Proxy re-encryption is a useful concept and many proxy re-encryption schemes have been proposed in the asymmetric encryption setting. In the asymmetric encryption setting, proxy re-encryption can be beautifully implemented because many operations are available to directly transform a cipher to another cipher without the proxy needs to access the plaintexts. However, in many situations, for a better performance, the data is encrypted using symmetric ciphers. Most symmetric ciphers do not support proxy cryptography because of malleability (that is needed to implement the proxy re-encryption) is not a desired property in a secure encryption scheme. In this paper, we suggest an idea to implement a pure proxy re-encryption for the symmetric ciphers by first transforming the plaintext into a random sequence of blocks using an All or nothing transform (AONT). We show an example of the proxy re-encryption scheme using a weak encryption (i.e. simple permutation) that has a simple conversion function to convert a permutation to another. The encryption scheme exploits three characteristics of an AONT transformation: (1) the output of an AONT is a pseudorandom, (2) the output of an AONT cannot be transformed back if any parts is missing, and (3) the output of an AONT cannot be transformed back without having all blocks with correct position. We show security argument of the proposed scheme and its performance evaluation.