Computability, Learnability and Breakability in Cryptanalysis

Cryptanalysis, the science and art of breaking secret codes, is both a mathematically intensive and a computational intelligence intensive subject. In the past, code-breaking was purely a military or government task, and in fact, the main task of the US National Security Agency (NSA) is "to collect, process and disseminate foreign signal intelligence". The term "signal intelligence" here is interpreted as "encrypted messages". Surprisingly, with the advent of modern computers, particularly the Internet, cryptanalysis is no more just a military or government task, but also an important task in e.g., secure e-commerce, since all the valuable business information, such as the credit card information, needs to be encrypted before sending over the insecure Internet, and more importantly, these sensitive and encrypted information must be unbreakable on all known possible attacks. In this paper, from a cryptanalytic point of view, we study the computability, learnability and breakability in cryptanalysis, particularly in RSA public-key cryptanalysis, in a unified way.