Authorship identification is the problem of estimating the author of a written text from a set of possible authors using clues from the written text itself. While this problem has been around for over 130 years, there yet remain several important questions regarding the fundamental limits of existing techniques. This paper is the first of our knowledge to build an information-theoretic framework around the problem of authorship identification. We present a model by which the limits of the problem may be studied as well as key definitions and metrics rooted in information theory. We also provide a test case from the historical archives of the authorship identification research, namely the Federalist Papers problem, and apply our methods to this well-studied set of texts. Given the adhoc nature of much of the research surrounding authorship identification (and related) problems, and the wealth of open fundamental questions regarding even modern methods based in machine learning and large language models, we anticipate that this work will lead to a number of future contributions in both authorship attribution and basic machine learning.

In this paper, we use a linear programming (LP) optimization approach to evaluate the equivocation when coding over a wiretap channel model where the main channel is noiseless and the eavesdropper’s channel is a binary symmetric channel (BSC). Using this technique, we present a numerically-derived upper bound for the achievable secrecy rate in the finite blocklength regime that is tighter than traditional infinite blocklength bounds. We also propose a secrecy coding technique that outperforms random binning codes. When there is one overhead bit, this coding technique is optimum and achieves the newly derived bound. For cases with additional bits of overhead, our coding scheme can achieve equivocation rates close to the new bound. Furthermore, we explore the patterns of the generator matrix and the parity-check matrix for linear codes and we present binning techniques for both linear and nonlinear codes using two different approaches: recursive and non-recursive. To our knowledge, this is the first optimization solution for secrecy coding obtained through linear programming. Our new bounds and codes mark a significant breakthrough towards understanding fundamental limits of performance (and how to achieve them in some instances) for the binary symmetric wiretap channel with real finite blocklength coding constructions. Our techniques are especially useful for codes of small to medium blocklength, such as those that may be required by applications with small payloads, such as the Internet of Things.

The performance and structure of wiretap codes are analyzed in the limit of large code size and very low- or very high-rate codes. Under these conditions, code performance may be calculated using the properties of subspaces of the available code space. Using this technique, a code defined by a generator matrix with a uniform distribution of nonzero columns is proven to be locally optimal.

Current methods for optimization of low-density parity-check (LDPC) codes analyze the degree distribution pair asymptotically as block length approaches infinity. This effectively ignores the discrete nature of the space of valid degree distribution pairs for LDPC codes of finite block length. While large codes are likely to conform reasonably well to the infinite block length analysis, shorter codes have no such guarantee. We present and analyze an algorithm for completely enumerating the space of all valid degree distribution pairs for a given block length, code rate, maximum variable node degree, and maximum check node degree. We then demonstrate this algorithm on an example LDPC code of finite block length. Finally, we discuss how the result of this algorithm can be utilized by discrete optimization routines to form novel methods for the optimization of small block length LDPC codes.

Polar codes have been shown to provide an effective mechanism for achieving physical-layer security over various wiretap channels. A majority of these schemes require channel state information (CSI) at the encoder for both intended receivers and eavesdroppers. In this paper, we consider a polar coding scheme for secrecy over a Gaussian wiretap channel when no CSI is available. We show that the availability of a shared keystream between friendly parties allows polar codes to be used for both secure and reliable communications, even when the eavesdropper knows a large fraction of the keystream. The scheme relies on a predetermined strategy for partitioning the bits to be encoded into a set of frozen bits and a set of information bits. The frozen bits are filled with bits from the keystream, and we evaluate the security gap when the cyclic redundancy check-aided successive cancellation list decoder is used at both receivers in the wiretap channel model.

In this paper, we consider the equivocation of finite blocklength coset codes when used over binary erasure wiretap channels. We make use of the equivocation matrix in comparing codes that are suitable for scenarios with noisy channels for both the intended receiver and an eavesdropper. Equivocation matrices have been studied in the past only for the binary erasure wiretap channel model with a noiseless channel for the intended recipient. In that case, an exact relationship between the elements of equivocation matrices for a code and its dual code was identified. The majority of work on coset codes for wiretap channels only addresses the noise-free main channel case, and extensions to noisy main channels require multi-edge type codes. In this paper, we supply a more insightful proof for the noiseless main channel case, and identify a new dual relationship that applies when two-edge type coset codes are used for the noisy main channel case. The end result is that the elements of the equivocation matrix for a dual code are known precisely from the equivocation matrix of the original code according to fixed reordering patterns. Such relationships allow one to study the equivocation of codes and their duals in tandem, which simplifies the search for best and/or good finite blocklength codes. This paper is the first work that succinctly links the equivocation/error correction capabilities of dual codes for two-edge type coset coding over erasure-prone main channels.

We propose adding an irregular quadrature amplitude modulation (QAM) constellation to a wireless transmission scheme in order to obtain greater control over the signal-to-noise ratio (SNR) required to successfully decode the signal. By altering the separation between adjacent symbols, the minimum required SNR is raised without degradation in the performance of the scheme. This allows the system to adapt to preferable channel conditions for the authorized user, making it harder for eavesdroppers to intercept and decode the transmission, thus making the communication safer. In addition, we show that by overlaying a coset code onto the QAM constellation, a new, stronger security gap metric can be further improved. Results show the effectiveness of this strategy with an interleaved coding for secrecy with a hidden key (ICSHK) scheme.

We propose a coding methodology for physical layer security with adaptive characteristics, whereby adaptive we mean that the system must be tunable to different operational points/signal-to-noise ratio levels of both the legitimate receiver and the eavesdropper. Based on interleaving and scrambling as techniques that shuffle the original message before transmission, we consider puncturing over an interleaving/scrambling key and/or over the message as a mechanism to provide the required adaptability to channel conditions. The proposed techniques have shown suitable adaptability to different channel quality levels of the legitimate receiver and eavesdropper, while still guaranteeing the desired reliability for the legitimate receiver and secrecy against the eavesdropper.

This paper presents a practical physical-layer security scheme based on coding methodologies combined with self-jamming to combat advantaged eavesdroppers, i.e., eavesdroppers that may possess an equal or even better channel than the legitimate receiver. We introduce a strengthened security gap notion, where reliability is assured by typical bit-error rate (BER) measurements, but secrecy is guaranteed by considering the entire distribution of messages upon reception, instead of average measures. Relying on this new security gap notion, we then propose a scheme that combines concatenated coding with self-jamming by the legitimate receiver for effective security and reliability even when eavesdroppers possess a channel with equal or better conditions than the legitimate receiver.

This paper applies channel sounding measurements to enable physical-layer security coding. The channel measurements were acquired in an indoor environment and used to assess the secrecy capacity as a function of physical location. A variety of Reed-Muller wiretap codes were applied to the channel measurements to determine the most effective code for the environment. The results suggest that deploying physical-layer security coding is a three-point design process, where channel sounding data guides 1) the physical placement of the antennas, 2) the power settings of the transmitter, and 3) the selection of wiretap coding.

In this paper we provide a real-world test of physical-layer security using channel sounding techniques in an indoor wireless network. We consider the possibility of exploiting issues that arise in practical receivers to manufacture a discrete memoryless wiretap channel model from the Gaussian case, and show how the secrecy capacity of the Gaussian wiretap channel model changes as these issues are considered. Results indicate that the secrecy capacity is a function of the manufactured channel model, physical antenna location, and power settings at the transmitter. These parameters can be optimized to maximize the potential for secrecy in the network.

The optimization of wiretap codes at finite block-length remains to date a challenging endeavor. We show that the equivocation ensured by coset coding over a binary erasure wiretap channel can be precisely calculated with only knowledge of the full-rank submatrices of the generator matrix. This simplification of the equivocation calculation results in significant computational savings when optimizing wiretap codes at finite blocklength.

We propose an adaptive secrecy scheme using polar codes with random frozen bits for a general wiretap channel, in which to protect the data from a potential eavesdropper, part or all of the frozen bits are randomly generated per message. To assess the secrecy level of the proposed scheme, three types of decoding strategies are evaluated: a matching decoder which knows the positions of all inserted bits inside the blocklength and tries to estimate them using the same decoding techniques, a blind decoder which treats all the frozen bits as the same value, and a random decoder which considers those dynamic bits as random at the receiver. Results are presented in terms of the system security gap, assuming an adaptive decoding strategy. It is shown that the system achieves combined secrecy and reliability. The proposed scheme does not assume knowledge of the eavesdropper's channel when defining the indices of information and frozen bits.

In this paper, we fill a void between information theoretic security and practical coding over the Gaussian wiretap channel using a three-stage encoder/decoder technique. Security is measured using Kullback-Leibler divergence and resolvability techniques along with a limited number of practical assumptions regarding the eavesdropper's decoder. The results specify a general coding recipe for obtaining both secure and reliable communications over the Gaussian wiretap channel, and one specific set of concatenated codes is presented as a test case for the sake of providing simulation-based evaluation of security and reliability over the network. It is shown that there exists a threshold in signal-to-noise ratio (SNR) over a Gaussian channel, such that receivers experiencing SNR below the threshold have no practical hope of receiving information about the message when the three-stage coding technique is applied. Results further indicate that the two innermost encoding stages successfully approximate a binary symmetric channel, allowing the outermost encoding stage (e.g., a wiretap code) to focus solely on secrecy coding over this approximated channel.

A majority of coding constructions for physical-layer security are based on linear block codes and their cosets. One issue with these codes is that they require knowledge of channel state information (CSI) for both the friendly party and the eavesdropper in the wiretap channel prior to constructing the code. In this paper, we present a framework for rateless physical-layer security codes over the wiretap channel by introducing both fixed and adaptive variants of rateless security coding schemes. These techniques can be used to reduce the requirements on CSI prior to code construction, because the codes will either adapt to the operating parameters of the legitimate user's channel on the fly and/or target a maximum allowable probability of intercept (POI) at the eavesdropper. All channels in play are packet erasure channels (PECs), as these channels are quite pervasive in most real-world network applications. We further present the details of an actual implementation of rateless physical-layer security coding over a Wi-Fi network.

This paper proposes a method to provide secrecy for digital communications with arbitrarily large quadrature amplitude modulation (QAM) constellations for transmission over a Gaussian fading wiretap channel. This is accomplished by breaking the constellation down into nested quadrature phase-shift keying (QPSK) symbols and randomizing the assignment between message bits and modulated symbols using channel state information (CSI). If enough random bits can be generated from CSI it becomes possible to uniquely map an arbitrary message to any symbol in the large QAM constellation. The proposed method can thereby provide perfect secrecy while maintaining high reliability by exclusively assigning minimum-distance-mapped constellations through the randomization for use by the legitimate decoder.

This paper presents a new technique for providing the analysis and comparison of wiretap codes in the small blocklength regime over the binary erasure wiretap channel. A major result is the development of Monte Carlo strategies for quantifying a code's equivocation, which mirrors techniques used to analyze forward error correcting codes. For this paper, we limit our analysis to coset-based wiretap codes, and give preferred strategies for calculating and/or estimating the equivocation in order of preference. We also make several comparisons of different code families. Our results indicate that there are security advantages to using algebraic codes for applications that require small to medium blocklengths.

We propose a systematic concatenated coding scheme based on the combination of interleaving with powerful channel codes and jamming for wireless secrecy under the practical assumption of codes in the finite blocklength regime. The basic idea lies in generating a short random key that is used to shuffle/interleave information at the source, Alice. This key is then sent to the legitimate receiver, Bob, during a brief period of advantageous communication over the eavesdropper Eve (e.g., due to more interference from a jammer). Finally, the key is decoded at Bob to properly deinterleave the original information. Bob receives a better quality version of the interleaving key, therefore having the needed advantage over Eve. Information reliability is provided by a strong inner code, while security against Eve results from the proper selection of the outer code and interference levels over the key. We propose a methodology for selection of the outer code with reliability and security constraints. For that, we introduce bit error complementary cumulative distribution function metrics, suitable for security and reliability analysis of error correcting codes.

The classic simple substitution cipher is an elementary cipher for which many automated ciphertext-only attack algorithms have been developed. The reliable performance of these algorithms is, however, conditioned on obtaining an error-free version of the ciphertext. Although cryptosystems are designed according to Kerckhoffs's assumption, i.e., the security of the cipher resides only in the secret key, the existence of practical physical-layer security codes may provide a vehicle to restricting attackers to error-prone ciphertext, and thus enhance cryptographic secrecy by means of natural phenomena in a noisy channel. This additional layer of security, however, must be quantified to understand the possible boons to multilayer security solutions with secrecy coding at the physical layer. This paper provides an experimental analysis of the behavior of an HMM-based substitution cipher attack to quantify the enhancement in security when errors occur as the ciphertext passes through a discrete memoryless symmetric channel. Results indicate that a bound on the performance of the attack can be directly linked to the mutual information between the inputs and outputs of the channel. Rough linear approximations to the high-end performance of the attack are also presented.

Recent accomplishments in physical-layer security research have shown that channel coding for secrecy can be effectively combined with security at other layers, such as cryptography at the application layer, in order to provide a significant security enhancement to communication systems. The goal of this previous work was to inhibit the passive eavesdropper in the wiretap channel model by encoding the ciphertext using nonsystematic low-density parity-check (LDPC) codes prior to transmission and by exploiting the advantage of feedback for legitimate parties. The net result was propagation of a single packet erasure to the detriment of the entire message. The security enhancement was characterized assuming statistically independent packet erasure channels (PECs) for the legitimate receiver and the eavesdropper. In this paper, we go beyond these results by addressing correlated erasure events across the two channels in a wiretap feedback framework. The intuitive notion that high correlation across channels reduces secrecy is shown through the complete characterization of the correlated channel scenario. Furthermore, it is shown that security improvements are still achievable in the face of positive correlation by means of judicious physical-layer design, even when the eavesdropper has a better channel than the legitimate receiver.

In this paper, we analyze an attack scenario for the simple substitution cipher using the wiretap channel model, where the attacker only has access to error-prone ciphertext at the output of a packet erasure channel (PEC). Each packet is comprised of exactly one symbol of ciphertext, and hence, the attacker's channel could be viewed as a symbol erasure channel. Information-theoretic cryptanalysis provides key and message equivocations for the cipher in general, and then gives the results as functions of the error-free ciphertext equivocations. The findings characterize the increase in equivocation that might be expected if encrypted data were further encoded using wiretap codes that introduce symbol erasures to passive eavesdroppers.

In this paper, we discuss the ability of channel codes to enhance cryptographic secrecy. Toward that end, we present the secrecy metric of degrees of freedom in an attacker's knowledge of the cryptogram, which is similar to equivocation. Using this notion of secrecy, we show how a specific practical channel coding system can be used to hide information about the ciphertext, thus increasing the difficulty of cryptographic attacks. The system setup is the wiretap channel model where transmitted data traverse through independent packet erasure channels (PECs) with public feedback for authenticated automatic repeat-request (ARQ). The code design relies on puncturing nonsystematic low-density parity-check (LDPC) codes with the intent of inflicting an eavesdropper with stopping sets in the decoder. The design amplifies errors when stopping sets occur such that a receiver must guess all the channel-erased bits correctly to avoid an error rate of one half in the ciphertext. We extend previous results on the coding scheme by giving design criteria that reduce the effectiveness of a maximum-likelihood (ML) attack to that of a message-passing (MP) attack. We further extend security analysis to models with multiple receivers and collaborative attackers. Cryptographic security is even enhanced by the system when eavesdroppers have better channel quality than legitimate receivers.

Physical-layer security based on wiretap codes can be used to complement cryptographic applications at higher layers of the protocol stack. We assume a passive eavesdropper that has access to noise-corrupted codewords with erasures that are statistically independent to those of the legitimate communication partners. Our goal is to minimize the information leaked to the eavesdropper. In this paper we present a low-complexity coding scheme for channels with feedback, which employs extensive interleaving of carefully punctured LDPC codewords. The key idea is to ensure that every transmitted packet is crucial for successful decoding. This is achieved by ensuring that stopping-set bit combinations for coded blocks are distributed among different packets and by enforcing that retransmission requests be restricted to the friendly parties. A probabilistic analysis reveals that an eavesdropper who uses a message-passing decoding algorithm will experience catastrophic decoding failure with high probability. This encoder thus provides physical-layer secrecy which is both independent from, and complementary of, the cryptographic layer. The proposed scheme works even when an eavesdropper has a better channel than the legitimate receiver.

In this paper we consider tandem error control coding and cryptography in the setting of the wiretap channel due to Wyner. In a typical communications system a cryptographic application is run at a layer above the physical layer and assumes the channel is error free. However, in any real application the channels for friendly users and passive eavesdroppers are not error free and Wyner's wiretap model addresses this scenario. Using this model, we show the security of a common cryptographic primitive, i.e. a keystream generator based on linear feedback shift registers (LFSR), can be strengthened by exploiting properties of the physical layer. A passive eavesdropper can be made to experience greater difficulty in cracking an LFSR- based cryptographic system insomuch that the computational complexity of discovering the secret key increases by orders of magnitude, or is altogether infeasible. This result is shown for two fast correlation attacks originally presented by Meier and Staffelbach, in the context of channel errors due to the wiretap channel model.

Traditional cryptography assumes an eavesdropper receives an error-free copy of the transmitted ciphertext. Wyner's wiretap channel model recognizes that at the physical layer both the intended receiver and the passive eavesdropper inevitably receive an error-prone version of the transmitted message which must be corrected prior to decryption. This paper considers the implications of using both channel and cryptographic codes under the wiretap channel model in a way that enhances the information-theoretic security for the friendly parties by keeping the information transfer to the eavesdropper small. We consider a secret-key cryptographic system with a linear feedback shift register (LFSR)-based keystream generator and observe the mutual information between an LFSR-generated sequence and the received noise-corrupted ciphertext sequence under a known-plaintext scenario. The effectiveness of a noniterative fast correlation attack, which reduces the search time in a brute-force attack, is shown to be correlated with this mutual information. For an iterative fast correlation attack on this cryptographic system, it is shown that an EXIT chart and mutual information are very good predictors of decoding success and failure by a passive eavesdropper.