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How to define the security of undeniable signature schemes is a challenging task. This paper presents two security definitions of undeniable signature schemes which are more useful or natural than the existing definition. It then proves their equivalence. The authors first define the UC-security, where UC means universal composability. They next show that there exists a UC-secure undeniable signature scheme which does not satisfy the standard definition of security that has been believed to be adequate so far.
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