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Cryptography is increasingly used in E-commerce, especially in untraceable payment system and electronic voting system. Protocols for these systems require anonymous digital signing, and blind signature is the answer to it. Chaum stated that every blind signature protocol should hold two fundamental properties, blindness and intractableness. All blind signature schemes proposed so far are based on one of the following: integer factorization problem, discrete logarithm problem, and quadratic residues. However, Lee et al. declared that none of the schemes is able to meet the two fundamental properties above. This paper proposes an elliptic curve based blind signature scheme that possesses both the above properties.