A Proxy Signature Using Multivariate Equations On Quaternion Ring

The digital signature schemes we have been using are all based on the research of the large factoring problem, discrete logarithm problem, and elliptic curve discrete logarithm problem. However, for the safety, schemes of the signature haven't met the demand of actual application. For the digital signature based on the quaternion ring has higher safety, it is applied to the proxy signature which will have the higher research value.This article introduces the knowledge to the digital signature and studies the signature scheme by Masahiro Yagisawa which is based on the quaternion ring. The scheme will introduce the multivariate function of high degree to non-commutative quaternion ring, and its safety depends on the difficulty in solving the multivariate equations of high degree. Then, the thought of the scheme applies to proxy signature and designs a proxy signature scheme. Finally, it gives the safety analysis of the proxy scheme.