This preliminary report presents cgVSS, a NI-VSS protocol that uses class groups for encryption. In cgVSS, the dealer encrypts the secret shares in the exponent through a class group encryption such that the parties can directly decrypt their shares. The existence of a subgroup where a discrete logarithm is tractable in a class group allows the receiver to efficiently decrypt the share though it is available in the exponent. This yields a novel-yet-simple VSS protocol where the dealer publishes the encryptions of the shares and the zero-knowledge proof of the correctness of the dealing. The linear homomorphic nature of the employed encryption scheme allows for an efficient zero-knowledge proof of correct sharing. Given the rise in demand for VSS protocols in the blockchain space, especially for publicly verifiable distributed key generation (DKG), our NI-VSS construction can be particularly interesting. We implement our cgVSS protocol using the BICYCL library and compare its performance with the state-of-the-art NI-VSS by Groth. Our protocol reduces the message complexity and the bit length of the broadcast message by at least 5.6x for a 150 party system, with a 1.8x speed-up in the dealer’s computation time and with similar receiver computation times.
Verifiable secret sharing (VSS) allows a dealer to send shares of a secret value to parties such that each party receiving a share can verify (often interactively) if the received share was correctly generated. Non-interactive VSS (NI-VSS) allows the dealer to perform secret sharing such that every party (including an outsider) can verify their shares along with others’ without any interaction with the dealer as well as among themselves. Existing NI-VSS schemes employing either exponentiated ElGamal or lattice-based encryption schemes involve zero-knowledge range proofs, resulting in higher computational and communication complexities.
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