(t,p)-Threshold Point Function Secret Sharing Scheme Based on Polynomial Interpolation and Its Application

Point function secret sharing(PFSS)was a special kind of function secret sharing(FSS)that was a special case of secret sharing, that the shared secret was a point function instead of a value. Motivated by the reason that the PFSS has very good application in the secure multi-party computations by investigating, and the existing PFSS scheme without threshold and inefficient. A new (t, p)-PFSS scheme based on polynomial interpolation was proposed, and this PFSS scheme is secure and efficient by analyzing the correctness, the security and the efficiency of the scheme, and is the first threshold PFSS scheme. Then an example was given to demonstrate scheme has effectiveness. Lastly, we respectively construct a (t, p)-threshold multi-server PIR and secure keyword search protocol, and a (t, p)-threshold incremental secret sharing protocol, both based on the proposed (t, p)-PFSS scheme, and simple analysis the correctness and the security of the first protocol.