Open Access

ARTICLE

New Collective Signatures Based on the Elliptic Curve Discrete Logarithm Problem

Tuan Nguyen Kim^1,*, Duy Ho Ngoc², Nikolay A. Moldovyan³

1 School of Computer Science, Duy Tan University, Da Nang, Vietnam
2 Department of Information Technology, Ha Noi, Vietnam
3 ITMO University, St. Petersburg, Russia

* Corresponding Author: Tuan Nguyen Kim. Email:

Computers, Materials & Continua 2022, 73(1), 595-610. https://doi.org/10.32604/cmc.2022.023168

Received 30 August 2021; Accepted 26 November 2021; Issue published 18 May 2022

Abstract

There have been many digital signature schemes were developed based on the discrete logarithm problem on a finite field. In this study, we use the elliptic curve discrete logarithm problem to build new collective signature schemes. The cryptosystem on elliptic curve allows to generate digital signatures with the same level of security as other cryptosystems but with smaller keys. To extend practical applicability and enhance the security level of the group signature protocols, we propose two new types of collective digital signature schemes based on the discrete logarithm problem on the elliptic curve: i) the collective digital signature scheme shared by several signing groups and ii) the collective digital signature scheme shared by several signing groups and several individual signers. These two new types of collective signatures have combined the advantages of group digital signatures and collective digital signatures. These signatures have a fixed size and do not depend on the number of members participating in the creation of the final collective signature. One of the advantages of the proposed collective signature protocols is that they can be deployed on top of the available public key infrastructures.

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Keywords

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