Yet, not all cryptographic assumptions are equally likely to be true. In 2005, Russell Impagliazzo gave an invited talk titled "A personal view of Average-Case Complexity" where he distinguished between the (minimal) "MiniCrypt" world where One-Way Functions exist and the (more adventurous) "Cryptomania" world where One-Way Functions with trapdoors exist.
Since then, the cryptographic community has become substantially more adventurous. In 2009, Craig Gentry suggested a candidate fully homomorphic encryption (FHE) scheme. If FHE exists, numerous long-standing open crypto problems could be solved. In 2013, Garg, Gentry, Halevi, Raykova, Sahai and Waters suggested a candidate construction for a yet more adventurous primitive called indistinguishability obfuscation (iO). If iO exists, it solves numerous further big open problems in cryptography. Sceptics call this world "Obfustopia".
Yet, iO is not only a strong assumption, but also a conceptually intriguing object. iO is mutually exclusive with other cryptographic assumptions that were believed before... ...and (unlike most of cryptography) iO exists if P equals NP! In the talk, we will discuss the conceptual oddities of iO.