Weight Equalization Algorithm for Tree Parity Machines

TL;DR

This work tackles the issue of nonuniform weight distributions in Tree Parity Machines (TPMs) used for quantum-proof key agreement by introducing a weight equalization algorithm. The method comprises three phases—equalization to rebalance weight frequencies, dropout to respect the theoretical secret length, and substitution with a hash function (SHA-256) to boost randomness—applied deterministically to synchronized TPMs. Empirical evaluation shows that equalization yields near-uniform weight distributions and substantially improves NIST SP 800-22 randomness test outcomes, suggesting stronger key quality and security with reduced mutual-learning overhead. The approach offers a practical, quantum-resistant alternative to factorization-based schemes and NBTPM variants, with future work needed to further assess attacK resilience and optimization.

Abstract

Key agreement plays a crucial role in ensuring secure communication in public networks. Although algorithms developed many years ago are still being used, the emergence of quantum computing has prompted the search for new solutions. Tree parity machines have been put forward as a potential solution. However, they possess inherent shortcomings, one of which is the uneven distribution of values in the secured key obtained after the key agreement process, especially when on-binary vectors are used during the synchronization process. This paper introduces a novel algorithm designed to address this issue. The results demonstrate a substantial enhancement in the quality of the secured key obtained.

Figures (3)

• Figure 1: Architecture of the tpm
• Figure 2: Weight probabilities before equalization
• Figure 3: Weight probabilities after equalization