Ideally, in any quantum key distribution (QKD) communication system, each sifted key is expected to be received without error. However in practice, due to infeasibility of generating pure single photon and device impairment problem, some of the sifted key may experience errors. This results to the increment of quantum bit error rate (QBER) that requires error reconciliation for correcting error. The main concept in error reconciliation is very much related to the capability of correcting all errors while minimizing eavesdrop information. The quantum error correcting code such as Hamming code which used in Winnow protocol is found to be more attractive. However the Winnow protocol can only correct one error out of seven bits. In this paper, a modified Hamming encoder/decoder to improve Winnow protocol by correcting two errors out of seven bits which leads to reducing the QBER is presented. This design utilizes a pair of forward and reverse order syndromes for error pattern recognition. A new reconciliation protocol has been developed to enhance the error correcting capability in BB84 protocol. It is carried out in a simple structure which can correct up to double erroneous bits and detect four erroneous bits for each seven bits.
Ideally, in any quantum key distribution (QKD) communication system, each sifted key is expected to be received without error. However in practice, due to infeasibility of generating pure single photon and device impairment problem, some of the sifted key may experience errors. This results to the increment of quantum bit error rate (QBER) that requires error reconciliation for correcting error. The main concept in error reconciliation is very much related to the capability of correcting all errors while minimizing eavesdrop information. The quantum error correcting code such as Hamming code which used in Winnow protocol is found to be more attractive. However the Winnow protocol can only correct one error out of seven bits. In this paper, a modified Hamming encoder/decoder to improve Winnow protocol by correcting two errors out of seven bits which leads to reducing the QBER is presented. This design utilizes a pair of forward and reverse order syndromes for error pattern recognition. A new reconciliation protocol has been developed to enhance the error correcting capability in BB84 protocol. It is carried out in a simple structure which can correct up to double erroneous bits and detect four erroneous bits for each seven bits.
Ideally, in any quantum key distribution (QKD) communication system, each sifted key is expected to be received without error. However in practice, due to infeasibility of generating pure single photon and device impairment problem, some of the sifted key may experience errors. This results to the increment of quantum bit error rate (QBER) that requires error reconciliation for correcting error. The main concept in error reconciliation is very much related to the capability of correcting all errors while minimizing eavesdrop information. The quantum error correcting code such as Hamming code which used in Winnow protocol is found to be more attractive. However the Winnow protocol can only correct one error out of seven bits. Adopting this classical error correcting code, an improved reconciliation scheme namely Siao Ping 1985 (SP 1985) protocol is proposed in this paper to correct more errors in faster pace without additional formulation for the overall simplicity criterion. This research is aimed at building up efficiency and effectiveness of reconciliation of the robust BB84 protocol in coping with noise interference. The proposed SP 1985 reconciliation protocol utilizes a pair of forward and reverse order syndromes for error pattern recognition. It is carried out in a simple structure which can correct up to double erroneous bits and detect four erroneous bits for each seven bits. Therefore, it is sufficient to deliver the desirable outcome after investigating its capability by correcting two errors out of seven bits compared to Winnow protocol. Its effectiveness can be measured based on simulation result which leads to reducing the QBER.
Quantum cryptography specifically called Quantum Key Distribution (QKD) provides acceptable levels of secure communications by utilising established laws of quantum mechanics. QKD protocol distributes a raw key through quantum channel between two cryptography users and then it removes errors occurred during communication from the distributed key by passing messages via public channel. Most popular error reconciliation protocols such as Binary, Cascade and Winnow are used to remove errors in a secure way. Among these three protocols, Buttler’s Winnow has the advantage of less communication complexity, however it is less effective at high error rates in a key and has the disadvantage of introducing errors during error reconciliation, and hence, causes reduction in reconciled key size and/or leave errors in the reconciled key. Winnow can handle quantum bit error rates a maximum up to 18 percent. However, after 13 percent error rate, Winnow becomes highly interactive and it may fail to reconcile the key. The deficiencies of high interactivity, reduction in reconciled key size, leaving errors in the reconciled key and failure of Winnow can be removed by enhancing the error reconciliation protocol by employing modified Bose, Chaudhuri, Hocquenghem (BCH) channel coding techniques. The enhanced BCH encoding algorithm is designed to handle a key at higher quantum bit error rates. BCH error detection and correction algorithms are enhanced to minimise the error percentage in the reconciled key. The modified block interleaver is introduced in the reconciliation protocol to obtain a long-size reconciled key with minimum iterations. The enhanced error reconciliation protocol can reconcile the key up to 50 percent initial bit error rate and reduces public channel communications. Finally, a long sized identical shared secret key with minimal error rate approaching zero is obtained within two iterations. The attained key can be used with secret key cipher to encrypt and decrypt information.
In data post-processing for quantum key distribution, it is essential to have a highly efficient error reconciliation protocol. Based on the key redistribution scheme, we analyze a one-way error reconciliation protocol by data simulation. The relationship between the error correction capability and the key generation efficiency of three kinds of Hamming code are demonstrated. The simulation results indicate that when the initial error rates are(0,1.5%],(1.5,4%], and(4,11%], using the Hamming(31,26),(15,11), and(7,4) codes to correct the error, respectively, the key generation rate will be maximized. Based on this, we propose a modified one-way error reconciliation protocol which employs a mixed Hamming code concatenation scheme. The error correction capability and key generation rate are verified through data simulation. Using the parameters of the posterior distribution based on the tested data, a simple method for estimating the bit error rate(BER) with a given confidence interval is estimated. The simulation results show that when the initial bit error rate is 10.00%, after 7 rounds of error correction, the error bits are eliminated completely, and the key generation rate is 10.36%; the BER expectation is 2.96×10-10, and when the confidence is 95% the corresponding BER upper limit is 2.17×10-9. By comparison, for the single(7,4) Hamming code error reconciliation scheme at a confidence of 95%,the key generation rate is only 6.09%, while the BER expectation is 5.92×10-9, with a BER upper limit of 4.34×10-8. Hence, our improved protocol is much better than the original one.
We describe an error-reconciliation protocol, which we call Winnow, based on the exchange of parity and Hamming's ``syndrome'' for N-bit subunits of a large dataset. The Winnow protocol was developed in the context of quantum-key distribution and offers significant advantages and net higher efficiency compared to other widely used protocols within the quantum cryptography community. A detailed mathematical analysis of the Winnow protocol is presented in the context of practical implementations of quantum-key distribution; in particular, the information overhead required for secure implementation is one of the most important criteria in the evaluation of a particular error-reconciliation protocol. The increase in efficiency for the Winnow protocol is largely due to the reduction in authenticated public communication required for its implementation.
In data post-processing for quantum key distribution, it is essential to have a highly efficient error reconciliation protocol. Based on the key redistribution scheme, we analyze a one-way error reconciliation protocol by data simulation. The relationship between the error correction capability and the key generation efficiency of three kinds of Hamming code are demonstrated. The simulation results indicate that when the initial error rates are (0,1.5%], (1.5,4%], and (4,11%], using the Hamming (31,26), (15,11), and (7,4) codes to correct the error, respectively, the key generation rate will be maximized. Based on this, we propose a modified one-way error reconciliation protocol which employs a mixed Hamming code concatenation scheme. The error correction capability and key generation rate are verified through data simulation. Using the parameters of the posterior distribution based on the tested data, a simple method for estimating the bit error rate (BER) with a given confidence interval is estimated. The simulation results show that when the initial bit error rate is 10.00%, after 7 rounds of error correction, the error bits are eliminated completely, and the key generation rate is 10.36%; the BER expectation is 2.96 × 10-10, and when the confidence is 95% the corresponding BER upper limit is 2.17 × 10-9. By comparison, for the single (7,4) Hamming code error reconciliation scheme at a confidence of 95%, the key generation rate is only 6.09%, while the BER expectation is 5.92 × 10-9, with a BER upper limit of 4.34 × 10-8. Hence, our improved protocol is much better than the original one.
In data post-processing for quantum key distribution, it is essential to have a highly efficient error reconciliation protocol. Based on the key redistribution scheme, we analyze a one-way error reconciliation protocol by data simulation. The relationship between the error correction capability and the key generation efficiency of three kinds of Hamming code are demonstrated. The simulation results indicate that when the initial error rates are(0,1.5%],(1.5,4%], and(4,11%], using the Hamming(31,26),(15,11), and(7,4) codes to correct the error, respectively, the key generation rate will be maximized. Based on this, we propose a modified one-way error reconciliation protocol which employs a mixed Hamming code concatenation scheme. The error correction capability and key generation rate are verified through data simulation. Using the parameters of the posterior distribution based on the tested data, a simple method for estimating the bit error rate(BER) with a given confidence interval is estimated. The simulation results show that when the initial bit error rate is 10.00%, after 7 rounds of error correction, the error bits are eliminated completely, and the key generation rate is 10.36%; the BER expectation is 2.96×10-10, and when the confidence is 95% the corresponding BER upper limit is 2.17×10-9. By comparison, for the single(7,4) Hamming code error reconciliation scheme at a confidence of 95%,the key generation rate is only 6.09%, while the BER expectation is 5.92×10-9, with a BER upper limit of 4.34×10-8. Hence, our improved protocol is much better than the original one.