Multivariate public key cryptography which relies on MQ (Multivariate Quadratic) problems is one of the main approaches to guarantee the security of communication in the post-quantum world. In this paper, we propose a combined MQ signature scheme based on the yet unbroken UOV (Unbalanced Oil and Vinegar) signature if parameters are properly chosen. Our scheme can not only reduce the public key size of the UOV signature, but also provide more tighter bound of security against chosen-message attack in the random oracle model. On the other hand, we propose a proxy signature scheme based on our proposed combined signature scheme. Additionally, we give a strict security proof for our proxy signature scheme. Finally, we present experiments for all of our proposed schemes and the baseline schemes. Comparisons with related schemes show that our work has some advantages on performance along
with more strict security.