Comment on Improvement of the Miyazaki-Takaragi Threshold Digital Signature Scheme

To enhance applications of smart cards, Miyazaki and Takaragi proposed a (t, n) threshold digital signature scheme based on the security of elliptic curve discrete logarithm (ECDLP). The advantages of their scheme are low communication bandwidth and computational complexity, which provides critical benefits for the use of smart cards in distributed environments. Recently Wu et al. pointed out that the Miyazaki-Takaragi threshold digital signature scheme cannot withstand the insider forgery attack. Then they further amended the scheme against the attack with a simple improvement. However, this paper will show that the attack proposed by Wu et al. is wrong, since they confused the point addition of elliptic curve with the vector addition on a finite field. Finally, we will point out that a general coalition attack can be also applied to both of the Miyazaki-Takaragi scheme and the Wu’s improvement.