### 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.

Available format(s)
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
See all versions
Short URL
https://ia.cr/2023/318

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}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.