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Title: TOWARDS DEPLOYABLE QUANTUM-SAFE CRYPTOSYSTEMS.
Creator: Koziel, Brian, Azarderakhsh, Reza, Florida Atlantic University, Department of Computer and Electrical Engineering and Computer Science, College of Engineering and Computer Science
Abstract/Description: It is well known that in the near future, a large-scale quantum computer will be unveiled, one that could be used to break the cryptography that underlies our digital infrastructure. Quantum computers operate on quantum mechanics, enabling exponential speedups to certain computational problems, including hard problems at the cornerstone of our deployed cryptographic algorithms. With a vulnerability in this security foundation, our online identities, banking information, and precious data is...
Show moreIt is well known that in the near future, a large-scale quantum computer will be unveiled, one that could be used to break the cryptography that underlies our digital infrastructure. Quantum computers operate on quantum mechanics, enabling exponential speedups to certain computational problems, including hard problems at the cornerstone of our deployed cryptographic algorithms. With a vulnerability in this security foundation, our online identities, banking information, and precious data is now vulnerable. To address this, we must prepare for a transition to post-quantum cryptography, or cryptosystems that are protected from attacks by both classical and quantum computers. This is a dissertation proposal targeting cryptographic engineering that is necessary to deploy isogeny-based cryptosystems, one known family of problems that are thought to be difficult to break, even for quantum computers. Isogeny-based cryptography utilizes mappings between elliptic curves to achieve public-key encryption, digital signatures, and other cryptographic objectives necessary to support our digital infrastructure's security. This proposal focuses on three aspects of isogeny-based cryptography: 1) cryptographic engineering of isogeny-based cryptosystems; 2) developing and optimizing security-enabling isogeny applications; and 3) improving the security from known and emerging implementation attacks. By improving each of these aspects, we are providing confidence in the deployability of isogeny-based cryptography and helping to prepare for a post-quantum transition.
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Date Issued: 2022
PURL: http://purl.flvc.org/fau/fd/FA00013998
Subject Headings: Cryptography, Quantum computers
Format: Document (PDF)

Title: Quantum-Resistant Key Agreement and Key Encapsulation.
Creator: Robinson, Angela, Steinwandt, Rainer, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: We explore quantum-resistant key establishment and hybrid encryption. We nd that while the discrete logarithm problem is e ciently solved by a quantum computer using Shor's algorithm, some instances are insecure even using classical computers. The discrete logarithm problem based on a symmetric group Sn is e - ciently solved in polynomial time. We design a PUF-based 4-round group key establishment protocol, adjusting the model to include a physical channel capable of PUF transmission, and...
Show moreWe explore quantum-resistant key establishment and hybrid encryption. We nd that while the discrete logarithm problem is e ciently solved by a quantum computer using Shor's algorithm, some instances are insecure even using classical computers. The discrete logarithm problem based on a symmetric group Sn is e - ciently solved in polynomial time. We design a PUF-based 4-round group key establishment protocol, adjusting the model to include a physical channel capable of PUF transmission, and modify adversarial capabilities with respect to the PUFs. The result is a novel group key establishment protocol which avoids computational hardness assumptions and achieves key secrecy. We contribute a hybrid encryption scheme by combining a key encapsulation mechanism (KEM) with a symmetric key encryption scheme by using two hash functions. We require only one-way security in the quantum random oracle model (QROM) of the KEM and one-time security of the symmetric encryption scheme in the QROM. We show that this hybrid scheme is IND-CCA secure in the QROM. We rely on a powerful theorem by Unruh that provides an upper bound on indistinguishability between the output of a random oracle and a random string, when the oracle can be accessed in quantum superposition. Our result contributes to the available IND-CCA secure encryption schemes in a setting where quantum computers are under adversarial control. Finally, we develop a framework and describe biometric visual cryptographic schemes generically under our framework. We formalize several security notions and de nitions including sheet indistinguishability, perfect indistinguishability, index recovery, perfect index privacy, and perfect resistance against false authentication. We also propose new and generic strategies for attacking e-BVC schemes such as new distinguishing attack, new index recovery, and new authentication attack. Our quantitative analysis veri es the practical impact of our framework and o ers concrete upper bounds on the security of e-BVC.
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Date Issued: 2018
PURL: http://purl.flvc.org/fau/fd/FA00013023
Subject Headings: Quantum computing, Data encryption (Computer science), Cryptography
Format: Document (PDF)

Title: Quantum Circuits for Symmetric Cryptanalysis.
Creator: Langenberg, Brandon Wade, Steinwandt, Rainer, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Quantum computers and quantum computing is a reality of the near feature. Companies such as Google and IBM have already declared they have built a quantum computer and tend to increase their size and capacity moving forward. Quantum computers have the ability to be exponentially more powerful than classical computers today. With this power modeling behavior of atoms or chemical reactions in unusual conditions, improving weather forecasts and traffic conditions become possible. Also, their...
Show moreQuantum computers and quantum computing is a reality of the near feature. Companies such as Google and IBM have already declared they have built a quantum computer and tend to increase their size and capacity moving forward. Quantum computers have the ability to be exponentially more powerful than classical computers today. With this power modeling behavior of atoms or chemical reactions in unusual conditions, improving weather forecasts and traffic conditions become possible. Also, their ability to exponentially speed up some computations makes the security of todays data and items a major concern and interest. In the area of cryptography, some encryption schemes (such as RSA) are already deemed broken by the onset of quantum computing. Some encryption algorithms have already been created to be quantum secure and still more are being created each day. While these algorithms in use today are considered quantum-safe not much is known of what a quantum attack would look like on these algorithms. Specifically, this paper discusses how many quantum bits, quantum gates and even the depth of these gates that would be needed for such an attack. The research below was completed to shed light on these areas and offer some concrete numbers of such an attack.
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Date Issued: 2018
PURL: http://purl.flvc.org/fau/fd/FA00013010
Subject Headings: Quantum computing, Cryptography, Cryptanalysis, Data encryption (Computer science), Computer algorithms
Format: Document (PDF)

Title: Efficient Implementations of Post-quantum Isogeny-based Cryptography.
Creator: Jalali, Amir, Azarderakhsh, Reza, Florida Atlantic University, College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
Abstract/Description: Quantum computers are envisioned to be able to solve mathematical problems which are currently unsolvable for conventional computers, because of their exceptional computational power from quantum mechanics. Therefore, if quantum computers are ever built in large scale, they will certainly be able to solve many classical exponential complexity problems such as the hard problems which the current public key cryptography is constructed upon. To counteract this problem, the design of post-quantum...
Show moreQuantum computers are envisioned to be able to solve mathematical problems which are currently unsolvable for conventional computers, because of their exceptional computational power from quantum mechanics. Therefore, if quantum computers are ever built in large scale, they will certainly be able to solve many classical exponential complexity problems such as the hard problems which the current public key cryptography is constructed upon. To counteract this problem, the design of post-quantum cryptography protocols is necessary to preserve the security in the presence of quantum adversaries. Regardless of whether we can estimate the exact time for the advent of the quantum computing era, security protocols are required to be resistant against potentially-malicious power of quantum computing. In this thesis, the main focus is on the sperformance improvement of one of the potential PQC candidates, isogeny-based cryptography. Several optimized implementations of cryptography applications based on this primitive are presented. From a general viewpoint, the proposed methods, implementation techniques and libraries have a practical impact on the performance evaluation of post-quantum cryptography schemes in a wide range of applications. In particular, the provided benchmarks and optimizations on ARM-powered processors provide a reference for comparison and evaluation of isogeny-based cryptography with other post-quantum candidates during the first round of NIST's PQC standardization process.
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Date Issued: 2018
PURL: http://purl.flvc.org/fau/fd/FA00013125
Subject Headings: Cryptography, Quantum computing, ARM microprocessors, Post-quantum cryptography
Format: Document (PDF)

Title: CONTRIBUTIONS TO QUANTUM-SAFE CRYPTOGRAPHY: HYBRID ENCRYPTION AND REDUCING THE T GATE COST OF AES.
Creator: Pham, Hai, Steinwandt, Rainer, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Quantum cryptography offers a wonderful source for current and future research. The idea started in the early 1970s, and it continues to inspire work and development toward a popular goal, large-scale communication networks with strong security guarantees, based on quantum-mechanical properties. Quantum cryptography builds on the idea of exploiting physical properties to establish secure cryptographic operations. A particular quantum-based protocol has gathered interest in recent years for...
Show moreQuantum cryptography offers a wonderful source for current and future research. The idea started in the early 1970s, and it continues to inspire work and development toward a popular goal, large-scale communication networks with strong security guarantees, based on quantum-mechanical properties. Quantum cryptography builds on the idea of exploiting physical properties to establish secure cryptographic operations. A particular quantum-based protocol has gathered interest in recent years for its use of mesoscopic coherent states. The AlphaEta protocol has been designed to exploit properties of coherent states of light to transmit data securely over an optical channel. AlphaEta aims to draw security from the uncertainty of any measurement of the transmitted coherent states due to intrinsic quantum noise. We propose a framework to combine this protocol with classical preprocessing, taking into account error-correction for the optical channel and establishing a strong provable security guarantee. Integrating a state-of-the-art solution for fast authenticated encryption is straightforward, but in this case the security analysis requires heuristic reasoning.
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Date Issued: 2019
PURL: http://purl.flvc.org/fau/fd/FA00013339
Subject Headings: Cryptography, Quantum computing, Algorithms, Mesoscopic coherent states
Format: Document (PDF)

Title: ALGORITHMS IN LATTICE-BASED CRYPTANALYSIS.
Creator: Miller, Shaun, Bai, Shi, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: An adversary armed with a quantum computer has algorithms[66, 33, 34] at their disposal, which are capable of breaking our current methods of encryption. Even with the birth of post-quantum cryptography[52, 62, 61], some of best cryptanalytic algorithms are still quantum [45, 8]. This thesis contains several experiments on the efficacy of lattice reduction algorithms, BKZ and LLL. In particular, the difficulty of solving Learning With Errors is assessed by reducing the problem to an instance...
Show moreAn adversary armed with a quantum computer has algorithms[66, 33, 34] at their disposal, which are capable of breaking our current methods of encryption. Even with the birth of post-quantum cryptography[52, 62, 61], some of best cryptanalytic algorithms are still quantum [45, 8]. This thesis contains several experiments on the efficacy of lattice reduction algorithms, BKZ and LLL. In particular, the difficulty of solving Learning With Errors is assessed by reducing the problem to an instance of the Unique Shortest Vector Problem. The results are used to predict the behavior these algorithms may have on actual cryptographic schemes with security based on hard lattice problems. Lattice reduction algorithms require several floating-point operations including multiplication. In this thesis, I consider the resource requirements of a quantum circuit designed to simulate floating-point multiplication with high precision.
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Date Issued: 2020
PURL: http://purl.flvc.org/fau/fd/FA00013543
Subject Headings: Cryptanalysis, Cryptography, Algorithms, Lattices, Quantum computing
Format: Document (PDF)

Title: EFFICIENT IMPLEMENTATION OF POST-QUANTUM CRYPTOGRAPHY.
Creator: Elkhatib, Rami, Azarderakhsh, Reza, Florida Atlantic University, Department of Computer and Electrical Engineering and Computer Science, College of Engineering and Computer Science
Abstract/Description: Cryptography relies on hard mathematical problems that current conventional computers cannot solve in a feasible amount of time. On the other hand, quantum computers, with their quantum mechanic construction, are presumed to be able to solve some of these problems in a reasonable amount of time. More specifically, the current hard problems that public key cryptography relies upon are expected to be easily broken during the quantum era, a time when large-scale quantum computers are available....
Show moreCryptography relies on hard mathematical problems that current conventional computers cannot solve in a feasible amount of time. On the other hand, quantum computers, with their quantum mechanic construction, are presumed to be able to solve some of these problems in a reasonable amount of time. More specifically, the current hard problems that public key cryptography relies upon are expected to be easily broken during the quantum era, a time when large-scale quantum computers are available. To address this problem ahead of time, researchers and institutions have proposed post-quantum cryptography (PQC), which is an area of research that focuses on quantum-resistant public key cryptography algorithms. One of the candidates in the NIST PQC standardization process is SIKE, an isogeny-based candidate. The main advantage of SIKE is that it provides the smallest key size out of all the NIST PQC candidates at the cost of performance. Therefore, the development of hardware accelerators for SIKE is very important to achieve high performance in time-constrained applications. In this thesis, we implement several accelerators for SIKE and its primitives using different design approaches, all of which are suitable for different applications. We deliver significant enhancements to SIKE’s most expensive component, the modular multiplier. We design SIKE using a hardware-based approach and a software-hardware codesign approach, the latter of which utilizes a RISC-V processor. We also design SIKE with multi-level security level support for applications that require support of multiple security levels with minimal area usage. We enclose our performance and area results, which provide a reference to evaluate our work with other implementations.
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Date Issued: 2022
PURL: http://purl.flvc.org/fau/fd/FA00013986
Subject Headings: Cryptography, Quantum computers, Cryptography--Mathematics
Format: Document (PDF)

Title: EFFICIENT AND SECURE IMPLEMENTATION OF CLASSIC AND POST-QUANTUM PUBLIC-KEY CRYPTOGRAPHY.
Creator: Bisheh, Niasar Mojtaba, Azarderakhsh, Reza, Florida Atlantic University, Department of Computer and Electrical Engineering and Computer Science, College of Engineering and Computer Science
Abstract/Description: To address the increased interest in crypto hardware accelerators due to performance and efficiency concerns, implementing hardware architectures of different public-key cryptosystems has drawn growing attention. Pure hardware methodology enhances architecture’s performance over a hardware/software co-design scheme at the cost of a more extended design cycle, reducing the flexibility, and demands customized data paths for different protocol-level operations. However, using pure hardware...
Show moreTo address the increased interest in crypto hardware accelerators due to performance and efficiency concerns, implementing hardware architectures of different public-key cryptosystems has drawn growing attention. Pure hardware methodology enhances architecture’s performance over a hardware/software co-design scheme at the cost of a more extended design cycle, reducing the flexibility, and demands customized data paths for different protocol-level operations. However, using pure hardware architecture makes the design smaller, faster, and more efficient. This dissertation mainly focuses on designing crypto accelerators that can be used in embedded systems and Internet-of-Things (IoT) devices where performance and efficiency are critical as a hardware accelerator to offload computations from the microcontroller units (MCU). In particular, our objective is to create a system-on-chip (SoC) crypto-accelerator with an MCU that achieves high area-time efficiency. Our implementation can also be integrated as an off-chip solution; however, other criteria, such as performance, are often as important or more important than efficiency in the external crypto-chip design, which is beyond of this work. Not only does our architecture inherently provide protection against timing and simple power analysis (SPA) attacks, but also some advanced security mechanisms to avoid differential power analysis (DPA) attacks are included, which is missing in the literature. In a nutshell, the contributions are summarized as follows:
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Date Issued: 2022
PURL: http://purl.flvc.org/fau/fd/FA00013981
Subject Headings: Cryptography, Public key cryptography, Curves, Elliptic, Quantum computers
Format: Document (PDF)

Title: Quantum Circuits for Cryptanalysis.
Creator: Amento, Brittanney Jaclyn, Steinwandt, Rainer, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Finite elds of the form F2m play an important role in coding theory and cryptography. We show that the choice of how to represent the elements of these elds can have a signi cant impact on the resource requirements for quantum arithmetic. In particular, we show how the Gaussian normal basis representations and \ghost-bit basis" representations can be used to implement inverters with a quantum circuit of depth O(mlog(m)). To the best of our knowledge, this is the rst construction with...
Show moreFinite elds of the form F2m play an important role in coding theory and cryptography. We show that the choice of how to represent the elements of these elds can have a signi cant impact on the resource requirements for quantum arithmetic. In particular, we show how the Gaussian normal basis representations and \ghost-bit basis" representations can be used to implement inverters with a quantum circuit of depth O(mlog(m)). To the best of our knowledge, this is the rst construction with subquadratic depth reported in the literature. Our quantum circuit for the computation of multiplicative inverses is based on the Itoh-Tsujii algorithm which exploits the property that, in a normal basis representation, squaring corresponds to a permutation of the coe cients. We give resource estimates for the resulting quantum circuit for inversion over binary elds F2m based on an elementary gate set that is useful for fault-tolerant implementation. Elliptic curves over nite elds F2m play a prominent role in modern cryptography. Published quantum algorithms dealing with such curves build on a short Weierstrass form in combination with a ne or projective coordinates. In this thesis we show that changing the curve representation allows a substantial reduction in the number of T-gates needed to implement the curve arithmetic. As a tool, we present a quantum circuit for computing multiplicative inverses in F2m in depth O(mlogm) using a polynomial basis representation, which may be of independent interest. Finally, we change our focus from the design of circuits which aim at attacking computational assumptions on asymmetric cryptographic algorithms to the design of a circuit attacking a symmetric cryptographic algorithm. We consider a block cipher, SERPENT, and our design of a quantum circuit implementing this cipher to be used for a key attack using Grover's algorithm as in [18]. This quantum circuit is essential for understanding the complexity of Grover's algorithm.
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Date Issued: 2016
PURL: http://purl.flvc.org/fau/fd/FA00004662, http://purl.flvc.org/fau/fd/FA00004662
Subject Headings: Artificial intelligence, Computer networks, Cryptography, Data encryption (Computer science), Finite fields (Algebra), Quantum theory
Format: Document (PDF)

Cryptography (9)	+ -
Quantum computing (5)	+ -
Data encryption (Computer science) (3)	+ -
Quantum computers (3)	+ -
Algorithms (2)	+ -

Cryptanalysis (2)	+ -
ARM microprocessors (1)	+ -
Artificial intelligence (1)	+ -
Computer algorithms (1)	+ -
Computer networks (1)	+ -
Cryptography--Mathematics (1)	+ -
Curves, Elliptic (1)	+ -
Finite fields (Algebra) (1)	+ -
Lattices (1)	+ -
Mesoscopic coherent states (1)	+ -
Post-quantum cryptography (1)	+ -
Public key cryptography (1)	+ -
Quantum theory (1)	+ -

Florida Atlantic University (9)	+ -
Charles E. Schmidt College of Science (5)	+ -
Department of Mathematical Sciences (5)	+ -
Azarderakhsh, Reza (4)	+ -
College of Engineering and Computer Science (4)	+ -

Department of Computer and Electrical Engineering and Computer Science (4)	+ -
Steinwandt, Rainer (4)	+ -
Amento, Brittanney Jaclyn (1)	+ -
Bai, Shi (1)	+ -
Bisheh, Niasar Mojtaba (1)	+ -
Elkhatib, Rami (1)	+ -
Jalali, Amir (1)	+ -
Koziel, Brian (1)	+ -
Langenberg, Brandon Wade (1)	+ -
Miller, Shaun (1)	+ -
Pham, Hai (1)	+ -
Robinson, Angela (1)	+ -

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