Bit Commitment Protocols Over Braid Groups

It is a tough problem to assure the confidentiality, integrity, authenticity of the Internet. To solve this problem, the network security concept is brought up. We can make the Internet to be a safe place through various protocols. Each network protocol may include some independent modules such as bit commitment protocol, oblivious transfer and zero- knowledge proof etc.This article focuses on the Bit Commitment over Braid Groups. After analyzing the braid-based bit commitment protocol and the biased bit commitment protocol, we propose four schemes: a braid-based commitment protocol, a braid-based biased bit commitment protocol and two weak bit string commitment protocols.Innovation and contribution of this paper are illustrated as follows:First, we construct a new bit commitment protocol based on the attributes of LB(B_n) andRB(B_n) of braid groups. This protocol is non-interactive in the commitment phase. It only needs sent a commitment message to the receiver in the commitment phase. The bit commitment protocol commitment phase can be completed without the participation of the receiver, thereby, the efficiency of the braid-based bit commitment protocol is increased. At the same time the proposed protocol is based on the CSP assumption in braid group, so it can resist the quantum attacks. Using the same technique, the proposed new braid-based biased bit commitment protocol is also non-interactive in the commitment phase.Second, under voting and lottery application background, we give a special bit commitment protocol, called weak bit string commitment protocol. It is a general biased bit commitment protocol. In the commitment stage, it requires the sender to reveal to the receiver some information of the bit string he will send. Based on the CSP assumption in braid group, we construct a weak bit commitment protocol, and a special weak bit commitment protocol which is non-interactive in the commitment phase.