Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1001.1197 · IEEE International Symposium on Information Theory (ISIT)

Construction of wiretap codes from ordinary channel codes

Masahito Hayashi, Ryutaroh Matsumoto

Published Jun 1, 2010• 38 citations
arXivHTMLPDF

Abstract

From an arbitrary given channel code over a discrete or Gaussian memoryless channel, we construct a wiretap code with the strong security. Our construction can achieve the wiretap capacity under mild assumptions. The key tool is the new privacy amplification theorem bounding the eavesdropped information in terms of the Gallager function.
DOI
10.1109/isit.2010.5513794

Related papers

A New Wiretap Channel Model and Its Strong Secrecy Capacity

Mohamed Nafea, Aylin Yener

In this paper, a new wiretap channel model is proposed, where the legitimate transmitter and receiver communicate over a discrete memoryless channel. The wiretapper has perfect access to a fixed-length subset of the transmitted code word symbols of her choosing. Additionally, she observes the remainder of the transmitted symbols through a discrete memoryless channel. This new model subsumes the classical wiretap channel and wiretap channel II with noisy main channel as its special cases, and is termed as the generalized wiretap channel for that reason. The strong secrecy capacity of the proposed channel model is identified. Achievability is established by solving a dual secret key agreement problem in the source model, and converting the solution to the original channel model using probability distribution approximation arguments. In the dual problem, a source encoder and decoder, who observe random sequences independent and identically distributed according to the input and output distributions of the legitimate channel in the original problem, communicate a confidential key over a public error-free channel using a single forward transmission, in the presence of a compound wiretapping source who has perfect access to the public discussion. The security of the key is guaranteed for the exponentially many possibilities of the subset chosen at the wiretapper by deriving a lemma which provides a doubly-exponential convergence rate for the probability that, for a fixed choice of the subset, the key is uniform and independent from the public discussion and the wiretapping source's observation. The converse is derived by using Sanov's theorem to upper bound the secrecy capacity of the generalized wiretap channel by the secrecy capacity when the tapped subset is randomly chosen by nature.

IEEE Transactions on Information Theory•Dec 22, 2017•26 citations

Wiretap Channels: Nonasymptotic Fundamental Limits

Wei Qing Yang, Rafael F. Schaefer, H. Vincent Poor

This paper investigates the maximal secret communication rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are uniformly tighter than existing bounds, and lead to the tightest bounds on the second-order coding rate for discrete memoryless and Gaussian wiretap channels. The exact second-order coding rate is established for semi-deterministic wiretap channels, which characterizes the optimal tradeoff between reliability and secrecy in the finite-blocklength regime. Underlying our achievability bounds are two new privacy amplification results, which not only refine the classic privacy amplification results, but also achieve secrecy under the stronger semantic-security metric.

arXiv:1706.03866•IEEE Transactions on Information Theory•Mar 12, 2019•141 citations

A New Wiretap Channel Model and its Strong Secrecy Capacity

Mohamed Nafea, Aylin Yener

In this paper, a new wiretap channel model is proposed, where the legitimate transmitter and receiver communicate over a discrete memoryless channel. The wiretapper has perfect access to a fixed-length subset of the transmitted codeword symbols of her choosing. Additionally, she observes the remainder of the transmitted symbols through a discrete memoryless channel. This new model subsumes the classical wiretap channel and wiretap channel II with noisy main channel as its special cases. The strong secrecy capacity of the proposed channel model is identified. Achievability is established by solving a dual secret key agreement problem in the source model, and converting the solution to the original channel model using probability distribution approximation arguments. In the dual problem, a source encoder and decoder, who observe random sequences independent and identically distributed according to the input and output distributions of the legitimate channel in the original problem, communicate a confidential key over a public error-free channel using a single forward transmission, in the presence of a compound wiretapping source who has perfect access to the public discussion. The security of the key is guaranteed for the exponentially many possibilities of the subset chosen at wiretapper by deriving a lemma which provides a doubly-exponential convergence rate for the probability that, for a fixed choice of the subset, the key is uniform and independent from the public discussion and the wiretapping source's observation. The converse is derived by using Sanov's theorem to upper bound the secrecy capacity of the new wiretap channel model by the secrecy capacity when the tapped subset is randomly chosen by nature.

arXiv:1701.07007•Jan 24, 2017•0 citations

Coding for secrecy

Matthieu R. Bloch, João Barros

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.

Cambridge University Press eBooks•Sep 22, 2011•3 citations

On an upper bound of the secrecy capacity for a general wiretap channel

H. Koga, N. Sato

This paper is concerned with coding theorems for a generalized wiretap channel. In the problem of the wiretap channel it is important to characterize the secrecy capacity, i.e., the maximum achievable rate of information securely transmitted from a sender to a legitimate receiver in the presence of a wiretapper. In our model, channels are not restricted to memoryless channels. We first define the secrecy capacity Csand evaluate Csfrom information-spectrum approach. We give a new upper bound of Csnot including auxiliary random variables and explore conditions under which the obtained upper bound becomes tight for the cascaded wiretap channel

IEEE International Symposium on Information Theory (ISIT)•Jan 1, 2005•13 citations

Achievable second-order coding rates for the wiretap channel

Vincent Y. F. Tan

We derive lower bounds to the second-order coding rates for the wiretap channel. The decoding error probability and the information leakage measured in terms of the variational distance secrecy metric are fixed at some constants εrand εsrespectively. We leverage on the connection between wiretap channel coding and channel resolvability to derive tighter secrecy bounds than those available in the literature. We then use central limit theorem-style analysis to evaluate these bounds for the discrete memoryless wiretap channel with cost constraints and the Gaussian wiretap channel.

IEEE International Conference on Communication Systems (ICCS)•Nov 1, 2012•21 citations
In this paper, a new wiretap channel model is proposed, where the legitimate transmitter and receiver communicate over a discrete memoryless channel. The wiretapper has perfect access to a fixed-length subset of the transmitted code word symbols of her choosing. Additionally, she observes the remainder of the transmitted symbols through a discrete memoryless channel. This new model subsumes the classical wiretap channel and wiretap channel II with noisy main channel as its special cases, and is termed as the generalized wiretap channel for that reason. The strong secrecy capacity of the proposed channel model is identified. Achievability is established by solving a dual secret key agreement problem in the source model, and converting the solution to the original channel model using probability distribution approximation arguments. In the dual problem, a source encoder and decoder, who observe random sequences independent and identically distributed according to the input and output distributions of the legitimate channel in the original problem, communicate a confidential key over a public error-free channel using a single forward transmission, in the presence of a compound wiretapping source who has perfect access to the public discussion. The security of the key is guaranteed for the exponentially many possibilities of the subset chosen at the wiretapper by deriving a lemma which provides a doubly-exponential convergence rate for the probability that, for a fixed choice of the subset, the key is uniform and independent from the public discussion and the wiretapping source's observation. The converse is derived by using Sanov's theorem to upper bound the secrecy capacity of the generalized wiretap channel by the secrecy capacity when the tapped subset is randomly chosen by nature.
This paper investigates the maximal secret communication rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are uniformly tighter than existing bounds, and lead to the tightest bounds on the second-order coding rate for discrete memoryless and Gaussian wiretap channels. The exact second-order coding rate is established for semi-deterministic wiretap channels, which characterizes the optimal tradeoff between reliability and secrecy in the finite-blocklength regime. Underlying our achievability bounds are two new privacy amplification results, which not only refine the classic privacy amplification results, but also achieve secrecy under the stronger semantic-security metric.
In this paper, a new wiretap channel model is proposed, where the legitimate transmitter and receiver communicate over a discrete memoryless channel. The wiretapper has perfect access to a fixed-length subset of the transmitted codeword symbols of her choosing. Additionally, she observes the remainder of the transmitted symbols through a discrete memoryless channel. This new model subsumes the classical wiretap channel and wiretap channel II with noisy main channel as its special cases. The strong secrecy capacity of the proposed channel model is identified. Achievability is established by solving a dual secret key agreement problem in the source model, and converting the solution to the original channel model using probability distribution approximation arguments. In the dual problem, a source encoder and decoder, who observe random sequences independent and identically distributed according to the input and output distributions of the legitimate channel in the original problem, communicate a confidential key over a public error-free channel using a single forward transmission, in the presence of a compound wiretapping source who has perfect access to the public discussion. The security of the key is guaranteed for the exponentially many possibilities of the subset chosen at wiretapper by deriving a lemma which provides a doubly-exponential convergence rate for the probability that, for a fixed choice of the subset, the key is uniform and independent from the public discussion and the wiretapping source's observation. The converse is derived by using Sanov's theorem to upper bound the secrecy capacity of the new wiretap channel model by the secrecy capacity when the tapped subset is randomly chosen by nature.
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.
This paper is concerned with coding theorems for a generalized wiretap channel. In the problem of the wiretap channel it is important to characterize the secrecy capacity, i.e., the maximum achievable rate of information securely transmitted from a sender to a legitimate receiver in the presence of a wiretapper. In our model, channels are not restricted to memoryless channels. We first define the secrecy capacity Csand evaluate Csfrom information-spectrum approach. We give a new upper bound of Csnot including auxiliary random variables and explore conditions under which the obtained upper bound becomes tight for the cascaded wiretap channel
We derive lower bounds to the second-order coding rates for the wiretap channel. The decoding error probability and the information leakage measured in terms of the variational distance secrecy metric are fixed at some constants εrand εsrespectively. We leverage on the connection between wiretap channel coding and channel resolvability to derive tighter secrecy bounds than those available in the literature. We then use central limit theorem-style analysis to evaluate these bounds for the discrete memoryless wiretap channel with cost constraints and the Gaussian wiretap channel.