Privacy Amplification in the Isolated Qubits Model

TL;DR

This paper introduces a new privacy amplification method for isolated qubits that ensures minimal information leakage in quantum cryptographic hardware, even against adversaries with advanced capabilities.

Contribution

It presents a novel privacy amplification technique using a fixed hash function secure against all adversaries in the isolated qubits model, enabling secure one-time memories.

Findings

Single-bit OTM's leak exponentially small information

Privacy amplification is secure against polynomially-bounded entangling adversaries

Method extends to more powerful adversarial models

Abstract

Isolated qubits are a special class of quantum devices, which can be used to implement tamper-resistant cryptographic hardware such as one-time memories (OTM's). Unfortunately, these OTM constructions leak some information, and standard methods for privacy amplification cannot be applied here, because the adversary has advance knowledge of the hash function that the honest parties will use. In this paper we show a stronger form of privacy amplification that solves this problem, using a fixed hash function that is secure against all possible adversaries in the isolated qubits model. This allows us to construct single-bit OTM's which only leak an exponentially small amount of information. We then study a natural generalization of the isolated qubits model, where the adversary is allowed to perform a polynomially-bounded number of entangling gates, in addition to unbounded local operations and classical communication (LOCC). We show that our technique for privacy amplification is also secure in this setting.