Improvement of the Miyazaki-Takaragi threshold digital signature scheme

To enhance the applications of smart cards, Miyazaki and Takaragi recently proposed a (t,n) threshold digital signature scheme based on the security of elliptic curve discrete logarithm problem (ECDLP). The advantages of their scheme are low communication bandwidth and computational complexity, which provides critical benefits for the use of smart cards in the distributed environments. Unfortunately, this paper will show that their scheme cannot withstand the forgery attack, which violates their security claim. We further amend the scheme against the attack with a simple improvement.