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After studying blind proxy signature scheme and a group of digital signature schemes based on two hard mathematical problems, a new blind proxy signature scheme based on both elliptic curve discrete logarithm problem and integer factoring problem is proposed and its security is analyzed. The analysis results show that the scheme satisfies all necessary security properties of the proxy signature schemes. Furthermore, the original signer can't confirm the proxy signer's identity from an effective proxy signature. This scheme's capability of anti-attacking is improved evidently comparing with existing blind proxy signature schemes based on one mathematical hard problem.