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We present the first tight security proofs for two general classes of Strong RSA (SRSA) based signature schemes. Among the covered signature schemes are the signature schemes by Cramer-Shoup, Zhu, Fischlin, and the SRSA-based Camenisch-Lysyanskaya scheme with slightly modified parameter sizes. We also present two variants of our signature classes in bilinear groups that output very short signatures. Similarly to before, these variants have tight security proofs under the Strong Diffie-Hellmandoi:10.1007/s00145-013-9173-6 fatcat:xvqby5svf5ashedbyuowdckcom