A novel method for developing post-quantum cryptoschemes and a practical signature algorithm

Abstract

PurposeThe practical purpose of this research is to propose a candidate for post-quantum signature standard that is free of significant drawback of the finalists of the NIST world competition, which consists in the large size of the signature and the public key. The practical purpose is to propose a fundamentally new method for development of algebraic digital signature algorithms.Design/methodology/approachThe proposed method is distinguished by the use of two different finite commutative associative algebras as a single algebraic support of the digital signature scheme and setting two different verification equation for a single signature. A single public key is computed as the first and the second public keys, elements of which are computed exponentiating two different generators of cyclic groups in each of the algebras.FindingsAdditionally, a scalar multiplication by a private integer is performed as final step of calculation of every element of the public key. The same powers and the same scalar values are used to compute the first and the second public keys by the same mathematic formulas. Due to such design, the said generators are kept in secret, providing resistance to quantum attacks. Two new finite commutative associative algebras, multiplicative group of which possesses four-dimensional cyclicity, have been proposed as a suitable algebraic support.Originality/valueThe introduced method is novel and includes new techniques for designing algebraic signature schemes that resist quantum attacks. On its base, a new practical post-quantum signature scheme with relatively small size of signature and public key is developed.

Signature Algorithms with a Hidden Group, Based on Difficulty of Solving Systems of Quadratic Equations

“…Recently proposed algebraic digital signature algorithms with a hidden group, based on the computational difficulty of so-called hidden DLP [13,14], have fairly small signature and public key sizes. However, there are problems justifying their post-quantum security associated with the potential possibility of reducing the hidden DLP to the usual DLP.…”

“…SIZE (IN BYTES) OF THE PUBLIC KEY AND SIGNATURE IN THE ALGORITHMS FROM SECTIONS III AND IV AND FROM[13] AND[14] …”