Abstract
Multivariate public key cryptography which relies on multivariate quadratic (MQ) problem is one of the main approaches to guarantee the security of communication in the post-quantum world. In this paper, we focus mainly on the yet unbroken (under proper parameter choice) Unbalanced Oil and Vinegar (UOV) scheme, and discuss the exact security of it. Then we propose a combined signature scheme which that (1) not only can reduce the public key size of the UOV signature scheme, and (2) but also can provide tighter security against chosen-message attack in the random oracle. On the other hand, we propose a novel aggregate signature scheme based on UOV signature scheme. Additionally, we give security proof for our aggregate signature scheme under the security of our proposed signature scheme.
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