Public Key Threshold Multi-Message Signcryption (PK-TMMS) scheme with (t, n) shared verification

In this paper, public key threshold multi-message signcryption (PK-TMMS) scheme with (t, n) shared verification based on discrete logarithm problem is proposed. The (t, n) threshold is built based on the Shamir´ secret sharing. The proposed scheme signcrypted multiple messages for each recipient using a multi-key generator. The multi-key generator played an important role for the communication overhead and computational cost saving in the PK-MM-MRS scheme. The proposed scheme has an efficient communication overhead and computational cost saving compared to Zheng multi-recipient signcryption scheme. The saving in communication overhead using the proposed scheme are 38.24 % for two messages, two recipients and 67.97 % for three messages, three recipients over Zheng multi-recipient signcryption scheme at the same parameters. The proposed scheme costs 50 % and 75 % less in computation cost for two and four signcrypted messages than does Zheng signcryption scheme. The saving in communication overhead and computational cost is increased as the number of messages and recipients increases.