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Our main result is that two problems in this class, which we call the chosen-target and known-target inversion problems, respectively, have polynomially equivalent computational complexity. We show how this leads to a proof of security for Chaum's RSA-based blind signature scheme in the random oracle model based on the assumed hardness of either of these problems. We define and prove analogous results for ``one-more-discrete-logarithm'' problems. Since the appearence of the preliminary version of this paper, the new problems we have introduced have found other uses as well.", issn="1432-1378", doi="10.1007/s00145-002-0120-1", doi_url="http://dx.doi.org/10.1007/s00145-002-0120-1", url="https://eprint.iacr.org/2001/002" } @inbook{RSA-HDF-KTIvCTI, author="Bellare, Mihir and Namprempre, Chanathip and Pointcheval, David and Semanko, Michael", editor="Syverson, Paul", chapter="The Power of RSA Inversion Oracles and the Security of Chaum's RSA-Based Blind Signature Scheme", title="Financial Cryptography: 5th International Conference", year="2002", publisher="Springer", address="Berlin, Heidelberg", pages="319--338", isbn="978-3-540-46088-6", doi="10.1007/3-540-46088-8_25", url="https://www.di.ens.fr/~pointche/Documents/Papers/2001_fcA.pdf" } @inbook{Coron2000, author="Coron, Jean-S{\'e}bastien", editor="Bellare, Mihir", chapter="On the Exact Security of Full Domain Hash", title="Advances in Cryptology --- CRYPTO 2000: 20th Annual International Cryptology Conference Santa Barbara, California, USA, August 20--24, 2000 Proceedings", year="2000", publisher="Springer Berlin Heidelberg", address="Berlin, Heidelberg", pages="229--235", isbn="978-3-540-44598-2", doi="10.1007/3-540-44598-6_14", doi_url="http://dx.doi.org/10.1007/3-540-44598-6_14", url="https://www.iacr.org/archive/crypto2000/18800229/18800229.pdf" }