Affine Determinant Programs: A Framework for Obfuscation and Witness Encryption

Abstract

An affine determinant program ADP: {0,1}^n → {0,1} is specified by a tuple (A,B_1,…,B_n) of square matrices over 𝔽_q and a function Eval: 𝔽_q → {0,1}, and evaluated on x ∈ {0,1}^n by computing Eval(det(A + ∑_{i∈[n]} x_i B_i)). In this work, we suggest ADPs as a new framework for building general-purpose obfuscation and witness encryption. We provide evidence to suggest that constructions following our ADP-based framework may one day yield secure, practically feasible obfuscation. As a proof-of-concept, we give a candidate ADP-based construction of indistinguishability obfuscation (i𝒪) for all circuits along with a simple witness encryption candidate. We provide cryptanalysis demonstrating that our schemes resist several potential attacks, and leave further cryptanalysis to future work. Lastly, we explore practically feasible applications of our witness encryption candidate, such as public-key encryption with near-optimal key generation.