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Scientific Reports

Fast and simple high-capacity quantum cryptography with error detection

Hong Lai, Ming‐Xing Luo, Josef Pieprzyk, Jun Zhang, Lei Pan, Shudong Li, Mehmet Ali Orgun

Published Apr 13, 2017• 8 citations
Publisher

Abstract

Quantum cryptography is commonly used to generate fresh secure keys with quantum signal transmission for instant use between two parties. However, research shows that the relatively low key generation rate hinders its practical use where a symmetric cryptography component consumes the shared key. That is, the security of the symmetric cryptography demands frequent rate of key updates, which leads to a higher consumption of the internal one-time-pad communication bandwidth, since it requires the length of the key to be as long as that of the secret. In order to alleviate these issues, we develop a matrix algorithm for fast and simple high-capacity quantum cryptography. Our scheme can achieve secure private communication with fresh keys generated from Fibonacci- and Lucas- valued orbital angular momentum (OAM) states for the seed to construct recursive Fibonacci and Lucas matrices. Moreover, the proposed matrix algorithm for quantum cryptography can ultimately be simplified to matrix multiplication, which is implemented and optimized in modern computers. Most importantly, considerably information capacity can be improved effectively and efficiently by the recursive property of Fibonacci and Lucas matrices, thereby avoiding the restriction of physical conditions, such as the communication bandwidth.

DOI
10.1038/srep46302

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Quantum cryptography is commonly used to generate fresh secure keys with quantum signal transmission for instant use between two parties. However, research shows that the relatively low key generation rate hinders its practical use where a symmetric cryptography component consumes the shared key. That is, the security of the symmetric cryptography demands frequent rate of key updates, which leads to a higher consumption of the internal one-time-pad communication bandwidth, since it requires the length of the key to be as long as that of the secret. In order to alleviate these issues, we develop a matrix algorithm for fast and simple high-capacity quantum cryptography. Our scheme can achieve secure private communication with fresh keys generated from Fibonacci- and Lucas- valued orbital angular momentum (OAM) states for the seed to construct recursive Fibonacci and Lucas matrices. Moreover, the proposed matrix algorithm for quantum cryptography can ultimately be simplified to matrix multiplication, which is implemented and optimized in modern computers. Most importantly, considerably information capacity can be improved effectively and efficiently by the recursive property of Fibonacci and Lucas matrices, thereby avoiding the restriction of physical conditions, such as the communication bandwidth.
Quantum cryptography and quantum key distribution (QKD) have been the most successful applications of quantum information processing, highlighting the unique capability of quantum mechanics, through the no-cloning theorem, to securely share encryption keys between two parties. Here, we present an approach to high-capacity, high-efficiency QKD by exploiting cross-disciplinary ideas from quantum information theory and the theory of light scattering of aperiodic photonic media. We propose a unique type of entangled-photon source, as well as a physical mechanism for efficiently sharing keys. The key-sharing protocol combines entanglement with the mathematical properties of a recursive sequence to allow a realization of the physical conditions necessary for implementation of the no-cloning principle for QKD, while the source produces entangled photons whose orbital angular momenta (OAM) are in a superposition of Fibonacci numbers. The source is used to implement a particular physical realization of the protocol by randomly encoding the Fibonacci sequence onto entangled OAM states, allowing secure generation of long keys from few photons. Unlike in polarization-based protocols, reference frame alignment is unnecessary, while the required experimental setup is simpler than other OAM-based protocols capable of achieving the same capacity and its complexity grows less rapidly with increasing range of OAM used.
Abstract In this paper, we develop a large-capacity quantum digital secret sharing (QDSS) scheme, combined the Fibonacci- and Lucas-valued orbital angular momentum (OAM) entanglement with the recursive Fibonacci and Lucas matrices. To be exact, Alice prepares pairs of photons in the Fibonacci- and Lucas-valued OAM entangled states, and then allocates them to two participants, say, Bob and Charlie, to establish the secret key. Moreover, the available Fibonacci and Lucas values from the matching entangled states are used as the seed for generating the Fibonacci and Lucas matrices. This is achieved because the entries of the Fibonacci and Lucas matrices are recursive. The secret key can only be obtained jointly by Bob and Charlie, who can further recover the secret. Its security is based on the facts that nonorthogonal states are indistinguishable, and Bob or Charlie detects a Fibonacci number, there is still a twofold uncertainty for Charlie' (Bob') detected value.
Quantum cryptography and quantum key distribution (QKD) have been the most successful applications of quantum information processing, highlighting the unique capability of quantum mechanics, through the no-cloning theorem, to protect the security of shared encryption keys. Here we present a new and fundamentally different approach to high-capacity, high-efficiency QKD by exploiting interplay between cross-disciplinary ideas from quantum information and light scattering of aperiodic photonic media. The novelty of the proposed approach relies on a unique type of entangled-photon source and a new physical mechanism for efficiently sharing keys. The new source produces entangled photons with orbital angular momenta (OAM) randomly distributed among Fibonacci numbers. Combining entanglement with the mathematical properties of Fibonacci sequences leads to a new QKD protocol. This Fibonacci protocol is immune to photon-number-splitting attacks and allows secure generation of long keys from few photons. Unlike other protocols, reference frame alignment and active modulation of production and detection bases are unnecessary, since security does not require use of non-orthogonal polarization measurements.
Quantum cryptography provides the inherent security for transmitting confidential information across free space or a fiber link. However, a high secure-key rate is still a challenge for a quantum-cryptography system. High-dimensional quantum cryptography, which can tolerate much higher channel noise, is a prospective way to share a higher secure-key rate between legitimate users, and has received substantial attention over the last decade. In particular, orbital angular momentum (OAM) can provide an abundant resource for high-dimensional quantum cryptography. Furthermore, combining spin angular momentum (SAM) with OAM can increase the encoding alphabet. Here we verify a prepare-and-measure quantum-cryptography scheme based on four-dimensional SAM-OAM hybrid states over kilometer-scale ring-core fibers. The measured quantum-bit error rates are $4.3\mathrm{%}$ for 4 km of fiber and $16.3\mathrm{%}$ for 25 km of fiber. The scheme simplifies the process of state preparation and measurement, with a compact and scalable setup.
Quantum cryptography is an emerging technology in which two parties may simultaneously generate shared, secret cryptographic key material using the transmission of quantum states of light. The security of these transmissions is based on the inviolability of the laws of quantum mechanics and information-theoretically secure post-processing methods. An adversary can neither successfully tap the quantum transmissions, nor evade detection, owing to Heisenberg's uncertainty principle. In this paper we describe the theory of quantum cryptography, and the most recent results from our experimental free-space system with which we have demonstrated for the first time the feasibility of quantum key generation over a point-to-point outdoor atmospheric path in daylight. We achieved a transmission distance of 0.5 km, which was limited only by the length of the test range. Our results provide strong evidence that cryptographic key material could be generated on demand between a ground station and a satellite (or between two satellites), allowing a satellite to be securely re-keyed on orbit. We present a feasibility analysis of surface-to-satellite quantum key generation.
Currently many symmetric key cryptographic tools which are known to be quantum-safe. They all share Secret symmetric keys through an untrusted medium which is usually done with public key methods which are prone to quantum attacks. One among the recommended solutions to the key distribution problem is Quantum Key Distribution (QKD). QKD utilizes an authenticated Communication channel along with a quantum communication channel so that a secret key is generated. Whatever may be the protocol to implement proposed QKD, they all need both a quantum channel, and an authenticated classical. OTP (One Time Pad) is used when two parties wish to communications have to share a key called pad. This pad is a randomly generated key and the length of the key should be equal to the message so it can be sent. The proposed QKD parameters that result in almost 35.67% smaller keys for quantum security and an implementation of QKD in network which is publicly available and usable in practice.