Post-Quantum Cyptography based on Codes: Ternary Syndrome Decoding
code-based cryptography, ternary syndrome decoding with large weight, decoding attack
Description
Due to the recent advances in quantum computers, the search for cryptosystems that survive quantum attacks is of great interest. Code-based cryptography is a promising candidate, since it is build on the NP-hard problem of decoding a random code [2].
Recently, different variants of the classical syndrome decoding problem (SDP) in the Hamming metric have been proposed [1,3].
The main reason for this is that it appears hard to build an efficient digital signature scheme around the classical SDP.
One such variant is the ternary syndrome decoding with large weight, in which the error has few or no zero-entries [1].
The goal of this topic is understanding the properties of the decoding problem and analyzing the cost of existing solvers such as Sterns algorithm [2].
Main Paper:
[1] Bricout, R., Chailloux, A., Debris-Alazard, T., & Lequesne, M. (2020). Ternary syndrome decoding with large weight. In Selected Areas in Cryptography–SAC 2019: 26th International Conference, Waterloo, ON, Canada, August 12–16, 2019, Revised Selected Papers 26 (pp. 437-466). Springer International Publishing.
can be found here: https://arxiv.org/pdf/1903.07464.pdf
References:
[2] Weger, V., Gassner, N., & Rosenthal, J. (2022). A Survey on Code-Based Cryptography. arXiv preprint arXiv:2201.07119.
[3] Baldi, M., Bitzer, S., Pavoni, A., Santini, P., Wachter-Zeh, A., & Weger, V. (2023). Generic Decoding of Restricted Errors. arXiv preprint arXiv:2303.08882.
Prerequisites
Security in Communications and Storage