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In this paper, the authors study a security issue in cloud computing: Non-Repudiation of Origin (NRO) with privacy protection on message originator. They first define two concrete goals of NRO: NRO-I and NRO-II. Both notions are inspired by the non-repudiation service they can have by using traditional handwritten signatures as the evidence of origin. Then, they 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.