AFHPS: An Authorized Function Homomorphic Proxy Signature Scheme with Sampling Batch Verification

Homomorphic signature allows any entity to generate a valid signature of new data without a secret key on behalf of the data owner (DO) by performing homomorphic operations on authenticated data. However, general homomorphic signature schemes have two problems: (i) the original signatures are generated by the DO, which may be computationally expensive; and (ii) the linear function f is randomly selected by the aggregator and cannot be specified by the DO, which limits the application scenarios of homomorphic signature. To address the problems above, in this paper we propose an authorized function homomorphic proxy signature scheme with sampling batch verification (AFHPS). Our scheme combines the advantages of homomorphic signature, proxy signature and functional signature, which enables DO to delegate the ability of signature of the original messages and the specified linear function f to the proxy signer and control its behavior. A concrete construction of our scheme is given in this paper, and we prove that it is secure under the co-CDH assumption. In addition, we show how to apply our scheme to realize authentication in blockchain.