# Browsing by Subject "Cryptography"

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Item Algebraic attacks : a survey(2007-12) Agrawal, Shweta Prem; Gal, A. (Anna)Show more Algebraic attacks have recently acquired great importance in the area of cryptography, not only due to the ciphers they have been able to break, but more importantly, because the principle of algebraic attacks is very generic and can be applied to break large classes of ciphers. Several ciphers, previously considered secure and widely used in practice were found to be potentially vulnerable to algebraic attacks. In this survey, we examine algebraic attacks against both public and symmetric key ciphers. We discuss the Boolean functions used in the design of ciphers from the perspective of algebraic attacks, and consider the ”cryptographic” complexity and explicit construction of these functions. We also briefly look at recently discovered methods of solving certain systems of multivariate polynomial equations since algebraic attacks rely on being able to solve such systems of equations efficiently.Show more Item Attribute-based encryption : robust and efficient constructions(2013-08) Rouselakis, Ioannis; Waters, Brent R., 1978-Show more Attribute-based encryption is a promising cryptographic primitive that allows users to encrypt data according to specific policies on the credentials of the recipients. For example, a user might want to store data in a public server such that only subscribers with credentials of specific forms are allowed to access them. Encrypting the data once for each party is not only impractical but also raises important privacy issues. Therefore, it would be beneficial to be able to encrypt only once for all desired parties. This is achievable by attribute-based encryption schemes, which come into several types and are applicable to a wide range of settings. Several attribute-based encryption schemes have been proposed and studied with a wide range of characteristics. For example, initial constructions proved to be significantly more challenging than constructing traditional public-key encryption systems and they imposed restrictions on the expressiveness of the Boolean formulas used during encryption. For several proposed schemes the total number of attributes was fixed during setup, while others allowed any string to be used as attribute ("large universe" constructions), but with considerable weaker security guarantees. Furthermore, these first constructions, although polynomial time, were impractical for wide deployment. This thesis is motivated by two main goals for ABE schemes: robustness and efficiency. For robustness, we propose a novel construction that achieves strong security guarantees and at the same time augments the capabilities of previous schemes. More specifically, we adapt existing techniques to achieve leakage-resilient ABE schemes with augmented robustness features making no compromises on security. For the second direction, our goal is to create practical schemes with as many features as possible, such as "large universe" and multi-authority settings. We showcase these claims with working implementations, benchmarks, and comparisons to previous constructions. Finally, these constructions lead us to new directions that we propose and intend to investigate further.Show more Item Cryptoraptor : high throughput reconfigurable cryptographic processor for symmetric key encryption and cryptographic hash functions(2014-12) Sayilar, Gokhan; Chiou, DerekShow more In cryptographic processor design, the selection of functional primitives and connection structures between these primitives are extremely crucial to maximize throughput and flexibility. Hence, detailed analysis on the specifications and requirements of existing crypto-systems plays a crucial role in cryptographic processor design. This thesis provides the most comprehensive literature review that we are aware of on the widest range of existing cryptographic algorithms, their specifications, requirements, and hardware structures. In the light of this analysis, it also describes a high performance, low power, and highly flexible cryptographic processor, Cryptoraptor, that is designed to support both today's and tomorrow's encryption standards. To the best of our knowledge, the proposed cryptographic processor supports the widest range of cryptographic algorithms compared to other solutions in the literature and is the only crypto-specific processor targeting the future standards as well. Unlike previous work, we aim for maximum throughput for all known encryption standards, and to support future standards as well. Our 1GHz design achieves a peak throughput of 128Gbps for AES-128 which is competitive with ASIC designs and has 25X and 160X higher throughput per area than CPU and GPU solutions, respectively.Show more Item Decrypting NTRU: An Introductory Mathematical Exploration of the NTRU Public Key Cryptosystem(2023-04) Shaw, HaydenShow more Provides an introductory analysis of the NTRU public key cryptosystem, including the mathematical background in which the system takes place, the specific workings of the system and how to break it, and a comparison to other relevant systems.Show more Item Deterministic extractors(2007-05) Kamp, Jesse John, 1979-; Zuckerman, David I.Show more Item Distributed computing and cryptography with general weak random sources(2011-08) Li, Xin, Ph. D.; Zuckerman, David I.; Alvisi, Lorenzo; Kalai, Yael; Klivans, Adam; Waters, BrentShow more The use of randomness in computer science is ubiquitous. Randomized protocols have turned out to be much more efficient than their deterministic counterparts. In addition, many problems in distributed computing and cryptography are impossible to solve without randomness. However, these applications typically require uniform random bits, while in practice almost all natural random phenomena are biased. Moreover, even originally uniform random bits can be damaged if an adversary learns some partial information about these bits. In this thesis, we study how to run randomized protocols in distributed computing and cryptography with imperfect randomness. We use the most general model for imperfect randomness where the weak random source is only required to have a certain amount of min-entropy. One important tool here is the randomness extractor. A randomness extractor is a function that takes as input one or more weak random sources, and outputs a distribution that is close to uniform in statistical distance. Randomness extractors are interesting in their own right and are closely related to many other problems in computer science. Giving efficient constructions of randomness extractors with optimal parameters is one of the major open problems in the area of pseudorandomness. We construct network extractor protocols that extract private random bits for parties in a communication network, assuming that they each start with an independent weak random source, and some parties are corrupted by an adversary who sees all communications in the network. These protocols imply fault-tolerant distributed computing protocols and secure multi-party computation protocols where only imperfect randomness is available. The probabilistic method shows that there exists an extractor for two independent sources with logarithmic min-entropy, while known constructions are far from achieving these parameters. In this thesis we construct extractors for two independent sources with any linear min-entropy, based on a computational assumption. We also construct the best known extractors for three independent sources and affine sources. Finally we study the problem of privacy amplification. In this model, two parties share a private weak random source and they wish to agree on a private uniform random string through communications in a channel controlled by an adversary, who has unlimited computational power and can change the messages in arbitrary ways. All previous results assume that the two parties have local uniform random bits. We show that this problem can be solved even if the two parties only have local weak random sources. We also improve previous results in various aspects by constructing the first explicit non-malleable extractor and giving protocols based on this extractor.Show more Item Efficient, provably secure code constructions(2011-05) Agrawal, Shweta Prem; Vishwanath, Sriram; Boneh, Dan; Zuckerman, David; Garg, Vijay; Caramanis, Constantine; Sanghavi, SujayShow more The importance of constructing reliable and efficient methods for securing digital information in the modern world cannot be overstated. The urgency of this need is reflected in mainstream media--newspapers and websites are full of news about critical user information, be it credit card numbers, medical data, or social security information, being compromised and used illegitimately. According to news reports, hackers probe government computer networks millions of times a day, about 9 million Americans have their identities stolen each year and cybercrime costs large American businesses 3.8 million dollars a year. More than 1 trillion worth of intellectual property has already been stolen from American businesses. It is this evergrowing problem of securing valuable information that our thesis attempts to address (in part). In this thesis, we study methods to secure information that are fast, convenient and reliable. Our overall contribution has four distinct threads. First, we construct efficient, "expressive" Public Key Encryption systems (specifically, Identity Based Encryption systems) based on the hardness of lattice problems. In Identity Based Encryption (IBE), any arbitrary string such as the user's email address or name can be her public key. IBE systems are powerful and address several problems faced by the deployment of Public Key Encryption. Our constructions are secure in the standard model. Next, we study secure communication over the two-user interference channel with an eavesdropper. We show that using lattice codes helps enhance the secrecy rate of this channel in the presence of an eavesdropper. Thirdly, we analyze the security requirements of network coding. Network Coding is an elegant method of data transmission which not only helps achieve capacity in several networks, but also has a host of other benefits. However, network coding is vulnerable to "pollution attacks" when there are malicious users in the system. We design mechanisms to prevent pollution attacks. In this setting, we provide two constructions -- a homomorphic Message Authentication Code (HMAC) and a Digital Signature, to secure information that is transmitted over such networks. Finally, we study the benefits of using Compressive Sensing for secure communication over the Wyner wiretap channel. Compressive Sensing has seen an explosion of interest in the last few years with its elegant mathematics and plethora of applications. So far however, Compressive Sensing had not found application in the domain of secrecy. Given its inherent assymetry, we ask (and answer in the affirmative) the question of whether it can be deployed to enable secure communication. Our results allow linear encoding and efficient decoding (via LASSO) at the legitimate receiver, along with infeasibility of message recovery (via an information theoretic analysis) at the eavesdropper, regardless of decoding strategy.Show more Item Elliptic curves(2010-08) Jensen, Crystal Dawn; Daniels, Mark L.; Armendáriz, Efraim P.Show more This report discusses the history, use, and future of elliptic curves. Uses of elliptic curves in various number theory settings are presented. Fermat’s Last Proof is shown to be proven with elliptic curves. Finally, the future of elliptic curves with respect to cryptography and primality is shown.Show more Item Explicit two-source extractors and more(2016-05) Chattopadhyay, Eshan; Zuckerman, David I.; Gal, Anna; Li, Xin; Waters, BrentShow more In this thesis we study the problem of extracting almost truly random bits from imperfect sources of randomness. This is motivated by the wide use of randomness in computer science, and the fact that most accessible sources of randomness generate correlated bits, and at best contain some amount of entropy. We follow Chor and Goldreich [CG88] and Zuckerman [Z90], and model weak sources using min-entropy, where an (n,k)-source X is a distribution on n bits and takes any string x with probability at most 2^-k. It is known that it is impossible to extract random bits from a single (n,k)-source, and Chor and Goldreich [CG88] raised the question of extracting randomness from two such independent (n,k)-sources. Existentially, such 2-source randomness extractors exist for min-entropy k >=log n + O(1), but the best known construction prior to work in this thesis requires min-entropy k >=0.499 n [B2]. One of the main contributions of this thesis is an explicit 2-source extractor for min-entropy log^C n, for some constant C. Other results in this thesis include improved ways of extracting random bits from various other sources of randomness, as well as stronger notions of randomness extraction. Our results have applications in privacy amplification [BBR88,Mau92,BBCM95], which is a classical problem in information cryptography, and give protocols that achieve almost optimal parameters. Other applications include explicit constructions of non-malleable codes, which is a relaxation of the notion of error-detection codes and have applications in tamper-resilient cryptography [DPW10].Show more Item Functional encryption : new proof techniques and advancing capabilities(2012-05) Lewko, Allison Bishop; Waters, Brent R., 1978-; Zuckerman, David; Klivans, Adam; Sahai, Amit; Shmatikov, Vitaly; Boneh, DanShow more We develop the dual system encryption methodology to provide fully secure functional encryption systems. We introduce new proof techniques and explore their applications, resulting in systems that advance the state of the art in terms of functionality, security, and efficiency. Our approach constructs versatile tools for adapting the dual system encryption methodology to new functionalities and efficiency goals. As particular demonstrations of our techniques, we obtain fully secure ciphertext-policy attribute-based encryption systems in the single authority and decentralized settings. Our work has provided the first fully secure attribute-based encryption schemes as well as the first decentralized schemes achieving desired levels of flexibility.Show more Item Genus 2 curves in pairing-based cryptography and the minimal embedding field(2007-08) Hitt, Laura Michelle, 1979-; Voloch, José FelipeShow more A pairing-friendly hyperelliptic curve over a finite field Fq is one whose group of Fq-rational points of its Jacobian has size divisible by a large prime and whose embedding degree is small enough for computations to be feasible but large enough for the discrete logarithm problem in the embedding field to be difficult. We give a sequence of Fq-isogeny classes for a family of Jacobians of curves of genus 2 over Fq, for q = 2m, and their corresponding small embedding degrees for the subgroup with large prime order. We give examples of the parameters for such curves with embedding degree k < (log q) 2 , such as k = 8, 13, 16, 23, 26, 37, 46, 52. For secure and efficient implementation of pairingbased cryptography on curves of genus g over Fq, it is desirable that the ratio ρ = g log2 q log2 ` be approximately 1, where ` is the order of the subgroup with embedding degree k. We show that for our family of curves, ρ is often near 1 and never more than 2. We construct examples to show that the minimal embedding field can be significantly smaller than Fq k . This has the implication that attacks on the DLP can be dramatically faster than expected, so there could be “pairingfriendly” curves that may not be as secure as previously believed.Show more Item Practicality of algorithmic number theory(2013-08) Taylor, Ariel Jolishia; Luecke, John EdwinShow more This report discusses some of the uses of algorithms within number theory. Topics examined include the applications of algorithms in the study of cryptology, the Euclidean Algorithm, prime generating functions, and the connections between algorithmic number theory and high school algebra.Show more Item Program obfuscation: new applications and constructions from standard assumptions(2018-08) Koppula, Venkata Vivek Kumar; Waters, Brent R., 1978-; Sahai, Amit; Klivans, Adam; Zuckerman, DavidShow more Code obfuscation has been one of the main focal points of cryptographic research over the last few years. This proposed thesis studies two different aspects of program obfuscation. In the first part, we examine the power of indistinguishability obfuscation. This notion of indistinguishability obfuscation requires that the obfuscation of two functionally identical programs must be computationally indistinguishable. In this work, we show how obfuscation for circuits can be used to obfuscate Turing machines. Our obfuscation scheme satisfies the succinctness requirement; that is, the obfuscation of a Turing machine M has size polynomial in the machine description |M| and a maximum bound on the input length n. Previous works that addressed this problem required an additional bound on the maximum space used by the Turing machine. Our construction is based on indistinguishability obfuscation for circuits, one way functions and injective pseudo random generators. In the second part of the proposed dissertation, we study constructions of obfuscation for restricted function classes under standard assumptions. We introduce the notion of lockable obfuscation. In a lockable obfuscation scheme there exists an obfuscation algorithm that takes as input a security parameter, a program P, a message m and “lock value” α and outputs an obfuscated program P̃. One can evaluate the obfuscated program P̃ on any input x where the output of evaluation is the message m if P(x) = α and otherwise receives a rejecting symbol. We proceed to provide a construction of lockable obfuscation and prove it secure under the Learning with Errors (LWE) assumption. Previous constructions of obfuscation under standard assumptions worked for much weaker function classes such as point functions and conjunctions. Next, we describe multiple applications of lockable obfuscation. The first application is a generic transformation of any attribute-based encryption (ABE) scheme into one in which the attributes used to encrypt the message are hidden from any user that is not authorized to decrypt the message. Similarly, we show how to upgrade broadcast encryption schemes to have one-sided anonymity. We also show applications of lockable obfuscation to separation and uninstantiability results.Show more Item Quantum copy protection and unclonable cryptography(2023-08-25) Liu, Jiahui, Ph. D.; Aaronson, Scott; Gál, Anna; Waters, Brent; Wu, David; Zhandry, MarkShow more While quantum computers are often seen as a threat to modern cryptographic systems, if honest parties and authorities make use of quantum computers, we can develop new cryptographic protocols and applications. These protocols, such as information-theoretic key exchange, unforgeable banknotes, and position-based cryptographic protocols, rely on the unclonability of quantum information and demonstrate a quantum advantage by offering classically unachievable security guarantees. Quantum copy protection, put forward by Aaronson(CCC'09), is one important example among the new capabilities. A copy protection scheme aims at preventing adversarial users from making pirate copies of a software program. We would like to achieve such a scheme by encoding a classical functionality into a quantum state so that any user with one copy of the state can run the program, but any malicious user trying to duplicate the state would fail. In this work, we investigate the feasibility of designing provably secure quantum copy protection protocols by combining classical post-quantum cryptographic tools with quantum information.Show more Item RSA in hardware(2010-12) Gillmore, Brooks Colin; Abraham, Jacob A.; McDermott, MarkShow more This report presents the RSA encryption and decryption schemes and discusses several methods for expediting the computations required, specifically the modular exponentiation operation that is required for RSA. A hardware implementation of the CIOS (Coarsely Integrated Operand Scanning) algorithm for modular multiplication is attempted on a XILINX Spartan3 FPGA in the TLL-5000 development platform used at the University of Texas at Austin. The development of the hardware is discussed in detail and some Verilog source code is provided for an implementation of modular multiplication. Some source code is also provided for an RSA executable to run on the TLL-6219 ARM-based development platform, to be used to generate test vectors.Show more Item The secrets behind cryptography : a mathematical overview(2010-08) Povondra, Amy Becker; Daniels, Mark L.; Armendáriz, Efraim P.Show more Daily advancements in technology influence many aspects of society. In today’s political and economic era, the need for secure, computerized convenience is apparent. Cryptosystems play a major role for everyone, from an individual making an online purchase to the government communicating with an ally during wartime. As technology advances, so do cryptosystems. The author of this paper discusses different types of cryptosystems, from substitution ciphers to public key cryptography, and introduces the mathematical foundations of such systems.Show more