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This paper analyzes the security of a very efficient signature scheme proposed by C.H. Tan, X. Yi and C.K. Siew: the TYS signature scheme. We show that this scheme is universally forgeable; more specifically, we show that anyone is able to produce a valid TYS signature on a chosen message from an arbitrary valid message/signature pair. We also suggest modifications to the TYS signature scheme and relate the resulting scheme to the Camenisch-Lysyanskaya signature scheme.