Collective Signature Protocols for Signing Groups based on Problem of Finding Roots Modulo Large Prime Number

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 w th root in the finite ground field GF(p) to build representative collective signature schemes, but the chosen modulo p has a special structure distinct p = Nt 0 t 1 t 2 + 1, where N is an even number and t 0 , t 1 , t 2 are prime numbers of equal magnitude, about 80 bits. The characteristics of the proposed scheme are: i) The private key of each signer consists of 2 components (K 1 , K 2 ), randomly selected, but the public key has only one component (Y ) calculated by the formula Y = K w 1 1 K w 2 2 ; w 1 = t 0 t 1 and w 2 = t 0 t 2 ; and ii) The generated signature consists of a set of 3 components (e, S 1 , S 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.

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Constructing Representative Collective Signature Protocols Using The GOST R34.10-1994 Standard

Kim¹,

Ngoc²,

Moldovyan³

2023

Computers, Materials &Amp; Continua

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The representative collective digital signature, which was suggested by us, is built based on combining the advantages of group digital signature and collective digital signature. This collective digital signature schema helps to create a unique digital signature that deputizes a collective of people representing different groups of signers and may also include personal signers. The advantage of the proposed collective signature is that it can be built based on most of the well-known difficult problems such as the factor analysis, the discrete logarithm and finding modulo roots of large prime numbers and the current digital signature standards of the United States and Russian Federation. In this paper, we use the discrete logarithmic problem on prime finite fields, which has been implemented in the GOST R34.10-1994 digital signature standard, to build the proposed collective signature protocols. These protocols help to create collective signatures: Guaranteed internal integrity and fixed size, independent of the number of members involved in forming the signature. The signature built in this study, consisting of 3 components (U, R, S), stores the information of all relevant signers in the U components, thus tracking the signer and against the "disclaim of liability" of the signer later is possible. The idea of hiding the signer's public key is also applied in the proposed protocols. This makes it easy for the signing group representative to specify which members are authorized to participate in the signature creation process.

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Collective Signature Protocols for Signing Groups based on Problem of Finding Roots Modulo Large Prime Number

Cited by 3 publications

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New Representative Collective Signatures Based on the Discrete Logarithm Problem

New Representative Collective Signatures Based on the Discrete Logarithm Problem

Constructing Collective Signature Schemes Using Problem of Finding Roots Modulo

Constructing Representative Collective Signature Protocols Using The GOST R34.10-1994 Standard

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