Indistinguishability Obfuscation from Well-Founded Assumptions

The classic theory of computation tells us that general computer programs can be converted into equivalent polynomials (albeit over finite fields, which we will focus on implicitly in the sequel). So the pseudo-canonicalization question posed above is equivalent to the pseudo-canonicalization question for general computer programs. Indeed, the question of hiding implementation details within a computer program has a long history, dating at least as far back as the groundbreaking 1976 work of Diffie and Hellman13 introducing the concept of public-key cryptography. Historically, this problem has been called "program obfuscation," albeit it was typically discussed in an ill-defined form. Discussed in these vague terms, it was folklore that truly secure program obfuscation would have revolutionary applications to computing, especially for securing intellectual property.