SIGNITC: Supersingular Isogeny Graph Non-Interactive Timed Commitments

Knud Ahrens

Paper 2024/1225

SIGNITC: Supersingular Isogeny Graph Non-Interactive Timed Commitments

Knud Ahrens, University of Passau

Abstract

Non-Interactive Timed Commitment schemes (NITC) allow to open any commitment after a specified delay. This is useful for sealed bid auctions and as primitive for more complex protocols. We present the first NITC without repeated squaring or black box algorithms like generic NIZK proofs or generic one-way functions. It has fast verification, almost arbitrary delay and satisfies IND-CCA hiding and perfect binding. Our protocol is based on isogenies between supersingular elliptic curves making it presumably quantum secure. It needs no trusted setup and can use a wide variety of primes. We also have a SageMath implementation.

Note: Revision 1: Minor changes to algorithms for commitment generation and decommitment verification to improve speed. Revision 2: Changes to algorithms for commitment generation and decommitment verification to include higher dimensional IdealToIsogeny algorithms. Also fixed problems with KLPT and pushforwards. Revision 3: Major revision with three main points. 1) We changed the algorithms for commitment generation and decommitment verification to use FullRepresentInteger to find shortcuts. This eliminates the need for KLPT or higher dimensional IdealToIsogeny algorithms and is more efficient. 2) We added a subsection on parallelization and updated the parameters. 3) We added an implementation and benchmarks.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: non-interactive timed commitments post-quantum isogeny walks Deuring correspondence
Contact author(s): knud ahrens @ uni-passau de
History: 2025-10-16: last of 3 revisions; 2024-07-31: received; See all versions
Short URL: https://ia.cr/2024/1225
License: CC BY

BibTeX

@misc{cryptoeprint:2024/1225,
      author = {Knud Ahrens},
      title = {{SIGNITC}: Supersingular Isogeny Graph Non-Interactive Timed Commitments},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/1225},
      year = {2024},
      url = {https://eprint.iacr.org/2024/1225}
}