Fast, efficient error reconciliation for quantum cryptography

Abstract

We describe a new error reconciliation protocol Winnow based on the exchange of parity and Hamming's "syndrome" for N −bit subunits of a large data set. Winnow 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 Winnow 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 Winnow is due largely to the reduction in authenticated public communication required for its implementation.

Quantum key distribution using gaussian-modulated coherent states

“…For high-loss lines, our protocol is at present limited by the reconciliation efficiency, but its intrinsic performances remain very high. Since most of the limitations of the present proof-of-principle experiment appear to be of a technical nature, there is still a considerable margin for improvement, both in the hardware (increased detection bandwidth, better homodyne efficiency, lower electronic noise), and in the software (better reconciliation algorithms [26] , see Appendix A). In conclusion, the way seems open for implementing the present proposal at telecommunications wavelengths as a practical, high bit-rate, quantum key distribution scheme over long distances.…”

A Novel Error Correction Scheme In Quantum Key Distribution (Qkd) Protocol

“…In addition, it skips detection of even multiple bits of error in each iteration. These withhold it in terms of efficiency [24,36,44]. For optimum performance, research has shown that block size of eight bits will minimize number of iterations required and amount of bit exposed [36].…”

“…In Winnow protocol, for an erroneous 7-bit block of sifted key that shows diverging parity during preliminary test, the difference between syndrome of the block of sifted key deduced by Alice and the one deduced by Bob, when computed by Bob during syndrome measurement to determine the associated correctable error pattern before the most probable single-bit error correction can be performed by Bob [24,36]. The reconciliation, which is complemented by privacy maintenance, is shown in Fig.…”

“…Remaining bits of sifted key in each block that equivalent to redundancy bits of a Hamming code's codeword, are also discarded before commencement of new round of reconciliation. Some erroneous bits that fall among the removed bits are thus discarded without undergoing error correction [24,36].…”

“…Winnow protocol has been introduced in [24] to reduce the disclosure of partial information to eavesdropper by taking advantage of both parity bit and Hamming code for single-bit error correction. However, the need of several iterations is necessary because Winnow protocol tends to correct a block of sifted secret key that is interspersed with three or more odd multiple bits of error inaccurately while abandoning detection of even multiple bits of error.…”