Some applications of arithmetic groups in cryptography

2018/03/30 by Kahrobaei, Delaram, Mallahi-Karai, Keivan
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1803.11528

Abstract

In this paper we will give various examples of exponentially distorted subgroups in linear groups, including some new example of subgroups of SL_n(ℤ[x]) for n ≥ 3, and show how they can be used to construct symmetric-key cryptographic platforms.

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• Cryptosystems using subgroup distortion
• Problems in group theory motivated by cryptography
• Random subgroups and analysis of the length-based and quotient attacks
• Group theory in cryptography
• A simple generalization of the ElGamal cryptosystem to non-abelian groups II