Paper 2020/1102
PQC: R-Propping of Public-Key Cryptosystems Using Polynomials over Non-commutative Algebraic Extension Rings
Abstract
Post-quantum cryptography (PQC) is a trend that has a deserved NIST status, and which aims to be resistant to quantum computers attacks like Shor and Grover algorithms. In this paper, we propose a method for designing post-quantum provable IND-CPA/IND-CCA2 public key cryptosystems based on polynomials over a non-commutative algebraic extension ring. The key ideas of our proposal is that (a) for a given non-commutative ring of rank-3 tensors, we can define polynomials and take them as the underlying work structure (b) we replace all numeric field arithmetic with GF(2^8) field operations. By doing so, it is easy to implement R-propped Diffie-Helman-like key exchange protocol and consequently ElGamal-like cryptosystems. Here R stands for Rijndael as we work over the AES field. This approach yields secure post-quantum protocols since the resulting multiplicative monoid is immune against quantum algorithms and resist classical linearization attacks like Tsaban’s Algebraic Span or Roman’kov. The protocols have been proved to be semantically secure. Finally, we present numerical examples of the proposed R-Propped protocols.
Note: Corrected source code
Metadata
- Available format(s)
-
PDF
- Category
- Cryptographic protocols
- Publication info
- Preprint.
- Keywords
- Post-quantum cryptography finite fields rings combinatorial group theory R-propping public-key cryptography non-commutative cryptography AES.
- Contact author(s)
- phecht @ dc uba ar
- History
- 2022-07-04: last of 2 revisions
- 2020-09-15: received
- See all versions
- Short URL
- https://ia.cr/2020/1102
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2020/1102,
author = {Pedro Hecht},
title = {{PQC}: R-Propping of Public-Key Cryptosystems Using Polynomials over Non-commutative Algebraic Extension Rings},
howpublished = {Cryptology {ePrint} Archive, Paper 2020/1102},
year = {2020},
url = {https://eprint.iacr.org/2020/1102}
}
