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2020 Algebraic cryptanalysis and new security enhancements
Vitaliĭ Roman’kov
Mosc. J. Comb. Number Theory 9(2): 123-146 (2020). DOI: 10.2140/moscow.2020.9.123

Abstract

We briefly discuss linear decomposition and nonlinear decomposition attacks using polynomial-time deterministic algorithms that recover the secret shared keys from public data in many schemes of algebraic cryptography. We show that in this case, contrary to common opinion, typical computational security assumptions are not very relevant to the security of the schemes; i.e., one can break the schemes without solving the algorithmic problems on which the assumptions are based. Also we present another and in some points similar approach, which was established by Tsaban et al.

Before demonstrating the applicability of these two methods to two well-known noncommutative protocols, we cryptanalyze two new cryptographic schemes that have not yet been analyzed.

Further, we introduce a novel method of construction of systems resistant against attacks via linear algebra. In particular, we propose improved versions of the well-known Diffie–Hellman-type (DH) and Anshel–Anshel–Goldfeld (AAG) algebraic cryptographic key-exchange protocols.

Citation

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Vitaliĭ Roman’kov. "Algebraic cryptanalysis and new security enhancements." Mosc. J. Comb. Number Theory 9 (2) 123 - 146, 2020. https://doi.org/10.2140/moscow.2020.9.123

Information

Received: 9 November 2019; Revised: 2 March 2020; Accepted: 25 March 2020; Published: 2020
First available in Project Euclid: 17 September 2020

zbMATH: 07211443
MathSciNet: MR4096117
Digital Object Identifier: 10.2140/moscow.2020.9.123

Subjects:
Primary: 20F10
Secondary: 20F70, 94A60

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.9 • No. 2 • 2020
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