Modified security analysis of device-independent quantum key distribution with random key basis

TL;DR

This paper improves the security analysis of device-independent quantum key distribution with random key basis by reformulating it as a strongly convex optimization problem, reducing computational costs while maintaining security guarantees.

Contribution

It introduces a more efficient convex optimization framework for security analysis of DIQKD with random basis, clarifies the original proof, and enhances analysis rigor.

Findings

Optimization cost is reduced without affecting key rate.

Security analysis reformulated as a strongly convex problem.

Explicit form of pessimistic error derived.

Abstract

Security analysis is a critical part in any cryptographic protocol, may it be classical or quantum. Without security analysis, one cannot ensure the secrecy of the distributed keys. To perform a conclusive security analysis, it is very often necessary to frame the problem as an optimization problem. However, solving such optimization problems is quite challenging. In this article, we focus on the security analysis of device-independent quantum key distribution (DIQKD) with random key basis protocol. We show that the optimization cost of the existing security analysis can be reduced without compromising the key rate. In particular, we reframe the entire security analysis of this protocol as a strongly convex optimization problem and demonstrate that unlike the original security proof, optimization of Bob's measurement angles for finding a lower bound on Eve's uncertainty about Alice's key generation basis can be done with lesser cost. We derive an explicit form of the pessimistic error that arises while optimizing the measurement angles of both the parties. We also clarify a few parts of the original security proof, making the analysis more rigorous and complete.