Quantum Fingerprints that Keep Secrets

TL;DR

This paper introduces quantum fingerprinting schemes that can verify string equality while leaking negligible information, surpassing classical limitations and maintaining efficiency and security.

Contribution

The authors develop the first quantum fingerprinting schemes that are both hiding and efficient, with minimal information leakage, unlike classical counterparts.

Findings

Quantum schemes map n-bit strings to O(log n) qubits with low error.

Pure state scheme leaks only O(1) bits, mixed state leaks at most 1/n^c bits.

Mixed-state scheme is proven optimal via a generic extraction strategy.

Abstract

We introduce a new type of cryptographic primitive that we call hiding fingerprinting. A (quantum) fingerprinting scheme translates a binary string of length $n$ to $d$ (qu)bits, typically $d\ll n$, such that given any string $y$ and a fingerprint of $x$, one can decide with high accuracy whether $x=y$. Classical fingerprinting schemes cannot hide information very well: a classical fingerprint of $x$ that guarantees error at most $\epsilon$ necessarily reveals $\Omega(\log(1/ epsilon))$ bits about $x$. We call a scheme hiding if it reveals $o(\log(1/\epsilon))$ bits; accordingly, no classical scheme is hiding. For any constant $c$, we construct two kinds of hiding fingerprinting schemes, both mapping $n$-bit strings to $O(\log n)$ qubits and guaranteeing one-sided error probability at most $1/n^c$. The first kind uses pure states and leaks at most O(1) bits, and the second kind uses mixed states and leaks at most $1/n^c$ bits, where the "leakage" is bounded via accessible information. The schemes are computationally efficient. Our mixed-state scheme is optimal, as shown via a generic strategy that extracts $1/\poly(n)$ bits from any fingerprint over $O(\log n)$ qubits.