Key Secrecy in a Quantum Cryptography System Based on Error-Correcting Codes

El Ashmawy, Mohamed Salah

Andrew Thangaraj, Souvik Dihidar, A.R. Calderbank +2 more

With the advent of quantum key distribution (QKD) systems, perfect (i.e. information-theoretic) security can now be achieved for distribution of a cryptographic key. QKD systems and similar protocols use classical error-correcting codes for both error correction (for the honest parties to correct errors) and privacy amplification (to make an eavesdropper fully ignorant). From a coding perspective, a good model for such a setting is the wire tap channel system introduced by Wyner in 1975. In this paper, we study fundamental limits and coding methods for wire tap channel systems. We provide a novel proof for the secrecy capacity theorem for wire tap channels and show how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel. We also consider binary erasure channel and binary symmetric channel special cases for the wiretap channel system and propose specific practical codes. In some cases our designs achieve the secrecy capacity and in others the codes provide complete security at rates below secrecy capacity in some specific cases.

Anindita Banerjee

Kirill A. Balygin, Andrey N. Klimov, S. P. Kulik +1 more

Key generation in a two-pass quantum cryptography system involving protocols on geometrically uniform coherent states is studied. Results on the correction of errors in this system without opening a part of the raw key to estimate the probability of errors but involving the monitoring of the parameters of the system and the quantum communication channel sufficient for an a priori estimate of the probability of errors, which is used to choose a correcting code, are reported.

Asel Sagingalieva, Dmitry Anatolevich Kronberg

Quantum cryptography provides methods for secret key distribution between the two distant users. An important step in quantum key distribution protocols is the correction of errors that occur during the transmission and implementation of the protocol. Here we consider error estimation and error correction with linear codes such as repetition code, Hamming code, low density parity check (LDPC) code. The paper investigates the increase in the efficiency of error correction using a combination of a repetition code and a LDPC code for a high error probability.

Masahito Hayashi, Satoshi Ishizaka, Akinori Kawachi +2 more