A Transformation for Lifting Discrete Logarithm Based mostly Cryptography to Publish-Quantum Cryptography
Paper 2023/318
A Transformation for Lifting Discrete Logarithm Based mostly Cryptography to Publish-Quantum Cryptography
, Division of Info Safety and Communication Applied sciences, Norwegian College of Science and Know-how – NTNUSummary
We assemble algebraic constructions the place rising to the non-associative energy indices is not tied with the Discrete Logarithm Downside however with an issue that has been analysed within the final 20 years and doesn’t have a quantum polynomial algorithm that solves it. The issue known as Exponential Congruences Downside. By this, emph{we disprove} the claims introduced within the ePrint report 2021/583 titled “Entropoids: Teams in Disguise” by Lorenz Panny that emph{“all instantiations of the entropoid framework must be breakable in polynomial time on a quantum laptop.”}
Moreover, we assemble an Arithmetic for energy indices and suggest generic recipe tips that we name “Entropic-Carry” for remodeling among the current classical cryptographic schemes that rely upon the hardness of Discrete Logarithm Downside to post-quantum cryptographic schemes that may base their safety on the hardness of the Exponential Congruences Downside.
As concrete examples, we present tips on how to remodel the classical Diffie-Hellman key alternate, DSA and Schnorr signature schemes.
We additionally publish one open downside: From the angle of provable safety, particularly from the standpoint of safety of post-quantum cryptographic schemes, to exactly formalize and analyze the potentials and limits of the Entropic-Carry transformation.
BibTeX
@misc{cryptoeprint:2023/318,
creator = {Danilo Gligoroski},
title = {A Transformation for Lifting Discrete Logarithm Based mostly Cryptography to Publish-Quantum Cryptography},
howpublished = {Cryptology ePrint Archive, Paper 2023/318},
12 months = {2023},
observe = {url{https://eprint.iacr.org/2023/318}},
url = {https://eprint.iacr.org/2023/318}
}