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Harnessing closed timelike curves for cryptographic protocols

Soumik Ghosh, Arnab Adhikary, Goutam Paul

Published Aug 11, 2017• 0 citations
OpenAlex

Abstract

Quantum bit commitment and Quantum Key Distribution (QKD) are the building blocks of secure quantum cryptographic protocols. Of the numerous QKD schemes, the BB84 protocol was the first one proposed and it is also the most popular. Bennett and Brassard, in their 1984 paper, proposed both quantum bit commitment and the BB84 scheme of QKD. However, their scheme for bit commitment was later shown to be vulnerable to an EPR attack. Also, in a world with Deutschian Closed Timelike Curves (D-CTCs), the BB84 protocol can be broken as the eavesdropper can intercept whatever key the two parties communicate with each other using a circuit which detects non-orthogonal quantum states. Later, the idea of this circuit was extended using Postselected Closed Timelike Curves (P-CTCs), a second variant of CTCs. In this paper, we first propose a secure quantum bit commitment protocol using the Deutschian model of closed timelike curves. Then, we take up the BB84 protocol and propose a secure version of the protocol, transforming it to an entanglement based scheme using the postselected model of closed timelike curves. In short, we show that in the presence of Closed Timelike Curves, unconditionally secure quantum bit commitment and secure quantum key distribution are both possible.

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Quantum bit commitment and Quantum Key Distribution (QKD) are the building blocks of secure quantum cryptographic protocols. Of the numerous QKD schemes, the BB84 protocol was the first one proposed and it is also the most popular. Bennett and Brassard, in their 1984 paper, proposed both quantum bit commitment and the BB84 scheme of QKD. However, their scheme for bit commitment was later shown to be vulnerable to an EPR attack. Also, in a world with Deutschian Closed Timelike Curves (D-CTCs), the BB84 protocol can be broken as the eavesdropper can intercept whatever key the two parties communicate with each other using a circuit which detects non-orthogonal quantum states. Later, the idea of this circuit was extended using Postselected Closed Timelike Curves (P-CTCs), a second variant of CTCs. In this paper, we first propose a secure quantum bit commitment protocol using the Deutschian model of closed timelike curves. Then, we take up the BB84 protocol and propose a secure version of the protocol, transforming it to an entanglement based scheme using the postselected model of closed timelike curves. In short, we show that in the presence of Closed Timelike Curves, unconditionally secure quantum bit commitment and secure quantum key distribution are both possible.
Cryptography is being introduced to secure data. Through Classical Cryptographic technique, we can encrypt our data and secure secret key also. But classical cryptography is based on mathematical techniques where reversing one-way function is possible with sufficient computing power and time. So, Quantum Cryptography is introduced to overcome those drawbacks of traditional classical cryptography. It is based on the values of quantum mechanics and photon. Scientists and researchers have brought up a new key distribution protocol based on Quantum Cryptography is called Quantum Key Distribution (QKD) Protocol. The first QKD protocol BB84 was introduced by Charles Bennett and Gilles Brassard in 1984. After that several QKD protocols have been created. In this paper we have improved BB84 Protocol by removing the drawbacks of the existing algorithm towards Eavesdropping which may not be detected or disclosing large portion of secret key. Steps of the existing BB84 algorithm along with the modified one is described in detail with example and pseudo code. Limitations of BB84 and comparative study of both the existing and the improved one based on their security has been made and described in this current work.
As the digital front becomes our new frontier, and digital data becomes increasingly vulnerable to highly sophisticated cyber attacks, conventional encryption approaches may no longer be sufficient to withstand a quantum attack. The focus of this work is to deploy a simulation of the BB84 protocol, one of the first Quantum Key Distribution (QKD) protocols developed by Charles Bennett and Gilles Brassard in 1984. The simulation involves two communicating parties, Alice and Bob, with Bob creating a secret keys generated cryptographically and sending it reliably over to Alice using quantum bits, or qubits. By leveraging quantum mechanics, this protocol ensures that any interception can be identified, thus bolstering both the integrity and confidentiality of the key exchange through scientists' understanding of superposition and the no-cloning principle. In the simulation, the potential of quantum communication to achieve secure key distribution over an insecure channel is demonstrated. Differently from traditional encryption protocols, QKD guarantees security not on computational but on physical basis. The aim of this paper is to show the feasibility and robustness of the BB84 protocol for actual cryptographic applications. This models the protocol between Alice and Bob, which paves the way for quantum-proof encryption systems and is a relevant step towards next generation cyber security.
Quantum Key Distribution (QKD) is a ground-breaking solution to secure communication that uses fundamental quantum mechanics principles to allow for the exchange of cryptographic keys with provable security. BB84 and E91, two of the first and most significant QKD systems, presented two different approaches to using quantum characteristics to prevent eavesdropping and maintain confidentiality. A brief literature review of these two fundamental protocols is presented in this paper. Bennett and Brassard created the BB84 protocol in 1984. It uses polarized photons and detects interception using the uncertainty principle. On the other hand, Bell's theorem and entangled photon pairs are used in the E91 protocol, which was first presented by Ekert in 1991, to guarantee the integrity of the shared key. Each protocol's theoretical foundations, methods of implementation, and relative benefits has been explored in addition to how they have influenced contemporary quantum cryptography systems. This paper attempts to give a basic understanding of QKD and its early advancements by examining the similarities and differences between BB84 and E91.
Quantum Key Distribution (QKD) is a technique that enables secure communication between two parties by sharing a secret key. One of the most well-known QKD protocols is the BB84 protocol, proposed by Charles Bennett and Gilles Brassard in 1984. In this protocol, Alice and Bob use a quantum channel to exchange qubits, allowing them to generate a shared key that is resistant to eavesdropping. This paper presents a comparative study of existing QKD schemes, including the BB84 protocol, and highlights the advancements made in the BB84 protocol over the years. The study aims to provide a comprehensive overview of the different QKD schemes and their strengths and weaknesses and demonstrate QKDs working principles through existing simulations and implementations. Through this study, we show that the BB84 protocol is a highly secure QKD scheme that has been extensively studied and implemented in various settings. Furthermore, we discuss the improvements made to the BB84 protocol to enhance its security and practicality, including the use of decoy states and advanced error correction techniques. Overall, this paper provides a comprehensive analysis of QKD schemes, focusing on the BB84 protocol in secure communication technologies.
Classical cryptographic systems are increasingly challenged by advances in computing power and new algorithmic techniques, particularly with the rise of quantum computing, which threatens the security of current encryption methods. This has spurred interest in quantum-resistant cryptography, aimed at creating algorithms that can withstand attacks from quantum computers. Traditionally, secure key transport over alternate channels has been a significant challenge, but quantum mechanics offers a solution. Quantum Key Distribution (QKD) is a revolutionary method for secure communication that leverages quantum principles. Unlike traditional methods, QKD provides unconditional security, with key security ensured by the laws of physics rather than computational difficulty. The BB84 protocol, introduced in 1984 by Bennett and Brassard, is a leading QKD scheme known for its simplicity and effectiveness in generating eavesdropping-resistant cryptographic keys. It facilitates secure key transport over alternate channels. This documentation aims to advance QKD security by practically implementing and analyzing the BB84 protocol. Through detailed theoretical analysis, simulation studies, and experimental validation, the practical impacts, and limitations of BB84-based QKD systems are examined. Additionally, a practical implementation of quantum key distribution using a sudoku key demonstrates the process's simplicity and effectiveness. These findings are expected to pave new paths in the field of cryptanalysis in the emerging Quantum Age.
Quantum key distribution (QKD) protocols make it possible for two parties to generate a secret shared key. One of the most important QKD protocols, BB84, was suggested by Bennett and Brassard in 1984. Various proofs of unconditional security for BB84 have been suggested, but the first security proofs were not composable. Here we improve a security proof of BB84 given by [Biham, Boyer, Boykin, Mor, and Roychowdhury, J. Cryptology, 19(4):381-439, 2006] to be composable and match the state-of-the-art results for BB84, and we extend it to prove unconditional security of several variants of the BB84 protocol. Our composable security proof for BB84 and its variants is mostly self-contained, algebraic, and relatively simple, and it gives tight finite-key bounds.