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.