Cryptology ePrint Archive: Report 2021/270

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.

Category / Keywords: cryptographic protocols / Post-quantum cryptography, finite fields, combinatorial group theory, R-propping, public-key cryptography, non-commutative cryptography, digital signature, IND-CCA2.

Date: received 3 Mar 2021

Contact author: qubit101 at gmail com

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Version: 20210304:132816 (All versions of this report)

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