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Constructing Collective Signature Schemes Using Problem of Finding Roots Modulo

Tuan Nguyen Kim1,*, 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:
(This article belongs to this Special Issue: Soft Computing and Machine Learning for Predictive Data Analytics)

Computers, Materials & Continua 2022, 72(1), 1105-1122.

Received 30 November 2021; Accepted 30 December 2021; Issue published 24 February 2022


Digital signature schemes are often built based on the difficulty of the discrete logarithm problems, of the problem of factor analysis, of the problem of finding the roots modulo of large primes or a combination of the difficult problems mentioned above. In this paper, we use the new difficult problem, which is to find the root in the finite ground field to build representative collective signature schemes, but the chosen modulo p has a special structure distinct , where is an even number and are prime numbers of equal magnitude, about . The characteristics of the proposed scheme are: i) The private key of each signer consists of 2 components (), randomly selected, but the public key has only one component () calculated by the formula and ; and ii) The generated signature consists of a set of 3 components (2). We use the technique of hiding the signer's public key Y, which is the coefficient λ generated by the group nanager, in the process of forming the group signature and representative collective signature to enhance the privacy of all members of the signing collective.


Computing roots; finding roots modulo; collective signature; signing collective; signing group

Cite This Article

T. Nguyen Kim, D. Ho Ngoc and N. A. Moldovyan, "Constructing collective signature schemes using problem of finding roots modulo," Computers, Materials & Continua, vol. 72, no.1, pp. 1105–1122, 2022.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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