Aggregate Proxy Signature and Verifiably Encrypted Proxy Signature

An aggregate signature is a single short string that convinces any verifier that, for all 1 ≤ i ≤ n, signer i signed message mi, where the n signers and n messages are distinct. The main motivation of aggregate signatures is compactness. In this paper, the concept of aggregate proxy signature (APS) is first proposed to compact the proxy signatures. Furthermore, a concrete APS scheme is constructed, which can be proved to be secure under the security model of APS. Additionally, as an application of APS, the concept of verifiably encrypted proxy signature (VEPS) is also first proposed in this paper, which can be used in contract signing. The VEPS allows the original signer to delegate another to sign the contract on its behalf. Finally, a VEPS construction is derived from the APS, which can be easily proved to be secure from the security of APS.