Quantum Privacy Amplification: A Secure Method for Cryptography

Takeshi Asai, Toyohiro Tsurumaru

Sujit Biswas, Rajat Subhra Goswami

Abstract Quantum cryptography is a technique used in the area of cryptography that relies on quantum mechanics to securely transfer a key between two parties. The BB84 protocol is a well-known quantum cryptography method that produces a shared key between Alice and Bob by using the polarisation states of photons. This paper presents a comprehensive analysis and implementation of the BB84 protocol with polarization states, using the IBM Quantum Lab Simulator. We demonstrated key generation, error correction, and privacy amplification steps, along with a theoretical analysis of security against eavesdropping attacks of the proposed protocol. Furthermore, the practical limitations and considerations for implementing the protocol are discussed, such as the effects of noise and decoherence in realistic quantum systems. Our findings suggest that the Enhanced BB84 Protocol with Error Correction and Privacy Amplification is a promising approach for secure key distribution in quantum communication and could serve as a foundation for future developments in quantum cryptography.

Yizhi Huang, Xingjian Zhang, Xiongfeng Ma

Abstract Privacy amplification is the key step to guarantee the security of quantum communication. The existing security proofs require accumulating a large number of raw key bits for privacy amplification. This is similar to block ciphers in classical cryptography that would delay the final key generation since an entire block must be accumulated before privacy amplification. Moreover, any leftover errors after information reconciliation would corrupt the entire block. By modifying the security proof based on quantum error correction, we develop a stream privacy amplification scheme, which resembles the classical stream cipher, to solve the problems of final key generation delay and error spread. The stream scheme can also help to enhance the security of trusted-relay quantum networks. Inspired by the connection between stream ciphers and quantum error correction in our security analysis, we further develop a generic information-theoretic tool to study the security of classical encryption algorithms.

Chiara Macchiavello

Toyohiro Tsurumaru

Privacy amplification (PA) is an indispensable component in classical and quantum cryptography. Error correction (EC) and data compression (DC) algorithms are also indispensable in classical and quantum information theory. We here study quantum algorithms of these three types (PA, EC, and DC) in the one-shot scenario, and show that they all become equivalent if modified properly. As an application of this equivalence, we take previously known security bounds of PA, and translate them into coding theorems for EC and DC which have not been obtained previously. Further, we apply these results to simplify and improve our previous result that the two prevalent approaches to the security proof of quantum key distribution (QKD) are equivalent. We also propose a new method to simplify the security proof of QKD.

Charles H. Bennett