Quantum Key Distribution is meant to be an ultimate computer security system that will not need upgrade/overhaul from time to time. QKD allows the generation of long key length on demand. QKD, coupled with the unconditional secure "one-time pad" encryption system, will be unbreakable for eavesdropper with infinite resources. Numerous experimental QKD prototypes have demonstrated that QKD is likely to be a reality before quantum computer. One of the steps in a Quantum Key Distribution protocol is to remove the transmission errors from quantum communication, which typically has a high error rate (one percent or higher). An interactive error control method is utilized in the reconciliation of QKD. This procedure divides transmitted bits into blocks. The size of the block is chosen so that the chance of having multiple error bits in one block is small. By checking parity and doing interactive BINARY search when a parity error is found, error bits can be located and removed. Some error bits escape the detection from the first pass. By repeating this procedure several times, each time randomly dividing bits into blocks, most error bits can be detected and removed. Each parity check means loss of one bit. The goal is to minimize the number of parity checks to locate all (or most) errors and to have a high reliability that the remaining bits have very small residue error rate. Brassard and Salvail devised a better error control procedure in 1993. By keeping track of block parity information from pass to pass, which they called CASCADE, the number of parity checks per error bit is reduced. They observed no errors left after four passes from 10 simulation runs. However, they offered upper bound of residue error rate that was much higher than observed from simulation. Therefore, there is a need to find the optimal block size and to improve the residue error rate analysis of this procedure. In this work, improvement in reconciliation procedure is obtained in throughput (i.e. the number of input bits minus the number of parity checks) and in lower residue error rate. Throughput is doubled at high input error rate and less throughput gain at low input error rate. Three most important factors that enhance the system throughput are: 1) Using larger block size to fully utilize the power of CASCADE method. 2) Avoiding any pair of bits to stay in the same block of any later pass, which allows the use of three passes only (instead of four passes in the BS procedure). 3) Some bits are already known to be lost from the current pass, so I avoid carrying these bits to the later pass. The residue error rate at the end of the second pass (and the third pass) for small initial block size is derived. The residue error rate at the end of the third pass is found much lower than the upper bound given by the previous workers. This residue error rate is found to be a function of input size and the block size. This error control method has many similar features and difficulties to the recent development of "turbo-code" in the error control-coding field.
Quantum Key Distribution is meant to be an ultimate computer security system that will not need upgrade/overhaul from time to time. QKD allows the generation of long key length on demand. QKD, coupled with the unconditional secure "one-time pad" encryption system, will be unbreakable for eavesdropper with infinite resources. Numerous experimental QKD prototypes have demonstrated that QKD is likely to be a reality before quantum computer. One of the steps in a Quantum Key Distribution protocol is to remove the transmission errors from quantum communication, which typically has a high error rate (one percent or higher). An interactive error control method is utilized in the reconciliation of QKD. This procedure divides transmitted bits into blocks. The size of the block is chosen so that the chance of having multiple error bits in one block is small. By checking parity and doing interactive BINARY search when a parity error is found, error bits can be located and removed. Some error bits escape the detection from the first pass. By repeating this procedure several times, each time randomly dividing bits into blocks, most error bits can be detected and removed. Each parity check means loss of one bit. The goal is to minimize the number of parity checks to locate all (or most) errors and to have a high reliability that the remaining bits have very small residue error rate. Brassard and Salvail devised a better error control procedure in 1993. By keeping track of block parity information from pass to pass, which they called CASCADE, the number of parity checks per error bit is reduced. They observed no errors left after four passes from 10 simulation runs. However, they offered upper bound of residue error rate that was much higher than observed from simulation. Therefore, there is a need to find the optimal block size and to improve the residue error rate analysis of this procedure. In this work, improvement in reconciliation procedure is obtained in throughput (i.e. the number of input bits minus the number of parity checks) and in lower residue error rate. Throughput is doubled at high input error rate and less throughput gain at low input error rate. Three most important factors that enhance the system throughput are: 1) Using larger block size to fully utilize the power of CASCADE method. 2) Avoiding any pair of bits to stay in the same block of any later pass, which allows the use of three passes only (instead of four passes in the BS procedure). 3) Some bits are already known to be lost from the current pass, so I avoid carrying these bits to the later pass. The residue error rate at the end of the second pass (and the third pass) for small initial block size is derived. The residue error rate at the end of the third pass is found much lower than the upper bound given by the previous workers. This residue error rate is found to be a function of input size and the block size. This error control method has many similar features and difficulties to the recent development of "turbo-code" in the error control-coding field.
Abstract : Quantum Key Distribution (QKD) is a method for transmitting a cryptographic key between a sender and receiver in a theoretically unconditionally secure way. Unfortunately, the present state of technology prohibits the flawless quantum transmission required to make QKD a reality. For this reason, error reconciliation protocols have been developed which preserve security while allowing a sender and receiver to reconcile the errors in their respective keys. The most famous of these protocols is Brassard and Salvail's Cascade, which is effective, but suffers from a high communication complexity and therefore results in low throughput. Another popular option is Buttler's Winnow protocol, which reduces the communication complexity over Cascade, but has the added detriment of introducing errors, and has been shown to be less effective than Cascade. Finally, Gallager's Low Density Parity Check (LDPC) codes have recently been shown to reconcile errors at rates higher than those of Cascade and Winnow with a large reduction in communication, but with greater computational complexity. This research seeks to evaluate the effectiveness of these LDPC codes in a QKD setting, while comparing real-world parameters such as runtime, throughput and communication complexity empirically with the well-known Cascade and Winnow algorithms. Additionally, the effects of inaccurate error estimation, non-uniform error distribution and varying key length on all three protocols are evaluated for identical input key strings. Analyses are performed on the results in order to characterize the performance of all three protocols and determine the strengths and weaknesses of each.
Quantum key distribution (QKD) relies on quantum and classical procedures in order to achieve the growing of a secret random string -the key- known only to the two parties executing the protocol. Limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping produce errors and information leakage from which the set of measured signals -the raw key- must be stripped in order to distill a final, information theoretically secure, key. The key distillation process is a classical one in which basis reconciliation, error correction and privacy amplification protocols are applied to the raw key. This cleaning process is known as information reconciliation and must be done in a fast and efficient way to avoid cramping the performance of the QKD system. Brassard and Salvail proposed a very simple and elegant protocol to reconcile keys in the secret-key agreement context, known as Cascade, that has become the de-facto standard for all QKD practical implementations. However, it is highly interactive, requiring many communications between the legitimate parties and its efficiency is not optimal, imposing an early limit to the maximum tolerable error rate. In this paper we describe a low-density parity-check reconciliation protocol that improves significantly on these problems. The protocol exhibits better efficiency and limits the number of uses of the communications channel. It is also able to adapt to different error rates while remaining efficient, thus reaching longer distances or higher secure key rate for a given QKD system.
Quantum key distribution (QKD) relies on quantum and classical procedures in order to achieve the growing of a secret random string -the key- known only to the two parties executing the protocol. Limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping produce errors and information leakage from which the set of measured signals -the raw key- must be stripped in order to distill a final, information theoretically secure, key. The key distillation process is a classical one in which basis reconciliation, error correction and privacy amplification protocols are applied to the raw key. This cleaning process is known as information reconciliation and must be done in a fast and efficient way to avoid cramping the performance of the QKD system. Brassard and Salvail proposed a very simple and elegant protocol to reconcile keys in the secret-key agreement context, known as Cascade, that has become the de-facto standard for all QKD practical implementations. However, it is highly interactive, requiring many communications between the legitimate parties and its efficiency is not optimal, imposing an early limit to the maximum tolerable error rate. In this paper we describe a low-density parity-check reconciliation protocol that improves significantly on these problems. The protocol exhibits better efficiency and limits the number of uses of the communications channel. It is also able to adapt to different error rates while remaining efficient, thus reaching longer distances or higher secure key rate for a given QKD system.
Quantum key distribution (QKD) relies on quantum and classical procedures in order to achieve the growing of a secret random string -the key- known only to the two parties executing the protocol. Limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping produce errors and information leakage from which the set of measured signals -the raw key- must be stripped in order to distill a final, information theoretically secure, key. The key distillation process is a classical one in which basis reconciliation, error correction and privacy amplification protocols are applied to the raw key. This cleaning process is known as information reconciliation and must be done in a fast and efficient way to avoid cramping the performance of the QKD system. Brassard and Salvail proposed a very simple and elegant protocol to reconcile keys in the secretkey agreement context, known as Cascade, that has become the de-facto standard for all QKD practical implementations. However, it is highly interactive, requiring many communications between the legitimate parties and its efficiency is not optimal, imposing an early limit to the maximum tolerable error rate. In this paper we describe a low-density parity-check reconciliation protocol that improves significantly on these problems. The protocol exhibits better efficiency and limits the number of uses of the communications channel. It is also able to adapt to different error rates while remaining efficient, thus reaching longer distances or higher secure key rate for a given QKD system.
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.
Quantum key distribution (QKD) relies on quantum and classical procedures in order to achieve the growing of a secret random string —the key— known only to the two parties executing the protocol. Limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping produce errors and information leakage from which the set of measured signals —the raw key— must be stripped in order to distill a final, information theoretically secure, key. The key distillation process is a classical one in which basis reconciliation, error correction and privacy amplification protocols are applied to the raw key. This cleaning process is known as information reconciliation and must be done in a fast and efficient way to avoid cramping the performance of theQKD system. Brassard and Salvail proposed a very simple and elegant protocol to reconcile keys in the secretkey agreement context, known as Cascade, that has become the de-facto standard for all QKD practical implementations. However, it is highly interactive, requiring many communications between the legitimate parties and its efficiency is not optimal, imposing an early limit to the maximum tolerable error rate. In this paper we describe a low-density parity-check reconciliation protocol that improves significantly on these problems. The protocol exhibits better efficiency and limits the number of uses of the communications channel. It is also able to adapt to different error rates while remaining efficient, thus reaching longer distances or higher secure key rate for a given QKD system.