Volume 14, Number 2

Constructing New Collective Signature Schemes Base on Two Hard Problems Factoring
and Discrete Logarithm

  Authors

Tuan Nguyen Kim¹, Nguyen Tran Truong Thien¹, Duy Ho Ngoc² and Nikolay A. Moldovyan³, ¹Duy Tan University, Vietnam, ²Department of Information Technology, Vietnam, ³SPIIRAS, Russia

  Abstract

In network security, digital signatures are considered a basic component to developing digital authentication systems. These systems secure Internet transactions such as e-commerce, e-government, ebanking, and so on. Many digital signature schemes have been researched and published for this purpose. In this paper, we propose two new types of collective signature schemes, namely i) the collective signature for several signing groups and ii) the collective signature for several individual signings and several signing groups. And then we used two difficult problems factoring and discrete logarithm to construct these schemes. To create a combination of these two difficult problems we use the prime module p with a special structure: p = 2n +1. Schnorr's digital signature scheme is used to construct related basic schemes such as the single signature scheme, the collective signature scheme, and the group signature scheme. The proposed collective signature schemes are built from these basic schemes. The proposed signature scheme is easy to deploy on existing PKI systems. It can support PKIs in generating and providing a unique public key, a unique digital signature, and a unique digital certificate for a collective of many members. This is essential for many collective transactions on today's Internet.

  Keywords

Network security, digital signature authentication, collective signature, group signature, signing group.