New blind signature protocols based on a new hard problem

Blind signature and blind multisignature schemes are useful in protocols that guarantee the anonymity of the participants. In practice, in some cases the electronic messages are to be signed by several signers and an electronic message is first blinded then passed to each of the signers, who then sign it using some special signature scheme such as collective signature protocol. In this paper, we propose a new blind signature scheme and two type new blind collective signature protocols. Our protocols are based on the difficulty of finding the k roots modulo a large prime p in the case when k is a prime such that kp-1. Our proposed protocols produce the signature (E′, S′), where E′ is a 160-bit value and S′ is a 1024-bit value. It seems that such primitives are attractive for applications in the electronic money systems in which the electronic banknotes are issued by one or several banks.