### PQC: R-Propping of a New Group-Based Digital Signature

Pedro Hecht

##### Abstract

Post-quantum cryptography or PQC is a trend that has a deserved NIST status, and which aims to be resistant to quantum computer attacks like Shor and Grover algorithms. We choose to follow a non-standard way to achieve PQC: taking any standard asymmetric protocol and replacing numeric field arithmetic with GF-256 field operations. By doing so, it is easy to implement R-propped asymmetric systems as present and former papers show. Here R stands for Rijndael as we work over the AES field. This approach yields secure post-quantum protocols since the resulting multiplicative monoid resists known quantum algorithm and classical linearization attacks like Tsaban Algebraic Span or Romankov linearization attacks. Here we develop an original group-based digital signature protocol and R-propped it. The protocol security relies on the intractability of a generalized discrete log problem, combined with the power sets of algebraic ring extension tensors. The semantic security and classical and quantum security levels are discussed. Finally, we present a numerical example of the proposed protocol.

Available format(s)
Category
Cryptographic protocols
Publication info
Preprint.
Keywords
Post-quantum cryptographyfinite fieldscombinatorial group theoryR-proppingpublic-key cryptographynon-commutative cryptographydigital signatureIND-CCA2.
Contact author(s)
qubit101 @ gmail com
History
Short URL
https://ia.cr/2021/270

CC BY

BibTeX

@misc{cryptoeprint:2021/270,
author = {Pedro Hecht},
title = {PQC: R-Propping of a New Group-Based Digital Signature},
howpublished = {Cryptology ePrint Archive, Paper 2021/270},
year = {2021},
note = {\url{https://eprint.iacr.org/2021/270}},
url = {https://eprint.iacr.org/2021/270}
}

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