SNARGs for NP from Unprovability of Mathematical Theorems (Or: How to Use the Simplicity of Cryptographic Reasoning)

Modern cryptography relies on the intractability of computational problems. We present an approach to build cryptography from a new source of hardness: proving mathematical theorems. Unprovability results are abundant in mathematics and theoretical computer science, yet to our knowledge, they have not been used as a resource for cryptography.