Paper 2023/318
A Transformation for Lifting Discrete Logarithm Based Cryptography to Post-Quantum Cryptography
Abstract
We construct algebraic structures where rising to the non-associative power indices is no longer tied with the Discrete Logarithm Problem but with a problem that has been analysed in the last two decades and does not have a quantum polynomial algorithm that solves it. The problem is called Exponential Congruences Problem. By this, \emph{we disprove} the claims presented in the ePrint report 2021/583 titled "Entropoids: Groups in Disguise" by Lorenz Panny that \emph{"all instantiations of the entropoid framework should be breakable in polynomial time on a quantum computer."} Additionally, we construct an Arithmetic for power indices and propose generic recipe guidelines that we call "Entropic-Lift" for transforming some of the existing classical cryptographic schemes that depend on the hardness of Discrete Logarithm Problem to post-quantum cryptographic schemes that will base their security on the hardness of the Exponential Congruences Problem. As concrete examples, we show how to transform the classical Diffie-Hellman key exchange, DSA and Schnorr signature schemes. We also post one open problem: From the perspective of provable security, specifically from the standpoint of security of post-quantum cryptographic schemes, to precisely formalize and analyze the potentials and limits of the Entropic-Lift transformation.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint.
- Keywords
- Post-Quantum CryptographyEntropoid-based CryptographyEntropic-Lift
- Contact author(s)
- DANILOG @ ntnu no
- History
- 2023-03-03: approved
- 2023-03-03: received
- See all versions
- Short URL
- https://ia.cr/2023/318
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2023/318, author = {Danilo Gligoroski}, title = {A Transformation for Lifting Discrete Logarithm Based Cryptography to Post-Quantum Cryptography}, howpublished = {Cryptology ePrint Archive, Paper 2023/318}, year = {2023}, note = {\url{https://eprint.iacr.org/2023/318}}, url = {https://eprint.iacr.org/2023/318} }