Self-certified threshold proxy signature schemes with message recovery, nonrepudiation, and traceability

In this paper, we propose a new (t, n) threshold proxy signature scheme, in which at least t out of n proxy signers delegated by the original signer can sign messages on behalf of the original signer. The proposed scheme has the following main properties: (i) Message recovery that the signing message is unnecessary to be transmitted and can be recovered from the proxy signature; (ii) Nonrepudiation that the verifier can identify the proxy group which is responsible for a threshold proxy signature; (iii) Traceability that the verifier can identify the actual proxy signers from the proxy group; (iv) Self-certified public keys that the authenticity of public keys can be verified without requiring any certificate and combined with the tasks of verifying of the proxy signature and recovering of the signing message in a single logical step. In addition, we propose an elliptic curve variant suitable for some cryptographic applications with limited computing power and storage space, e.g., smart card or Java card. As compared with the previous works based on the certificate-based public key system, the proposed schemes are more secure and efficient.