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arXiv:2103.11423 · IEEE Statistical Signal Processing Workshop (SSP)

Comparison of Short Blocklength Slepian-Wolf Coding for Key Reconciliation

Mahdi Shakiba-Herfeh, Arsenia Chorti

Published Jul 11, 2021• 14 citations
arXivHTMLPDF

Abstract

In this work, we focus on Slepian-Wolf (SW) coding in the short blocklength for reconciliation in secret key generation and physical unclonable functions (PUF). In the problem formulation, two legitimate parties wish to generate a common secret key from a noisy observation of a common random source in the presence of a passive eavesdropper. We consider three different families of codes for key reconciliation. All the selected codes show promising performances in information transmission in the short blocklength regime. We implement and compare the performance of the codes for SW reconciliation in the terms of reliability and decoding complexity for different blocklengths.

DOI
10.1109/ssp49050.2021.9513785

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In this work, we focus on Slepian-Wolf (SW) coding in the short blocklength for reconciliation in secret key generation and physical unclonable functions (PUF). In the problem formulation, two legitimate parties wish to generate a common secret key from a noisy observation of a common random source in the presence of a passive eavesdropper. We consider three different families of codes for key reconciliation. All the selected codes show promising performances in information transmission in the short blocklength regime. We implement and compare the performance of the codes for SW reconciliation in the terms of reliability and decoding complexity for different blocklengths.
We analyze the error performance of coding scheme that is found in the protocol for secret key agreement based on the Gaussian channel. The approach is regarded as the Slepian-Wolf coding or the source coding with side information at the decoder. One remarkable feature of the coding in the key agreement is that two parties may extract the set of reliable signals before Slepian-Wolf coding is performed. We derive a tight upper bound on the error probability of this coding scheme, which allows us to quantify the effect of signal extraction.
The problem of key reconciliation based on Low-Density Parity-Check (LDPC) codes and Slepian-Wolf coding for physical layer key generation is investigated.When using the channel-state-information (CSI) of a reciprocal wireless channel for key generation between two legitimate users, independent noise components, quantization, and synchronization errors at the end nodes give rise to key differences that need to be corrected by sending side information.We provide a comparison of three different quantization schemes in terms of key disagreement rate and output probability distributions and present the loglikelihood formulations required by a soft decision LDPC decoder to perform key reconciliation, for the investigated quantization methods.
In this paper, we show how to compute the Slepian-Wolf lower bound for the reconciliation of physical layer secret keys between two radio terminals. Two coding approaches, including the syndrome method and the parity method, have been proven to require the same number of bits exchanged between two terminals for the reconciliation in the noiseless environment. We also present a practical coding approach based on LDPC codes, and the gap between the practical approach and the Slepian-Wolf bound is given.
Physical layer approaches for generating secret encryption keys for wireless systems using channel information has attracted increased interest from researchers in recent years. This paper presents a new approach for secret key generation that is based on one-bit quantization of channel measurements along with log-likelihood ratios (LLRs) that are calculated based on the difference between channel estimates at legitimate reciprocal nodes. The proposed approach, which implements advantage distillation along with information reconciliation using Slepian-Wolf low-density parity check (LDPC) codes, is discussed and illustrated with numerical results obtained from simulations. These show the probability of bit disagreement for keys generated through the proposed approach and compare it with that of alternative methods for key generation based on channel state information.
The quantum key reconciliation is an essential step of QKD protocol. Its main objective is to correct the transmission error after the distribution of quantum objects over a quantum channel, where two legitimate parties use a classical interactive communication for agreeing on their common key. This paper presents an alternative quantum key reconciliation method based on the Slepian-Wolf coding scheme with the chosen optimal set of BCH code rates as close to the Slepian-Wolf bound. In the proposed scheme, the BCH decoder is modified by adding one-bit feedback based on syndrome decoding to detect uncorrectable errors whenever the decoding process fails. The performance evaluation of this proposed scheme can achieve the reconciliation efficiency and reduce the cost of interactive communication via an error-free public channel comparable to the well-known reconciliation protocols. It is then suitable to apply for higher-speed discrete-variable QKD applications.
In this chapter, we discuss the construction of practical codes for secrecy. The design of codes for the wiretap channel turns out to be surprisingly difficult, and this area of information-theoretic security is still largely in its infancy. To some extent, the major obstacles in the road to secrecy capacity are similar to those that lay in the path to channel capacity: the random-coding arguments used to establish the secrecy capacity do not provide explicit code constructions. However, the design of wiretap codes is further impaired by the absence of a simple metric, such as a bit error rate, which could be evaluated numerically. Unlike codes designed for reliable communication, whose performance is eventually assessed by plotting a bit-error-rate curve, we cannot simulate an eavesdropper with unlimited computational power; hence, wiretap codes must possess enough structure to be provably secure. For certain channels, such as binary erasure wiretap channels, the information-theoretic secrecy constraint can be recast in terms of an algebraic property for a code-generator matrix. Most of the chapter focuses on such cases since this algebraic view of secrecy simplifies the analysis considerably. As seen in Chapter 4, the design of secret-key distillation strategies is a somewhat easier problem insofar as reliability and security can be handled separately by means of information reconciliation and privacy amplification. Essentially, the construction of coding schemes for key agreement reduces to the design of Slepian–Wolf-like codes for information reconciliation, which can be done efficiently with low-density parity-check (LDPC) codes or turbo-codes.