Khoongming Khoo

Information Reconciliation (IR) protocols, which achieve error correction of shared secrets by public discussion, is an important process in Quantum Key Distribution (QKD). We provide an analysis of Brassard’s BINARY and CASCADE IR protocols, two protocols commonly used in QKD. Using generating functions, we give an accurate result on BINARY. We derive the error probability distribution at each pass, which allows us to compute the decoding error probability and the number of “leaked” bits; two quantities crucial in the proof of security for QKD. We then corroborate the probability distribution computed by our formulas with actual simulation results. Finally we show that our formulas give better estimate for the decoding error probability of BINARY than the upper bound derived by Brassard for CASCADE. Because CASCADE should have better decoding performance than BINARY, this shows that Brassard’s estimate of CASCADE may be too loose and can be improved. Our accurate formulas for BINARY can also be used as a basis on which to derive more accurate formulas for CASCADE.

Information Reconciliation is an essential step in Quantum Key Distribution to correct errors in the shared secret between Alice and Bob. In this poster, we generalize the Winnow Information Reconciliation Protocol by replacing the single-bit parity check and Hamming[7,4,3] error-correction code of Winnow by other error detection/correction codes. The error detection codes we investigate include various Cyclic Redundancy Checks (CRC) while the error correction codes we look at include various Hamming, Golay and BCH codes. We simulate Generalized Winnow by considering all possible combinations of these CRC parity-checks and linear codes for QBER between 3%-9%. From our experiments, we identify for each QBER the optimal combination which can correct all errors by (a) Leaking the least number of bits or (b) Using the least number of passes.