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

Abstract

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.