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This paper studies a security issue in cloud computing: non-repudiation of origin (NRO) with privacy protection on message originator. We first define two concrete goals of NRO: NRO-I and NRO-II. Both notions are inspired by the non-repudiation service we can have by using traditional handwritten signatures as the evidence of origin. Then we show that existentially unforgeable digital signatures can provide NRO-I but not always NRO-II, by giving a counterexample. Another contribution of this paper is a communication protocol accommodating non-repudiation of origin and privacy of message originator. Our protocol satisfies NRO-I and NRO-II, and the recipient is unable to convince any other entities about the identity of message originator. The essence of our protocol is a designated verifier signature scheme with unforgeability against the designated verifier.