A (k, n) Threshold Nominative Proxy Signature Scheme for Electronic Commerce

By using the Lagrange interpolation formula and the technology of signature of equality, a (k, n) threshold nominative proxy signature scheme is proposed, where an original signer delegates his (her) signing power to a proxy, who generates a nominative signature on behalf of the original signer and only k or more active verifiers in the n nominees (verifiers) nominated by the proxy signer can verify the signature signed by the proxy. If necessary, these (k or more) active nominees (verifiers) can prove its validity to a third party. In this scheme, the secret shares are generated and encrypted by the original signer. At the same time, the ciphertexts of the secret shares are used as parts of the signature. Then, the secret shares need not be sent to the nominees (verifiers) secretly. The ordinary nominative proxy signature can be viewed as a (1, 1) threshold nominative proxy signature. The ordinary nominative proxy signature can be viewed as a special case of a (k, n) threshold nominative proxy signature. According to the security analysis of this paper, it is found that our scheme is secure against a proxy signing key forgery attack and existential forgery on an adaptive chosen message attack.