# An Accurate Analysis of the BINARY Information Reconciliation Protocol by Generating Functions (QCRYPT 2013)

Sean Seet,
Ruth Ii-Yung Ng,
Khoongming Khoo

January 0001

### Abstract

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.

Publication

In *International Conference on Quantum Cryptography (QCRYPT) Poster Session*