Large N Quantum Cryptography

TL;DR

This paper explores how repeating quantum cryptographic tasks multiple times can enhance security, enabling partial or near-perfect security even when single implementations are insecure, demonstrated through protocols for bit commitment and random number generation.

Contribution

It introduces the concept that multiple executions of quantum cryptographic tasks can achieve security levels unattainable by single executions, with practical protocols for bit commitment and randomness.

Findings

Multiple copies can provide useful partial security.

Protocols for quantum bit string commitment.

Protocols for quantum random number generation.

Abstract

In quantum cryptography, the level of security attainable by a protocol which implements a particular task $N$ times bears no simple relation to the level of security attainable by a protocol implementing the task once. Useful partial security, and even near-perfect security in an appropriate sense, can be obtained for $N$ copies of a task which itself cannot be securely implemented. We illustrate this with protocols for quantum bit string commitment and quantum random number generation between mistrustful parties.