Improved group-oriented digital signature schemes based on elliptic curve cryptography

A group-oriented digital signature scheme allows a group of signers to generate a valid signature in a way that any malicious signer cannot forge a valid signature by himself. Recently, Su, Chang, and Lu proposed three group-oriented digital signature schemes, a (n, n) multisignature scheme and two (t, n) threshold digital signature schemes, based on the elliptic curve discrete logarithm problem. Their schemes provide the same security level as Harn's schemes, while with shorter key lengths, smaller bandwidth, and lower power consumption. This paper, however, will demonstrate the forgery attacks on Su et al.'s schemes to show that their claimed security requirements cannot be achieved. Finally, we give the improvements to withstand the proposed forgery attacks.