Oblivious Lookup Tables

TL;DR

This paper introduces the concept of oblivious lookup tables, enabling the evaluation of functions on encrypted data without decryption, and provides a concrete construction along with security analysis and future research directions.

Contribution

It presents the first construction of oblivious lookup tables that work with group-homomorphic encryption, expanding capabilities for secure computation.

Findings

Existence of oblivious lookup tables demonstrated

Concrete construction provided and analyzed for security

Discussion of relations to other cryptographic primitives

Abstract

We consider the following question: given a group-homomorphic public-key encryption $E$, a ciphertext $c=E(x,pk)$ hiding a value $x$ using a key $pk$, and a "suitable" description of a function $f$, can we evaluate $E(f(x), pk)$ without decrypting $c$? We call this an "oblivious lookup table" and show the existence of such a primitive. To this end, we describe a concrete construction, discuss its security and relations to other cryptographic primitives, and point out directions of future investigations towards generalizations.