A Threshold Digital Signature Issuing Scheme without Secret Communication

This paper describes an efficient (k, n) threshold digital signature scheme. In the scheme, k out of n signers cooperate to issue a signature without using trusted center. No secret communication is required among signers across the network. As a base scheme, Pedersen's verifiable secret sharing (VSS) is applied to generate shared secret keys in such a way that no secret communication is required in the following signature issuing phase. Then, Nyberg-Ruepple or ElGamal type digital signature scheme is employed which uses only linear combination of two shared secrets when applied to the (k, n) threshold scenario. It is considered that the (k, n) threshold scheme without using encryption is meaningful in an environment where strongly enciphered message cannot be sent across the network. The proposed (k, n) threshold digital signature scheme is proved to be as secure as the Nyberg-Ruepple or ElGamal type digital signature against chosen message attacks. It is discussed that the proposed VSS is also applicable to encryption. An application to (k, n) threshold sign-encryption is also presented.