Error correction is a necessary step in quantum cryptography since the quantum bit error rate(QBER)is thought as unavoidable as the practical quantum system containing probability unknown in phase and amplitude.These errors come from the experimental imperfection even if there is no exist of eavesdroppers.The error correction protocol used today is based on two-way communication via classical channel that leads to reduction of the key rate.The distilled bits available for practical encryption will decrease further after private amplification and authentication.This paper proposes one-way correction that can combine the authentication and correction altogether.This protocol is based on periodic structure analysis that any defect in the periodic structure reports an error so that the error is correctly allocated.Theoretical and digital simulation demonstrated that this protocol makes direct private communication possible by using quantum sifted keys.In this protocol the quantum sifted keys before correction was divided into two parts.The first part is used for authentication.In practice,Alice encoded her question several times with different quantum sifted key in a manner same as one-time-pad.Bob can recognize her question only if had he made correction of his quantum sifted keys.Bob does his bit error correction by himself with the cryptogram he received and his sifted keys only if the error bit rate is allowable since some kind of periodic structure can be found in the decrypted text.By comparison of the periodic features of the bit strings he can allocate the error bit and calculate error bite rate that is possible to lead to a correction of the error bits without any reduction of the key.After his error correction for the decrypted text he can recognize Alice's question and makes a correct answer to her.The answer may be encoded with his corrected key and then send back to Alice.Alice is easy to check if Bob has perfectly responded.The sifted keys should be abandoned if the QBER is high and therefor unsafe.The security proof and authentication are completed all together.An error matrix can be obtained exclusively if the quantum bit error rate is low enongh to guarantee a security quantum key distribution.The error matrix can be used to correct the errors in the decrypted text instead of that in the quantum sifted key as usual.This protocol leads to direct private communication with quantum sifted key safely.Therefore there is no need to store that distilled keys in computer as usual where it is still possible for some else to make a copy.
Error correction is a necessary step in quantum cryptography since the quantum bit error rate(QBER)is thought as unavoidable as the practical quantum system containing probability unknown in phase and amplitude.These errors come from the experimental imperfection even if there is no exist of eavesdroppers.The error correction protocol used today is based on two-way communication via classical channel that leads to reduction of the key rate.The distilled bits available for practical encryption will decrease further after private amplification and authentication.This paper proposes one-way correction that can combine the authentication and correction altogether.This protocol is based on periodic structure analysis that any defect in the periodic structure reports an error so that the error is correctly allocated.Theoretical and digital simulation demonstrated that this protocol makes direct private communication possible by using quantum sifted keys.In this protocol the quantum sifted keys before correction was divided into two parts.The first part is used for authentication.In practice,Alice encoded her question several times with different quantum sifted key in a manner same as one-time-pad.Bob can recognize her question only if had he made correction of his quantum sifted keys.Bob does his bit error correction by himself with the cryptogram he received and his sifted keys only if the error bit rate is allowable since some kind of periodic structure can be found in the decrypted text.By comparison of the periodic features of the bit strings he can allocate the error bit and calculate error bite rate that is possible to lead to a correction of the error bits without any reduction of the key.After his error correction for the decrypted text he can recognize Alice's question and makes a correct answer to her.The answer may be encoded with his corrected key and then send back to Alice.Alice is easy to check if Bob has perfectly responded.The sifted keys should be abandoned if the QBER is high and therefor unsafe.The security proof and authentication are completed all together.An error matrix can be obtained exclusively if the quantum bit error rate is low enongh to guarantee a security quantum key distribution.The error matrix can be used to correct the errors in the decrypted text instead of that in the quantum sifted key as usual.This protocol leads to direct private communication with quantum sifted key safely.Therefore there is no need to store that distilled keys in computer as usual where it is still possible for some else to make a copy.
Quantum secure direct communication is one of the important mode of quantum communication, which sends secret information through a quantum channel directly without setting up a prior key. Over the past decade, numerous protocols have been proposed, and part of them have been experimentally demonstrated. However, the strict security proof is still in suspense. Two-way protocol is seen as one of the most practical protocol, in this paper, the security of the two-way quantum secure direct communication protocol will be proved against general attacks when the noisy and lossy channel is taken into account. There are two steps included in the proof, firstly, we need to prove that the mutual information between Alice and Bob is larger than the mutual information shared between Alice and the eavesdropper when the error rate in control mode is less than the predetermined threshold. Secondly, once the error rate is lower than the threshold, one can always find out a forward error correction code to guarantee the security of information transmission.
Quantum cryptography is essentially the quantum key distribution (QKD). In the context of QKD, one from two partners (Alice) generates and sends a sequence of qubits through a private quantum channel to another partner (Bob) and Bob receives the sequence and measures the state of each qubit. After the quantum transmission stage, Alice and Bob have almost identical qubit sequences. The erros are due to physical imperfections in the channel and presence of an eavesdropper. The next stage in QKD is key reconciliation (i.e. finding and correcting discrepancies between Alice's string and that of Bob). This reconciliation can be done by public discussion. Let us suppose there is a secret quantum channel between Alice and Bob through which Alice transmits a n-bit string A=(A1, A2,...,An)ε{0,1}n. Then Bob receives a n-bit string B=(B1, B2,...,Bn)ε{0,1)n. The string B differs from A due to the presence of noise and eavesdropper in the channel. One can estimate the bit error probability in the channel. For example, Bob can choose a random subset from his string and send it to Alice in public. Then Alice compares the received string with her corresponding subset and calculates the total number of protocol steps. The cascade scheme uses the interaction over the public channel to correct the secret strings by dividing them into the blocks of a fixed length. The length is determined from the bit error probability. A simple interactive routine is applied in each of these blocks. An error found in some block results in some action with other blocks. It is important to optimize the error-finding routines in standalone blocks as well as to organize the effective constrution of blocks with the object of protocol benchmark, information leakage and number of interactions between partners.
In a standard quantum key distribution (QKD) scheme such as BB84, two procedures, error correction and privacy amplification, are applied to extract a final secure key from a raw key generated from quantum transmission. To simplify the study of protocols, it is commonly assumed that the two procedures can be decoupled from each other. While such a decoupling assumption may be valid for individual attacks, it is actually unproven in the context of ultimate or unconditional security, which is the Holy Grail of quantum cryptography. In particular, this means that the application of standard efficient two-way error-correction protocols like Cascade is not proven to be unconditionally secure. Here, I provide the first proof of such a decoupling principle in the context of unconditional security. The method requires Alice and Bob to share some initial secret string and use it to encrypt their communications in the error correction stage using one-time-pad encryption. Consequently, I prove the unconditional security of the interactive Cascade protocol proposed by Brassard and Salvail for error correction and modified by one-time-pad encryption of the error syndrome, followed by the random matrix protocol for privacy amplification. This is an efficient protocol in terms of both computational power and key generation rate. My proof uses the entanglement purification approach to security proofs of QKD. The proof applies to all adaptive symmetric methods for error correction, which cover all existing methods proposed for BB84. In terms of the net key generation rate, the new method is as efficient as the standard Shor-Preskill proof.
Objective of this paper is the study of Quantum Key Distribution (QKD) protocols based on classical error-correcting codes. The Quantum Key Distribution (QKD) systems and related protocols, in particular conditions, can use the classic channel coding techniques, instead of quantum error-correcting codes, both for correcting errors that occurred during the exchange of a cryptographic key between two authorized users, and to allow privacy amplification, in order to make completely vain a possible intruder attempt. The secret key is transmitted over a quantum, and thus safe, channel, characterized by very low transmission rates and high error rates. This channel is safe for the properties of a quantum system, where each measurement on the system perturbs the system itself, allowing the authorized users to “feel” if there is any intruder listening. Moreover, as shown by accurate experimental studies, the communication channel used for quantum key exchange is not able to reach high levels of reliability (the Quantum Bit Error Rate (QBER) takes values between 0.05 and 0.11), both because of the inherent characteristics of the system, and of the presence of a possible attacker. Thus, in order to obtain acceptable residual error rates, it is necessary to use a parallel classical and public channel, conversely characterized by high transmission rates and low error rates, on which to transmit only the redundancy bits of systematic channel codes with performance possibly close to the capacity limit.
Privacy and authenticity are two main tasks for secure communication. In this paper, a quantum authenticated encryption scheme is proposed. This scheme is devised to encrypt and authenticate classical information using quantum states. We assume that Alice and Bob share a classical bits string y as their private key. Alice generates quantum cipher text and authentication tag using her secret key. Bob can decrypt and verify the authenticity of the received message. Security analysis shows that the proposed protocol is a computationally secure encryption and statistically secure authentication scheme.
This paper analyzes and adapts the known method of error correction of CV-QKD systems, proposed by Mario Milicevic, which modulates a code word with a correlated Gaussian sequence in amplitude and phase quadratures of coherent states, for use in DV-QKD systems, in which information is encoded by single-photon polarization states, by using a sieved key in the form of classical bits, from which the codeword is created, and also a one-time pad (Vernam cipher), which uses a fairly easy to implement classic Boolean “exclusive OR” operation (XOR). The main task of error correction is to correct errors in order to share the same secure key between the two parties (usually called Alice and Bob). Various factors can cause errors. The unreliability of the quantum channel is due to the fact that photons can cause noise when changing the polarization vector of the photon. In the proposed solution, the quantum component of the protocol occurs only in the first stage of transmission of the protected key, where the exchange of photons. The quantum key distribution system has inevitable errors in the sieved key, which must be corrected by the error correction algorithm to create a secure key. Unlike other known QKD systems, where at the stage of error correction the sifted keys are corrected and passed to the next stage of increasing confidentiality, in the modified method it is proposed to use sifted keys as keys in disposable Vernam ciphers, and the vector that will go to the next stage way and combine with the sifted key. The difference in the sieved keys between the two parties is corrected by means of low-density parity check matrices (LDPC), which are known to both of them in advance. Parity check matrices are created by an algorithm proposed by David MacKay and Radford Neal. Radford Neal open-source program code, is used to create final work program to checking proposed algorithm.