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Modified error correction method using one-time pad in qkd systems

Богдан Білаш

Published Jul 26, 2020• 0 citations
Publisher

Abstract

This paper analyzes and adapts the known method of error correction of CV-QKD systems, proposed by Mario Milicevic, which modulates a code word with a correlated Gaussian sequence in amplitude and phase quadratures of coherent states, for use in DV-QKD systems, in which information is encoded by single-photon polarization states, by using a sieved key in the form of classical bits, from which the codeword is created, and also a one-time pad (Vernam cipher), which uses a fairly easy to implement classic Boolean “exclusive OR” operation (XOR). The main task of error correction is to correct errors in order to share the same secure key between the two parties (usually called Alice and Bob). Various factors can cause errors. The unreliability of the quantum channel is due to the fact that photons can cause noise when changing the polarization vector of the photon. In the proposed solution, the quantum component of the protocol occurs only in the first stage of transmission of the protected key, where the exchange of photons. The quantum key distribution system has inevitable errors in the sieved key, which must be corrected by the error correction algorithm to create a secure key. Unlike other known QKD systems, where at the stage of error correction the sifted keys are corrected and passed to the next stage of increasing confidentiality, in the modified method it is proposed to use sifted keys as keys in disposable Vernam ciphers, and the vector that will go to the next stage way and combine with the sifted key. The difference in the sieved keys between the two parties is corrected by means of low-density parity check matrices (LDPC), which are known to both of them in advance. Parity check matrices are created by an algorithm proposed by David MacKay and Radford Neal. Radford Neal open-source program code, is used to create final work program to checking proposed algorithm.

DOI
10.18372/2310-5461.46.14803

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This paper analyzes and adapts the known method of error correction of CV-QKD systems, proposed by Mario Milicevic, which modulates a code word with a correlated Gaussian sequence in amplitude and phase quadratures of coherent states, for use in DV-QKD systems, in which information is encoded by single-photon polarization states, by using a sieved key in the form of classical bits, from which the codeword is created, and also a one-time pad (Vernam cipher), which uses a fairly easy to implement classic Boolean “exclusive OR” operation (XOR). The main task of error correction is to correct errors in order to share the same secure key between the two parties (usually called Alice and Bob). Various factors can cause errors. The unreliability of the quantum channel is due to the fact that photons can cause noise when changing the polarization vector of the photon. In the proposed solution, the quantum component of the protocol occurs only in the first stage of transmission of the protected key, where the exchange of photons. The quantum key distribution system has inevitable errors in the sieved key, which must be corrected by the error correction algorithm to create a secure key. Unlike other known QKD systems, where at the stage of error correction the sifted keys are corrected and passed to the next stage of increasing confidentiality, in the modified method it is proposed to use sifted keys as keys in disposable Vernam ciphers, and the vector that will go to the next stage way and combine with the sifted key. The difference in the sieved keys between the two parties is corrected by means of low-density parity check matrices (LDPC), which are known to both of them in advance. Parity check matrices are created by an algorithm proposed by David MacKay and Radford Neal. Radford Neal open-source program code, is used to create final work program to checking proposed algorithm.
In this paper, the parity-check matrices that can be used in low density parity check (LDPC) based error correction method for quantum key distribution are analyzed. The quantum key distribution system has inevitable errors in sifted key that must be corrected by an error correction algorithm to create a secure key. In this analysis, 1000-bit sifted keys are divided into 50 parts. The algorithm creates 50 syndromes corresponding to each part by multiplying 10 × 20 bit parity-check matrices. The algorithm sends the generated syndrome to the other side, which also divides the sifted key into 50 parts, creates a syndrome from each part, and compares with the received syndrome. If the syndromes are different, these sifted key parts are discarded. However, there may be situations where different parts may have the same syndromes. Therefore, it is necessary to find such an optimal matrix that removes the probability of getting the same syndromes at different parts of the sifted key.
Error correction is a necessary step in quantum cryptography since the quantum bit error rate(QBER)is thought as unavoidable as the practical quantum system containing probability unknown in phase and amplitude.These errors come from the experimental imperfection even if there is no exist of eavesdroppers.The error correction protocol used today is based on two-way communication via classical channel that leads to reduction of the key rate.The distilled bits available for practical encryption will decrease further after private amplification and authentication.This paper proposes one-way correction that can combine the authentication and correction altogether.This protocol is based on periodic structure analysis that any defect in the periodic structure reports an error so that the error is correctly allocated.Theoretical and digital simulation demonstrated that this protocol makes direct private communication possible by using quantum sifted keys.In this protocol the quantum sifted keys before correction was divided into two parts.The first part is used for authentication.In practice,Alice encoded her question several times with different quantum sifted key in a manner same as one-time-pad.Bob can recognize her question only if had he made correction of his quantum sifted keys.Bob does his bit error correction by himself with the cryptogram he received and his sifted keys only if the error bit rate is allowable since some kind of periodic structure can be found in the decrypted text.By comparison of the periodic features of the bit strings he can allocate the error bit and calculate error bite rate that is possible to lead to a correction of the error bits without any reduction of the key.After his error correction for the decrypted text he can recognize Alice's question and makes a correct answer to her.The answer may be encoded with his corrected key and then send back to Alice.Alice is easy to check if Bob has perfectly responded.The sifted keys should be abandoned if the QBER is high and therefor unsafe.The security proof and authentication are completed all together.An error matrix can be obtained exclusively if the quantum bit error rate is low enongh to guarantee a security quantum key distribution.The error matrix can be used to correct the errors in the decrypted text instead of that in the quantum sifted key as usual.This protocol leads to direct private communication with quantum sifted key safely.Therefore there is no need to store that distilled keys in computer as usual where it is still possible for some else to make a copy.
Error correction plays a central role in Quantum Key Distribution (QKD) because the raw keys produced by Alice and Bob rarely match exactly. Channel noise, detector fluctuations, and basis mismatches routinely introduce discrepancies that must be resolved before a usable secret key can be formed. Methods such as Cascade and LDPC generally perform well under moderate noise conditions; however, they depend on repeated message exchanges or computationally intensive decoding, which limits their effectiveness when several bits flip together within short time windows. These issues become particularly evident in high-noise environments where correlated errors appear in bursts. To address these challenges, this work presents a syndrome-based multi-bit error-correction technique combined with a chaotic masking approach for securely transmitting the necessary check-sequence data. The technique forms a decimal-summation matrix from each key block and extracts a compact syndrome vector capable of identifying one-, two-, or three-bit errors in a single step. To prevent classical-channel leakage, the required check-sequence is masked using a Tent-map sequence initialized from the entropy associated with the unmatched quantum indices. Simulation results demonstrate a 50–70% reduction in post-correction bit-error rate compared with Cascade, LDPC, and Polar codes across key lengths of 128 to 1024 bits and error probabilities up to 0.5. Overall, the proposed model offers a noise-tolerant and computationally lightweight reconciliation approach and forms the error-correction component of the patented Q-RAPTOR framework (Indian Patent Application No. 202541093982).
In quantum key distribution (QKD), public discussion over the authenticated classical channel inevitably leaks information about the raw key to a potential adversary, which must later be mitigated by privacy amplification. To limit this leakage, a one-time pad (OTP) has been proposed to protect message exchanges in various settings. Building on the security proof of Tomamichel and Leverrier, which is based on a non-asymptotic framework and considers the effects of finite resources, we extend the analysis to the OTP-protected scheme. We show that when the OTP key is drawn from the entropy pool of the same QKD session, the achievable quantum key rate is identical to that of the reference protocol with unprotected error-correction exchange. This equivalence holds for a fixed security level, defined via the diamond distance between the real and ideal protocols modeled as completely positive trace-preserving maps. At the same time, the proposed approach reduces the computational requirements: for non-interactive low-density parity-check codes, the encoding problem size is reduced by the square of the syndrome length, while privacy amplification requires less compression. The technique preserves security, avoids the use of QKD keys between sessions, and has the potential to improve performance.
New near-capacity continuous-variable quantum key distribution (CV-QKD) reconciliation schemes are proposed, where both the authenticated classical channel (ClC) and the quantum channel (QuC) for QKD are protected by separate forward error correction (FEC) coding schemes. More explicitly, all of the syndrome-based QKD reconciliation schemes found in literature rely on syndrome-based codes, such as low-density parity-check (LDPC) codes. Hence at the current state-of-the-art the channel codes that cannot use syndrome decoding such as the family of convolutional codes (CCs) and polar codes cannot be directly applied. Moreover, the ClC used for syndrome transmission in these schemes is generally assumed to be idealistically error-free, where the realistic additive white Gaussian noise (AWGN) and Rayleigh fading of the ClC have not been taken into account. To circumvent this limitation, a new codeword-based -rather than syndrome-based -QKD reconciliation scheme is proposed, where Alice sends an FEC-protected codeword to Bob through a ClC, while Bob sends a separate FEC protected codeword to Alice through a QuC. Upon decoding the codeword received from the other side, the final key is obtained by applying a simple modulo-2 operation to the local codeword and the decoded remote codeword. As a result, first of all, the proposed codeword-based QKD reconciliation system ensures protection of both the QuC and of the ClC. Secondly, the proposed system has a similar complexity at both sides, where both Alice and Bob have an FEC encoder and an FEC decoder. Thirdly, the proposed system makes QKD reconciliation compatible with a wide range of FEC schemes, including polar codes, CCs and irregular convolutional codes (IRCCs), where a near-capacity performance can be achieved for both the QuC and for the ClC. Our simulation results demonstrate that thanks to the proposed regime, the performance improvements of the QuC and of the ClC benefit each other, hence leading to an improved secret key rate (SKR) that inches closer to both the Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound and to the maximum achieveable rate bound.
Continuous-variable (CV) quantum key distribution (QKD) employs the quadratures of a bosonic mode to establish a secret key between two remote parties, and this is usually achieved via a Gaussian modulation of coherent states. The resulting secret key rate depends not only on the loss and noise in the communication channel, but also on a series of data processing steps that are needed for transforming shared correlations into a final string of secret bits. Here we consider a Gaussian-modulated coherent-state protocol with homodyne detection in the general setting of composable finite-size security. After simulating the process of quantum communication, the output classical data are postprocessed via procedures of parameter estimation, error correction, and privacy amplification. In particular, we analyze the high signal-to-noise regime, which requires the use of high-rate (nonbinary) low-density parity check codes. We implement all these steps in a python-based library that allows one to investigate and optimize the protocol parameters to be used in practical experimental implementations of short-range CV-QKD.