Publicly verifiable function secret sharing

Abstract

Function secret sharing (FSS) allows a dealer to split a secret function into n sub-functions, described by n evaluation keys, such that only a combination of all of these keys could reconstruct the secret function. However, it is impossible to recover the secret correctly if there exist some sharers deviating from intended behaviours. To settle this problem, we propose a new primitive called publicly verifiable function secret sharing (PVFSS), in which any client could verify the validity of secret in constant time. Furthermore, we define three important properties: public delegation, public verification and high efficiency, which are an essential part of our scheme. Finally, we construct a PVFSS scheme for point function then we prove its security and make performance analysis in two major directions: key length and algorithm efficiency. The analysis validates that our proposed scheme is asymptotic to FSS. It would be applicable to cloud computing.