Post-quantum signature algorithms based on the hidden discrete logarithm problem

Abstract

New options of the hidden discrete logarithm problem are proposed as cryptographic primitive of the post-quantum signature algorithms. Two signature schemes using computations in finite non-commutative algebras with associative multiplication operation are introduced. The main feature of the proposed signature algorithms consists in using locally invertible elements of algebras. Two different types of algebras are used: i) containing global bi-side unit and ii) containing a large set of global right-side units.

Keywords

• finite associative algebra
• non-commutative algebra
• global unit
• local unit
• right-side units
• local invertibility
• discrete logarithm problem
• public-key cryptoscheme
• digital signature
• post-quantum cryptography