Bilinear-pairings based designated-verifier multi-proxy signatue scheme

In a multi-proxy signature scheme, one original signer delegates a group of n proxy signers to sign messages on behalf of himself or herself. When the proxy signature is created, n proxy signers cooperate to generate valid proxy signatures. Based on Cha and Cheon´s ID-based signature scheme, a designated-verifier multi-proxy signature scheme is proposed. The proposed scheme can provide the security properties of proxy protection, verifiability, strong identifiability, strong unforgeability, strong repudiability, distinguishability and prevention of misuse of proxy signing power. That is, internal attacks, external attacks, collusion attacks, equation attacks and public key substitution attacks can be resisted.