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

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.

Constructing Collective Signature Schemes Using Problem of Finding Roots Modulo

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 wth 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 coefficientλgenerated 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.

New Representative Collective Signatures Based on the Discrete Logarithm Problem

The representative collective digital signature scheme allows the creation of a unique collective signature on document M that represents an entire signing community consisting of many individual signers and many different signing groups,each signing group is represented by a group leader.On document M,a collective signature can be created using the representative digital signature scheme that represents an entire community consisting of individual signers and signing groups,each of which is represented by a group leader.The characteristic of this type of letter is that it consists of three elements(U,E,S),one of which(U)is used to store the information of all the signers who participated in the formation of the collective signature on document M.While storing this information is necessary to identify the signer and resolve disputes later,it greatly increases the size of signatures.This is considered a limitation of the collective signature representing 3 elements.In this paper,we propose and build a new type of collective signature,a collective signature representing 2 elements(E,S).In this case,the signature has been reduced in size,but it contains all the information needed to identify the signer and resolve disputes if necessary.To construct the approved group signature scheme,which is the basic scheme for the proposed representative collective signature schemes,we use the discrete logarithm problem on the prime finite field.At the end of this paper,we present the security analysis of the AGDS scheme and a performance evaluation of the proposed collective signature schemes.

New Collective Signatures Based on the Elliptic Curve Discrete Logarithm Problem

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.