These lecture notes are a compilation of some of my readings while I was preparing two lectures given at EPFL on provable security in cryptography. They are essentially based on a book chapter from David Pointcheval called “Provable Security for Public Key Schemes”, on Victor Shoup’s tutorial on game playing techniques, on Coron’s Crypto’00 paper on the exact security of the Full Domain Hash, and on Victor Shoup’s Journal of Cryptology paper on OAEP+.