A novel method for development of post-quantum digital signature schemes

Abstract

Introduction: Development of post-quantum digital signature standards represents a current challenge in the area of cryptography. Recently, the signature schemes based on the hidden discrete logarithm problem had been proposed. Further development of this approach represents significant practical interest, since it provides possibility of designing practical signature schemes possessing small size of public key and signature. Purpose: Development of the method for designing post-quantum signature schemes and new forms of the hidden discrete logarithm problem, corresponding to the method. Results: A method for designing post-quantum signature schemes is proposed. The method consists in setting the dependence of the publickey elements on masking multipliers that eliminates the periodicity connected with the value of discrete logarithm of periodic functions constructed on the base of the public parameters of the cryptoscheme. Two novel forms for defining the hidden discrete logarithm problem in finite associative algebras are proposed. The first (second) form has allowed to use the finite commutative (non-commutative) algebra as algebraic support of the developed signature schemes. Practical relevance: Due to significantly smaller size of public key and signature and approximately equal performance in comparison with the known analogues, the developed signature algorithms represent interest as candidates for practical post-quantum cryptoschemes.

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

“…The technique of doubling the verification equation when designing a signature scheme was previously used in [12,14], but in the proposed method it is extended to the case of using two different algebras as a single algebraic carrier of the signature scheme. At the same time, it has a new purpose, which is to provide binding of public key elements to a fixed hidden group in each of the used algebras.…”

“…As a substantiation of resistance to quantum attacks, it should be noted that the proposed signature scheme satisfies the general criterion of post-quantum security used to develop HDLP-based signature schemes described in the papers [12][13][14]. The mentioned criterion is formulated as follows [12]: "Based on the public parameters of the signature scheme, the construction of a periodic function containing a period with the length depending on the discrete logarithm value should be a computationally intractable task."…”

“…The finalists in the category of post-quantum digital signatures were Falcon [17] and Crystals-Dilithium [16], and Rainbow [18]. It is interesting to compare the proposed signature scheme with the finalists, with other HDLP-based signatures [12,14], and with 2048-bit RSA signature algorithm [19]. Table 3 presents a rough comparison which uses the published results of comparing the performance of the finalists with each other and with the algorithm RSA-2048.…”

“…Nevertheless, the finalists have successfully passed long security testing. Like, the recently introduced HDLP-based post-quantum signature schemes [12,14], the proposed algorithm only show a potential possibility to significantly reduce the size of the signature and public key. If further independent security investigation confirm the authors' expectations, then we can say that there is a way to solve the said important practical problem.…”

“…Different forms of the HDLP were used to develop signature algorithms on non-commutative FAAs [7,12,13]. For the first time, a HDLP-based signature algorithm on a commutative FAA was proposed in [14].…”