A New Type of Collusion Attacks against Threshold Proxy Signature Schemes

In a (t, n) threshold proxy signature scheme, the original signer can delegate the signing power to n proxy signers such that any t or more out of n proxy signers can sign messages on behalf of the original signer, but t - 1 or less of the proxy signers cannot generate a proxy signature. In this paper, we classify the attacks against the threshold proxy signature schemes. In addition, we present a new type of collusion attacks. Xie's threshold proxy signature scheme is insecure against the new type of collusion attack. It seems that if the threshold proxy signature schemes only require some secret (t - 1)-degree polynomials to fulfil the proxy share generation and the signature generation, the threshold proxy signature schemes will always suffer from the type of collusion attacks.