Collective Signature Schemes.pdf

The schemes are designed to support authentication for a group of signers with different functions, using a single public key and signature.

The first scheme is for a collective made up of several groups, each with a large number of members and a group leader. The second scheme is for a collective with several individual signers and several signing groups.

The schemes use Schnorr's digital signature protocol with a specially structured prime modulo p = 2n + 1, where n = q'q, and q' and q are large prime numbers. The factorization problem is used to find q' and q from n.

The paper also proposes a modification to the Schnorr scheme, including a new prime modulus and changes to the signature generation and verification procedures. The security of the schemes is based on the factorization of the value n = (p-1)/2.

The single signature scheme (SDS-2.1) is described, which includes the signature generation and verification procedures. The scheme uses a one-way hash function, such as SHA-1 or SHA-2, and produces a signature pair (E, S).

The scheme is designed to be easy to deploy on existing Public Key Infrastructure (PKI) systems and can support the generation and provision of a unique public key, digital signature, and digital certificate for a collective of many members.

Key features of the proposed schemes include:

Support for authentication for a group of signers with different functions
Use of a single public key and signature
Based on two hard problems: factoring and discrete logarithm
Uses Schnorr's digital signature protocol with a specially structured prime modulo
Designed to be easy to deploy on existing PKI systems
Can support the generation and provision of a unique public key, digital signature, and digital certificate for a collective of many members.