Cryptographic competitiveness of cryptosystems based on noncommutative groups
DOI:
https://doi.org/10.30837/rt.2025.2.221.10Keywords:
post-quantum cryptography, noncommutative groups, MST3, logarifmic signature, quantum computing, cryptographic securityAbstract
The rapid development of quantum computing poses a direct threat to RSA, DSA, and ECC modern cryptographic systems due to the Shor's algorithm potential application. In response to this threat, the NIST is conducting post-quantum cryptography standardization, having selected lattice-based and hash-function-based algorithms in 2022. Cryptosystems based on noncommutative groups, despite their potential resistance to quantum attacks owing to natural properties of noncommutative algebraic structures, were not included in the first set of standards due to the complexity of security analysis. This research conducts a comprehensive analysis of the cryptographic competitiveness of noncommutative group-based systems, evaluates their advantages and disadvantages compared to existing post-quantum solutions, and determines prospects for practical application as an alternative or complementary solution to ensure cryptographic diversification under quantum threats.
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