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In a (t, n) threshold proxy signature scheme, the original signer can delegate his/her signing capability to n proxy signers such that any t or more proxy signers can sign messages on behalf of the former, but t-1 or less of them cannot do the same thing. Such schemes have been suggested for use in a number of applications, particularly, in distributed computing where delegation of rights is quite common. Based on the RSA cryptosystem, [M. -S. Hwang et al. (2003) recently proposed an efficient (t, n) threshold proxy signature scheme. We identify several security weaknesses in their scheme and show that their scheme is insecure.