Multi-Party Concurrent Signatures Based On Multivariate Public Key Cryptosystems

Fair exchange in digital signatures is one of the fundamental problems in cryptography. It is a necessary feature in many widespread applications for electronic commerce. With the development of internet, the volume of business on internet is increase and the problem of fair exchange is more and more important. Compared with former schemes, concurrent signature is an effective way to the fair exchange without trusted third party and do not rely on the balance of users'computing capability. Multi-party concurrent signature is the generalization of concurrent signature. However, the expansion from two-party concurrent signature to multi-party concurrent signature is difficulty.The appearance of quantum computer pose a threat to the classical public key cryptosystem and the demand for highly effective of public key cryptosystem increase day by day, which enables the multivariable public key cryptography to become more and more important. The existing concurrent signature schemes are based on the traditional cipher system, under quantum computer, it is no longer safe. In this paper we research the multi-party concurrent signature based on multivariate public key cryptosystem primarily, and the main work as following:In this paper a multi-party concurrent signature based on the rainbow signature scheme is proposed. And we analyzed its security and efficiency. In the case of appropriate parameters, our scheme can resist all known attacks for the rainbow signature scheme and satisfies security of concurrent signature. The new plan is security and highly effective. It can be applied to the multi-party fair electronic contract signing.A multi-party concurrent signature based on the Oil-Vinegar signature scheme is proposed. We also analyzed its security. In the case of appropriate parameters, our scheme not only satisfies security of concurrent signature, and also resist all known attacks for the Oil-Vinegar signature scheme. Moreover, with comparison of the two schemes, we know that they are equally safe and highly effective and they have certain usability.