Linearly Homomorphic Signatures with Adaptively Sublinear Public Keys in the Standard Model

Linearly homomorphic signatures (LHS) allow users to outsource signed datasets to a server for computing linear functions. Users can verify the correctness of results returned by the server using public keys. Constructing a LHS scheme with short public keys in the standard model is a challenging and useful open problem. Most existing standard-model LHS schemes have public key sizes of O(N) that are linearly proportional to the dataset size N. Only one scheme achieves sublinear public keys of size ON12. This limits LHS schemes from efficiently processing large-scale datasets in the most secure way; for a dataset with ≥1014 data items (e.g., LHC dataset), the public key size of the existing standard-model LHS schemes may exceed one GB, imposing significant storage costs.In this paper, we propose a new LHS scheme with adaptively sublinear public keys of size ON1c in the standard model, where the value of c can be adaptively selected by users according to different dataset sizes N to minimize N1c. For a large dataset with N=1015 data items, compared to the state-of-the-art LHS scheme, our scheme reduces the public key size and key generation time by approximately a factor of 105, and the offline verification time by approximately a factor of 104, while maintaining comparable performance in the other algorithms. Our scheme enables verifiers to verify the correctness of results calculated on large datasets with extremely low storage overhead (KB level) and in the most secure way.