Blind signatures are the central cryptographic component of digital cash schemes. In this paper, we investigate the security of the first such scheme proposed, namely Chaum’s RSA-based blind signature scheme, in the random-oracle model. This leads us to formulate and investigate a new class of RSA-related computational problems which we call the “one-more-RSA-inversion” problems. Our main result is that two problems in this class which we call the chosen-target and known-target inversion problems, have polynomially-equivalent computational complexity. This leads to a proof of security for Chaum’s scheme in the random oracle model based on the assumed hardness of either of these problems.