo com
History: 2023-09-24: approved; 2023-09-23: received; See all versions
Short URL: https://ia.cr/2023/1459
License: CC BY

BibTeX

@misc{cryptoeprint:2023/1459,
      author = {Shahla Atapoor},
      title = {Identity-Based Threshold Signatures from Isogenies},
      howpublished = {Cryptology ePrint Archive, Paper 2023/1459},
      year = {2023},
      note = {\url{https://eprint.iacr.org/2023/1459}},
      url = {https://eprint.iacr.org/2023/1459}
}