In 2009, Lin et al. proposed a digital multi-signature scheme based on the concepts of generalized conic curves over Zn. They claimed that the multi-signature scheme is well secured and the forgery attack is infeasible on it. Unfortunately, three weaknesses on their proposed multi-signature have been observed and it has been shown that an attacker can compute the secret pairs of all signers using the technique to solve the linear Diophantine equation, a malicious signer can generate a forged signature based on the signatures of other signers, called inside forgery attack, which is very difficult to disproof by the verifier. Also an outsider can compute a forged signature against the valid multi-signature, may be termed as outsider forgery attack.
Hafizul Islam, SK and P. Biswas, G.
"Cryptanalysis of Lin et al.’s Digital Multi-Signature Scheme on the Generalized Conic Curve Over Zn,"
Information Sciences Letters: Vol. 3
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Available at: https://digitalcommons.aaru.edu.jo/isl/vol3/iss2/4