Leftover Hashing Against Quantum Side Information

TL;DR

This paper extends the Leftover Hash Lemma to quantum side information, enabling secure cryptographic key agreement even against quantum adversaries, and broadens its applicability to almost two-universal hash families.

Contribution

It proves a more general version of the Leftover Hash Lemma valid with quantum side information and for nearly two-universal hash functions.

Findings

Validates security against quantum adversaries

Applicable to almost two-universal hash functions

Enables quantum-resistant cryptographic protocols

Abstract

The Leftover Hash Lemma states that the output of a two-universal hash function applied to an input with sufficiently high entropy is almost uniformly random. In its standard formulation, the lemma refers to a notion of randomness that is (usually implicitly) defined with respect to classical side information. Here, we prove a (strictly) more general version of the Leftover Hash Lemma that is valid even if side information is represented by the state of a quantum system. Furthermore, our result applies to arbitrary delta-almost two-universal families of hash functions. The generalized Leftover Hash Lemma has applications in cryptography, e.g., for key agreement in the presence of an adversary who is not restricted to classical information processing.