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In this dissertation, we present an information hiding approach incorporating anonymity that builds on existing classical steganographic models. Current security definitions are not sufficient to analyze the proposed information hiding approach as steganography offers data privacy by hiding the existence of data, a property that is distinct from confidentiality (data existence is known but access is restricted) and authenticity (data existence is known but manipulation is restricted). Combinations of the latter two properties are common in analyses, such as Authenticated Encryption with Associated Data (AEAD), yet there is a lack of research on combinations with steganography. This dissertation also introduces the security definition of Authenticated Stegotext with Associated Data (ASAD), which captures steganographic properties even when there is contextual information provided alongside the hidden data. We develop a hierarchical framework of ASAD variants, corresponding to different channel demands. We present a real-world steganographic embedding scheme, Authenticated SteGotex with Associated tRansaction Data (ASGARD), that leverages a blockchain-based application as a medium for sending hidden data. We analyze ASGARD in our framework and show that it meets Level-4 ASAD security. Finally, we implement ASGARD on the Ethereum platform as a proof-of-concept and analyze some of the ways an adversary might detect our embedding activity by analyzing historical Ethereum data., Lieutenant, United States Navy, Approved for public release. Distribution is unlimited.

How can we measure and classify neural network robustness across differently distributed data to avoid misuse of machine learning tools? This thesis adopts several metrics to measure the initial condition robustness of feedforward neural networks, allowing the creators of such networks to measure and refine their robustness and performance. This could allow highly robust neural networks to be used reliably on untrained data distributions and prevent the use of less robust networks as a black box in a poor environment. We test this measurement of robustness on a series of differently sized neural networks trained to detect and classify microgrid power system faults, giving examples of both robust and nonrobust networks, along with suggestions on how to maximize robustness. The analysis reveals that collecting data from segments along trajectories enhances the robustness of neural networks. In such data sets, the distribution of data points is dominated by the dynamics of the system, not the initial state distribution.

The applications of machine learning are broad and useful for a variety of industry and military objectives, but are the current methods robust? Robustness requires more than accuracy in ideal conditions; it means the system is resistant to perturbations in the data, both from natural and adversarial causes. This research aims to analyze the robustness of neural networks used for power-grid fault classifications. We focus on data generated from simulations of the classical 9-bus model; however, these methods and results can be extended to more complex microgrids, such as those found on naval ships, submarines, and bases. First, we measure the effects of random and adversarial noise on the testing data and compare three network types. Then we test different structures by varying the number of nodes and layers. Finally, we test whether adding noise to the training data can improve robustness. Before machine learning methods are adopted on submarines, we must first understand their weaknesses and potential for error. This research provides the foundation for how to test robustness, where neural networks are at risk from random or adversarial noise, and how to modify networks to improve their robustness.

NPS NRP Technical Report, Navy networks and infrastructures are under frequent cyberattack. One developing area of application of Artificial Intelligence (AI) and Machine Learning (ML) is cybersecurity. However, some weakness of machine learning, such as the lack of interpretability and the susceptibility to adversarial data, are important issues that must be studied for reliable and safe applications of AI tools. The robustness of deep learning (DL) techniques used in computer vision and language processing have been extensively studied. However, less is currently known about the vulnerabilities and robustness of DL methods suitable in cybersecurity applications. The goal of this research is to investigate mathematical concepts and quantitative measures of robustness and vulnerability to adversarial data for cybersecurity DL and to create computational algorithms capable of quantitatively evaluating the robustness and vulnerability of DL tools. The tasks of the project include literature review, an innovative study of mathematical concepts, the development of computational algorithms, the validation of the concepts and algorithms through examples. The deliverables of the project include technical reports, student thesis, and technical papers for publication. This work will enhance understanding of vulnerabilities of deep learning systems that could be incorporated in future DoN networks, and provide the US Navy with computational tools capable of measuring the robustness of the AI enabled systems., Navy Cyber Defense Operations Command, N2/N6 - Information Warfare, This research is supported by funding from the Naval Postgraduate School, Naval Research Program (PE 0605853N/2098). https://nps.edu/nrp, Chief of Naval Operations (CNO), Approved for public release. Distribution is unlimited.

This dissertation investigates a newly defined cryptographic differential, called a c-differential, and its relevance to the nonlinear substitution boxes of modern symmetric block ciphers. We generalize the notions of perfect nonlinearity, bentness, and avalanche characteristics of vectorial Boolean and p-ary functions using the c-derivative and a new autocorrelation function, while capturing the original definitions as special cases (i.e., when c=1). We investigate the c-differential uniformity property of the inverse function over finite fields under several extended affine transformations. We demonstrate that c-differential properties do not hold in general across equivalence classes typically used in Boolean function analysis, and in some cases change significantly under slight perturbations. Thus, choosing certain affine equivalent functions that are easy to implement in hardware or software without checking their c-differential properties could potentially expose an encryption scheme to risk if a c-differential attack method is ever realized. We also extend the c-derivative and c-differential uniformity into higher order, investigate some of their properties, and analyze the behavior of the inverse function's second order c-differential uniformity. Finally, we analyze the substitution boxes of some recognizable ciphers along with certain extended affine equivalent variations and document their performance under c-differential uniformity., Commander, United States Navy, Approved for public release. Distribution is unlimited.

A physical layer security framework is developed that may be tailored to a particular wireless communications link. Alternating space-time coding and Gray code hopping techniques are presented that may be implemented individually or concurrently. The first technique may be utilized in any multiple-input multiple-output system with choice of single- or multi-space-time code configurations. Orthogonal, non-orthogonal, and spatially-multiplexed space-time codes are included to achieve a desired diversity-multiplexing balance in addition to demonstrated security benefits. Gray code hopping may be used in any system with common digital modulation schemes to "hop" between alternative binary reflected Gray code mappings of bits to complex-valued modulation symbols. Unlike similar constellation remapping techniques, Gray code hopping provides improved physical layer security against plaintext attacks without sacrificing bit error rate performance. To facilitate these schemes, we present two series of algorithms that systematically build large sets of unique alternative space-time codes and modulation mappings. Decoding methods are discussed to allow for channel equalization and symbol co-phasing when employing an alternating space-time code. Equivalent modulation/demodulation approaches are provided for Gray code hopping. Information-theoretic and computational security analysis, Monte Carlo simulations, and over-the-air testing are completed as confirmation of proposed methods., Lieutenant Commander, United States Navy, Approved for public release. Distribution is unlimited.

Encryption is ubiquitous in the modern environment. While public/private key architecture has provided an amazing and powerful way to encrypt information so that only one intended recipient can decrypt, the computation required for this approach means that this encryption method can quickly grow extremely expensive. With that in mind, there are a variety of open-source stream ciphers that seek to provide relatively inexpensive stream ciphers to securely encrypt information. But these stream ciphers all operate using very different techniques to generate their keystream, as seen in the stark differences in paradigms between ciphers. As such, it is not immediately clear what operations are required to achieve the desired level of encryption. What cryptographic primitives are most common or efficacious in achieving security? Examining the Data Encryption Standard, Advanced Encryption Standard, and the stream cipher winners of the eStream II competition, an underlying trend composed of two operations emerges. Despite observing no clear n-grams defining precise cryptographic primitives, we identify a general structure common to all stream ciphers. Additionally, we identify that substitution boxes or multiplication operations are not necessary for stream ciphers, whereas addition and rotation operations seem to be essential., Major, United States Army, Approved for public release. Distribution is unlimited.

We discuss in this paper the independence numbers and algebraic properties of I-graphs. The I-graphs are a further generalization of the Generalized Petersen graphs whose independence numbers have been previously researched. Specifically, we give bounds for the independence number of different I-graphs and sub-classes of I-graphs, and exactly determine the independence number for other I-graphs and sub-classes of I-graphs. We also analyze the automorphism groups of the I-graphs. These groups have been characterized in previous papers; in this paper, we examine them via their Cayley graphs. These Cayley graphs are characterized completely and examined according to their graph theoretical and algebraic properties., Ensign, United States Navy, Approved for public release. distribution is unlimited

Cryptography is widely used by everybody in day-to-day activities. Many cryptographic algorithms rely on pseudorandom number sequences. One of the quickest methods of pseudorandom number generation is using linear feedback shift registers (LFSR) to generate sequences. LFSR sequences exhibit good statistical properties, but alone are not adequately secure due to their low linear complexity. To enhance the security, separate LFSR sequences can be combined into a single pseudorandom string by using a combiner. In this thesis, creating a combiner function using another pseudorandom sequence derived from the chaotic motion of a double pendulum is investigated. Using the information from this driving function, an iterative process occurs whereby certain LFSR sequence blocks are selected and combined. The resultant sequences are sufficiently random as proven by the 15 tests adopted by the National Institute of Standards and Technology to evaluate the randomness of binary strings.

Moving target defense (MTD) is a promising strategy for gaining advantage over cyber attackers, but these dynamic reconfigurations can impose significant overhead. We propose implementing MTD within an optimization framework so that we seize defensive advantage while minimizing overhead. This dissertation presents an MTD scheme that leverages partially observable Markov decision processes (POMDP) with absorbing states to select the optimal defense based on partial observations of the cyber attack phase. In this way, overhead is minimized as reconfigurations are triggered only when the potential benefit outweighs the cost. We formulate and implement a POMDP within a system with Monte-Carlo planning-based decision making configured to reflect defender-defined priorities for the cost-benefit tradeoff. The proposed system also includes a performance -monitoring scheme for continuous validation of the model, critical given attackers' ever-changing techniques. We present simulation results that confirm the system fulfills the design goals, thwarting 99% of inbound attacks while sustaining system availability at greater than 94% even as probability of attack phase detection dropped to 0.74. A comparable system that triggered MTD techniques pseudorandomly maintained just 43% availability when providing equivalent attack suppression, which illustrates the utility of our proposed scheme.

The double pendulum is a system of two connected masses, one tethered to a point in space and the other tethered to the first mass. The double pendulum exhibits chaotic motion under the influence of an external force such as the gravitational force. The chaotic motion is sensitive to the initial conditions or positions of the masses, resulting in an infinite number of possible motion paths. The chaotic motion paths produced by the double pendulum can be exploited to produce binary sequences. This thesis focuses on determining if the chaotic motion of the double pendulum can be used as a pseudorandom number generator (PRNG) by modeling the motion and using different methods of extracting bits from the motion paths to produce pseudorandom binary sequences. The pseudorandom binary sequences are then evaluated using tests for randomness as defined by the National Institute of Standards and Technology (NIST). The methods of bit extraction can then be compared based on their NIST test results to ultimately determine the practicality of the double pendulum as a PRNG. Considerations can be made for different methods of bit extraction or the use of different chaotic motions.

In this paper, we study the independence number of various classes of I-graphs. I-graphs are generalizations of the Generalized Petersen Graphs. We provide constructions of independent sets given any parameters, as well as bounds for some subclasses of I-graphs. We also prove exact results for some specific I-graphs., Ensign, United States Navy, Approved for public release. distribution is unlimited

The purpose of this thesis is to analyze the cryptographic properties of a pseudorandom bit generator that combines Blum Blum Shub and linear feedback shift register sequences using a shrinking generator configuration. We sought to answer the questions: (1) What are the strengths and weaknesses of this type of combiner? (2) What constraints must be placed on the input parameters to ensure good cryptographic properties of the output sequence? We generated sequences using variations of this combiner. We then evaluated their cryptographic suitability with the National Institute of Standards and Technology (NIST) statistical test suite. We identified lower bounds on the input parameters to increase the probability that the combiner would perform well under the NIST test suite. Our scheme produced consistently excellent results under NIST testing but is computationally too slow for many practical uses as a stream cipher. Future work could focus on methods to increase the speed of the generator without a loss of excellent cryptographic properties., Major, United States Army, Approved for public release. distribution is unlimited

In this digital age, cryptography has formed the backbone of many computer functions. Cryptography drives online commerce and allows privileged information safe transit between two parties as well as many other critical internet uses. The presence of a strong pseudo-random number generator (PRNG) is an absolute requirement in modern cryptography. All modern ciphers draw their strength from having this strong generator. There are currently many ways to generate a secure PRNG. Most current PRNGs generate their stream as a sequence of bits. As a result, most tests performed to ensure randomness are made for binary streams. This thesis introduces a way to generate an integer random number stream using generalized Boolean functions. Additionally, this thesis discusses how to test an integer stream using binary tests. Data from this thesis suggests that high levels of complexity can be obtained using simple quadratic (or other higher degree) generalized combiners. Additionally, our data discusses the ability to generate sequences with high degrees of randomness using a variety of combiner choices for the generalized Boolean function.

Cryptography forms the backbone of modern secure communication. Many different methods are available for encrypting and decrypting data, each with advantages and disadvantages. If communicating parties require speed of encryption more than incredibly robust security, they may use a stream cipher, which is based on generating long strings of bits with linear feedback shift registers (LFSRs), then making those strings cryptographically secure by combining them with a nonlinear Boolean function called a combiner. In this thesis, we investigate a modification to the classical combiner method by introducing a (nonsecure) probabilistic randomization to the order in which the LFSRs are input into the combiner function at each bit. We implemented two different designs for the probabilistic combiner: one that randomly ordered four LFSRs and put them into a four-variable Boolean function, and another that selected only three out of four LFSRs to use as inputs in a three-variable function. Our tests on the resulting output strings show a drastic increase in complexity, while simultaneously passing the stringent randomness tests required by the National Institute of Standards and Technology for pseudorandom numbers.

Cryptography is essential for secure online communications. Many different types of ciphers are implemented in modern-day cryptography, but they all have one common factor. All ciphers require a source of randomness, which makes them unpre-dictable. One such source of this randomness is a random number generator. This thesis focuses on Pseudorandom Number Generators (PRNG), specifically, a PRNG called Blum-Blum-Shub (BBS). In this thesis, we make two modifications to BBS, and test our modified generators for randomness using the National Institute of Standards and Technology (NIST) tests. The original BBS is a quadratic generator that generates bits based on the output of squaring terms in a sequence. The first modification replaces the quadratic generator with a cubic generator. The second modification generates bits faster by using more bits per iteration. Data collected in this thesis suggests that the cubic modification performs just as well as the original generator. In addition, data from this thesis suggests that taking more bits per iteration can speed up this process while retaining randomness. In addition, we propose a new cryptosystem based upon the modification of the BBS PRNG introduced in this thesis.

Blum-Blum-Shub (BBS) is a (probabilistically) secure pseudorandom bit/number generator which outputs a sequence by repeatedly reducing squares modulo the product of two Blum-primes. Our goal for this thesis is to modify the algorithm by using a modulus which is the product of three Blum-primes.We evaluate the effect of this modification using the suite of tests from National Institute of Standards and Technology (NIST). Previous research has evaluated the limit on the number of least important bits that can be extracted per iteration of the BBS algorithm while still maintaining the pseudorandom properties. In this paper, we go beyond the proposed limit and compare the modified BBS with the original BBS using the NIST tests. This paper also discusses the cryptosystem based on the modified BBS as well as the original BBS. We use three metrics for the comparison of performance: the type of tests, the overall performance of sequences against NIST tests, and the time to generate sequences. Our test data shows that both versions performed in a similar manner when subjected to NIST tests. Furthermore, bit generation is significantly faster for sequences generated by taking the last 50 bits or more, while still maintaining pseudorandom properties.

In this paper, we deal with the problem of bisecting binomial coefficients. We find many (previously unknown) infinite classes of integers which admit nontrivial bisections, and a class with only trivial bisections. As a byproduct of this last construction, we show conjectures Q2 and Q4 of Cusick and Li [7]. We next find several bounds for the number of nontrivial bisections and further compute (using a supercomputer) the exact number of such bisections for n ≤ 51.

In this paper we introduce generalized hyperbent functions from F2n to Z2k, and investigate decompositions of generalized (hyper)bent functions. We show that generalized (hyper)bent functions from F2n to Z2k consist of components which are generalized (hyper)bent functions from F2n to Z2k′ for some k′ < k. For odd n, we show that the Boolean functions associated to a generalized bent function form an affine space of semibent functions. This complements a recent result for even n, where the associated Boolean functions are bent.

In this paper we proved that generalized bent (gbent) functions defined on Z (n/2) with values in Z(2k) are regular and find connections between the (generalized) Walsh spectrum of these function and their components. We comprehensively characterize generalized bent and semibent functions with values in Z(16), which extends earlier results on gbent function with values in Z(4) and Z(8). We also show that the Gray images of gbent functions with values in (2k) are semibent/plateaued when k = 3,4.

In this paper we generalize the partial spread class and completely describe it for generalized Boolean functions from F(n/2) to Z(2t). Explicitly, we describe gbent function from F(n/2) to Z(2t), which can be seen as a gbent versio of Dillon's PS(ap) class. For the first time, we also introduce the concept of a vectorial gbent function from F(n/2) to Z(m/q), and determine the maximal value which m can attain for the q =2(t). Finally we point to a relation between vectorial gbent function and relative difference sets.

In this paper, we investigate the properties of generalized bent functions defined on Zn2 with values in Zq, where q greater or equal to 2 is any positive integer. We characterize the class of generalized bent functions symmetric with respect to two variables, provide analogues of Maiorana-McFarland type bent functions and Dillon's functions in the generalized set up. A class of bent functions called generalized spreads is introduced and we show that it contains all Dillon type generalized bent functions and Maiorana-McFarland type generalized bent functions. Thus, unification of two different types of generalized bent functions is achieved. The cross-correlation spectrum of generalized Dillon type bent functions is also characterized. We further characterize generalized bent Boolean functions defined on Zn2 with values in Z4 and Z8. Moreover, we propose several constructions of such generalized bent functions for both n even and n odd.

Process Algebra forms a cornerstone in the formal methods area of Computer Science. Among the more widely used approaches is Milner's Communication and Concurrency Systems (CCS). Recently CCS has been extended by Schmidt and Bibighaus through the introduction of Doubly Labeled Transition Systems. This framework has enhanced the model's ability to capture security and availability properties. In this thesis we reformulate, simplify, and extend Bibighaus' work using a graph theoretic framework. The intent is that this abstract mathematical view will make the results more accessible and stimulate additional research. Existing definitions and theorems are redefined and proved using Labeled and Doubly Labeled Transition Graphs (LTG and DLTG). CCS simulation concepts are recast as graph morphisms and the notion of abstraction and refinement are explained through the use of graphs. Bibighaus' work is extended by showing how to carry out non-atomic DLTG refinement, and by developing a form of graph composition involving graph refinements that share a common abstract graph. This type of composition is proven to always be possible with DLTG refinements, and we demonstrate that the composite graph is both a refinement of the abstract graph, and an abstract graph for the refinements from which it was made., http://archive.org/details/refinementcompos109453269, US Navy (USN) author.