PATS: Let Parties Have a Say in Threshold Group Key Sharing

We present a password-authenticated (2, 3)-threshold group key share (PATS) mechanism. Although PATS resembles threshold secret sharing schemes, it has a different structure. The innovative perspective of the PATS mechanism that makes a difference from the standard secret-sharing schemes is that it involves parties in the generation of the shares. PATS allows parties to communicate securely to establish their shares over insecure channels. Parties (shareholders) construct a secret (key) using shares obtained at the end of the protocol. PATS takes advantage of zero-knowledge proofs compared to well-known threshold key exchange schemes and will tolerate the existence of semi-trusted parties. We present two variants of PATS, centralized and distributed, and then generalize PATS to (t, n)-threshold scheme. PATS supports the distributed operation and optionally facilitates group key verification by a trusted third party, which may also partake in group key sharing. In this paper, we present PATS, which employs finite fields and elliptic curves, along with its security and complexity analyses.