TanjaCrypt 14 December 2017 Part 1: Understanding Security Notions and Attack Definitions

Security notions and attack definitions (CPA and CCA), semantic security, ciphertext indistinguishability. schoolbook RSA is not CCA-II secure; IND-CCA security as game between attacker and challenger; the attacker should not have higher probability than guessing in deciding which of two messages m0 and m1 was encrypted, given the messages and one ciphertext.

To make RSA a randomized encryption one uses some padding. We discussed PKCS v1.5 as a negative example and looked at Bleichenbacher's attack. Take a look at https://robotattack.org/ for a very recent use of Bleichenbacher's attack in practice. You should be able to understand details of the full paper Return Of Bleichenbacher's Oracle Threat. RSA-OAEP is a better padding scheme.

Factorization methods: trial division, factoring numbers of the form p*nextprime(p+1), Fermat factorization, p-1 method.