In a proxy re-signatures (PRS) scheme, a semi-trusted proxy is given some information which allows it to translate a user i's signature on a message m into another user j's signature on the same message m. However, the proxy cannot, on it own, compute signatures for either i or j. This notion introduced by Blaze et a. at EUROCRYPT 1998, and then revisited by Ateniese and Hohenberger at CCS 2005. The existence of multi-use unidirectional PRS scheme is an open problem left by AH05. Whereafter, at CCS 2008, Libert and Vergnaud constructed the first multi-use unidirectional PRS scheme. However, there is a major drawback in the LV08 scheme that the size of the signatures is linear in the number of translations. Hence, Libert and Vergnaud said that a more challenging task would be to find out implementations of such primitives where the size of signatures and the verification cost do not grow linearly with the number of translations. In this work we resolve this task by constructing a such PRS scheme in the standard model by using indistinguishability obfuscation. A shortcoming of our construction is that the security is selective but not full.