Cryptology ePrint Archive: Report 2020/889

Affine Determinant Programs: A Framework for Obfuscation and Witness Encryption

James Bartusek and Yuval Ishai and Aayush Jain and Fermi Ma and Amit Sahai and Mark Zhandry

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 \in {0,1}^n by computing Eval(det(A + sum_{i \in [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.

Category / Keywords: foundations / obfuscation, witness encryption

Original Publication (with minor differences): Innovations in Theoretical Computer Science (ITCS 2020)

Date: received 15 Jul 2020, last revised 16 Jul 2020

Contact author: bartusek james at gmail com,yuvali@cs technion ac il,aayushjain@cs ucla edu,fermima@alum mit edu,sahai@cs ucla edu,mzhandry@princeton edu

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Version: 20200716:133746 (All versions of this report)

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