In Eurocrypt 2003, Boneh et al. proposed verifiably encrypted signatures from the concept of aggregate signatures that support aggregation. Such signatures enable verifiers to test that a given ciphertext is the encryption of a signature on a given message. Verifiably encrypted signatures are used in fair exchange protocols of signatures. In this paper, we first show that Boneh et al.'s verifiably encrypted signature is not secure against rogue-key attacks. Moreover, the fairness of fair exchange protocols of signatures with the adjudicator relies on the neutrality of the adjudicator, which has become a major practical hindrance to fair exchange protocols of signatures getting widely deployed. Then we propose a fair exchange protocol of signatures from pairings by using aggregate signatures. We not only enhance the fair exchange protocol of signatures against three types of inside attackers but also relax the need of the trust in the adjudicator so that it only needs to be trusted by the signer.