On ElGamal Signature Scheme

In 1985, Elgamal proposed a digital signature scheme based on discrete logarithms. Until now, this scheme is still secure under its cryptographic assumption (discrete logarithm problem). To more secure, he had claimed that If any k is used twice in the signing, then the system of equations is uniquely determined and x can be recovered. So for the system to be secure, any value of k should never be used twice in the Note 2 [2]. After we analyze the security of this note, we can found that the ElGamal signature scheme still can be work even though the random number k is used twice in this article.