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The notion of a Secretly Embedded Trapdoor with Universal Protection (SETUP) has been recently introduced. In this paper we extend the study of stealing information securely and subliminally from black-box cryptosystems. The SETUP mechanisms presented here, in contrast with previous ones, leak secret key information without using an explicit subliminal channel. This extends this area of threats, which we call "kleptography". We introduce new definitions of SETUP attacks (strong, regular, and weak SETUPS) and the notion of m out of n leakage bandwidth. We show a strong attack which is based on the discrete logarithm problem. We then show how to use this setup to compromise the Diffie-Hellman key exchange protocol. We also strengthen the previous SETUP against RSA. The strong attacks employ the discrete logarithm as a one-way function (assuring what is called "forward secrecy"), public-key cryptography, and a technique which we call probabilistic bias removal.