Proxy re-signature is proposed by Blaze, Blemmer and Strauss (BBS), in which a semi-trusted proxy acts as a translator converts a signature from Alice into a signature from Bob on the same message. Proxy re-signature is a very useful tool for the interoperable DRM architecture and the proof of passed path in cloud computing. However, cloud users usually are mobile devices which are constrained with processing and power limitations. When a mobile user obtain the converted signature from the proxy (cloud server), it still can not verify it due to the heavy computation cost. We propose a new definition of server-aided verification proxy re-signature which consist of a proxy re-signature scheme and a server-aided verification protocol. With the server-aided verification protocol, some computational tasks for a proxy re-signature verification are carried out by the proxy (cloud server), which is generally untrusted, therefore, it is very useful for mobile devices. We present, on the basis of Ateniese and Hohenberger's unidirectional proxy re-signature scheme, two novel existential unforgeability server-aided verification proxy re-signature schemes.