Physical Sciences and Mathematics Commons^™

Closing The Gap: Leveraging Aes-Ni To Balance Adversarial Advantage And Honest User Performance In Argon2i, Nicholas Harrell, Nathaniel Krakauer

CERIAS Technical Reports

The challenge of providing data privacy and integrity while maintaining efficient performance for honest users is a persistent concern in cryptography. Attackers exploit advances in parallel hardware and custom circuit hardware to gain an advantage over regular users. One such method is the use of Application-Specific Integrated Circuits (ASICs) to optimize key derivation function (KDF) algorithms, giving adversaries a significant advantage in password guessing and recovery attacks. Other examples include using graphical processing units (GPUs) and field programmable gate arrays (FPGAs). We propose a focused approach to close the gap between adversarial advantage and honest user performance by leveraging the …

The History Of The Enigma Machine, Jenna Siobhan Parkinson

History Publications

The history of the Enigma machine begins with the invention of the rotor-based cipher machine in 1915. Various models for rotor-based cipher machines were developed somewhat simultaneously in different parts of the world. However, the first documented rotor machine was developed by Dutch naval officers in 1915. Nonetheless, the Enigma machine was officially invented following the end of World War I by Arthur Scherbius in 1918 (Faint, 2016).

On The Cryptographic Deniability Of The Signal Protocol, Nihal Vatandas

Dissertations, Theses, and Capstone Projects

Offline deniability is the ability to a posteriori deny having participated in a particular communication session. This property has been widely assumed for the Signal messaging application, yet no formal proof has appeared in the literature. In this work, we present the first formal study of the offline deniability of the Signal protocol. Our analysis shows that building a deniability proof for Signal is non-trivial and requires strong assumptions on the underlying mathematical groups where the protocol is run.

To do so, we study various implicitly authenticated key exchange protocols, including MQV, HMQV, and 3DH/X3DH, the latter being the core …

Performance Improvements In Inner Product Encryption, Serena Riback

Honors Scholar Theses

Consider a database that contains thousands of entries of the iris biometric. Each entry identifies an individual, so it is especially important that it remains secure. However, searching for entries among an encrypted database proves to be a security problem - how should one search encrypted data without leaking any information to a potential attacker? The proximity searchable encryption scheme, as discussed in the work by Cachet et al., uses the notions of inner product encryption developed by Kim et al.. In this paper, we will focus on the efficiency of these schemes. Specifically, how the symmetry of the bilinear …

Provably Weak Instances Of Plwe Revisited, Again, Katherine Mendel

CSB and SJU Distinguished Thesis

Learning with Errors has emerged as a promising possibility for postquantum cryptography. Variants known as RLWE and PLWE have been shown to be more efficient, but the increased structure can leave them vulnerable to attacks for certain instantiations. This work aims to identify specific cases where proposed cryptographic schemes based on PLWE work particularly poorly under a specific attack.

An Adaptive Cryptosystem On A Finite Field, Awnon Bhowmik, Unnikrishnan Menon

Publications and Research

Owing to mathematical theory and computational power evolution, modern cryptosystems demand ingenious trapdoor functions as their foundation to extend the gap between an enthusiastic interceptor and sensitive information. This paper introduces an adaptive block encryption scheme. This system is based on product, exponent, and modulo operation on a finite field. At the heart of this algorithm lies an innovative and robust trapdoor function that operates in the Galois Field and is responsible for the superior speed and security offered by it. Prime number theorem plays a fundamental role in this system, to keep unwelcome adversaries at bay. This is a …

The Generalized Riemann Hypothesis And Applications To Primality Testing, Peter Hall

University Scholar Projects

The Riemann Hypothesis, posed in 1859 by Bernhard Riemann, is about zeros
of the Riemann zeta-function in the complex plane. The zeta-function can be repre-
sented as a sum over positive integers n of terms 1/ns when s is a complex number
with real part greater than 1. It may also be represented in this region as a prod-
uct over the primes called an Euler product. These definitions of the zeta-function
allow us to find other representations that are valid in more of the complex plane,
including a product representation over its zeros. The Riemann Hypothesis says that
all …

Unclonable Secret Keys, Marios Georgiou

Dissertations, Theses, and Capstone Projects

We propose a novel concept of securing cryptographic keys which we call “Unclonable Secret Keys,” where any cryptographic object is modified so that its secret key is an unclonable quantum bit-string whereas all other parameters such as messages, public keys, ciphertexts, signatures, etc., remain classical. We study this model in the authentication and encryption setting giving a plethora of definitions and positive results as well as several applications that are impossible in a purely classical setting.

In the authentication setting, we define the notion of one-shot signatures, a fundamental element in building unclonable keys, where the signing key not only …

Rationality And Efficient Verifiable Computation, Matteo Campanelli

Dissertations, Theses, and Capstone Projects

In this thesis, we study protocols for delegating computation in a model where one of the parties is rational. In our model, a delegator outsources the computation of a function f on input x to a worker, who receives a (possibly monetary) reward. Our goal is to design very efficient delegation schemes where a worker is economically incentivized to provide the correct result f(x). In this work we strive for not relying on cryptographic assumptions, in particular our results do not require the existence of one-way functions.

We provide several results within the framework of rational proofs introduced by Azar …

Blockchain In Payment Card Systems, Darlene Godfrey-Welch, Remy Lagrois, Jared Law, Russell Scott Anderwald, Daniel W. Engels

SMU Data Science Review

Payment cards (e.g., credit and debit cards) are the most frequent form of payment in use today. A payment card transaction entails many verification information exchanges between the cardholder, merchant, issuing bank, a merchant bank, and third-party payment card processors. Today, a record of the payment transaction often records to multiple ledgers. Merchant’s incur fees for both accepting and processing payment cards. The payment card industry is in dire need of technology which removes the need for third-party verification and records transaction details to a single tamper-resistant digital ledger. The private blockchain is that technology. Private blockchain provides a linked …

Quantum Attacks On Modern Cryptography And Post-Quantum Cryptosystems, Zachary Marron

Senior Honors Theses

Cryptography is a critical technology in the modern computing industry, but the security of many cryptosystems relies on the difficulty of mathematical problems such as integer factorization and discrete logarithms. Large quantum computers can solve these problems efficiently, enabling the effective cryptanalysis of many common cryptosystems using such algorithms as Shor’s and Grover’s. If data integrity and security are to be preserved in the future, the algorithms that are vulnerable to quantum cryptanalytic techniques must be phased out in favor of quantum-proof cryptosystems. While quantum computer technology is still developing and is not yet capable of breaking commercial encryption, these …

Application Of Huffman Data Compression Algorithm In Hashing Computation, Lakshmi Narasimha Devulapalli Venkata,

Masters Theses & Specialist Projects

Cryptography is the art of protecting information by encrypting the original message into an unreadable format. A cryptographic hash function is a hash function which takes an arbitrary length of the text message as input and converts that text into a fixed length of encrypted characters which is infeasible to invert. The values returned by the hash function are called as the message digest or simply hash values. Because of its versatility, hash functions are used in many applications such as message authentication, digital signatures, and password hashing [Thomsen and Knudsen, 2005].

The purpose of this study is to apply …

Implementing And Testing A Novel Chaotic Cryptosystem, Samuel Jackson, Scott Kerlin, Jeremy Straub

Jeremy Straub

Cryptography in the domain of small satellites is a relatively new area of research. Compared to typical desktop computers, small satellites have limited bandwidth, processing power, and battery power. Many of the current encryption schemes were developed for desktop computers and servers, and as such may be unsuitable for small satellites. In addition, most cryptographic research in the domain of small satellites focuses on hardware solutions, which can be problematic given the limited space requirements of small satellites.

This paper investigates potential software solutions that could be used to encrypt and decrypt data on small satellites and other devices with …

Testing A Novel Cryptosystem For Use In Securing Small Satellite Communications, Samuel Jackson, Scott Kerlin, Jeremy Straub

Jeremy Straub

Cryptography in the domain of Small Satellites is a topic of growing importance. While large satellites are likely to have the hardware requirements to run common cryptographic algorithms, small satellites are extremely limited in both hardware capabilities, which limits the speed and security of cryptosystems implemented in software, and available physical space, which limits the ability to include cryptosystems implemented in hardware. However, small satellites are growing in popularity, and as such securing communications becomes a necessity for some. The Department of Defense is exploring the possibility of using CubeSats, a type of small satellite, in their operations, as are …

Circuit Principles And Weak Pigeonhole Variants, Chris Pollett, Norman Danner

Norman Danner

This paper considers the relational versions of the surjective, partial surjective, and multifunction weak pigeonhole principles for PV, , , and formulas as well as relativizations of these formulas to higher levels of the bounded arithmetic hierarchy. We show that the partial surjective weak pigeonhole principle for formulas implies that for each k there is a string of length 2^2nk which is hard to block-recognize by circuits of size n^k. These principles in turn imply the partial surjective principle for formulas. We show that the surjective weak pigeonhole principle for formulas in implies …

Structure And Randomness Of The Discrete Lambert Map, Jingjing Chen, Mark Lotts

Mathematical Sciences Technical Reports (MSTR)

We investigate the structure and cryptographic applications of the Discrete Lambert Map (DLM). The mapping is closely related to the Discrete Log Problem, but has received far less attention since it is considered to be a more complicated map that is likely even harder to invert. However, this mapping is quite important because it underlies the security of the ElGamal Digital Signature Scheme. Using functional graphs induced by this mapping, we were able to find non-random properties that could potentially be used to exploit the ElGamal DSS.

The Square Discrete Exponentiation Map, A Wood

Mathematical Sciences Technical Reports (MSTR)

We will examine the square discrete exponentiation map and its properties. The square discrete exponentiation map is a variation on a commonly seen problem in cryptographic algorithms. This paper focuses on understanding the underlying structure of the functional graphs generated by this map. Specifically, this paper focuses on explaining the in-degree of graphs of safe primes, which are primes of the form p = 2q + 1, where q is also prime.

Algebraic Solutions To Overdefined Systems With Applications To Cryptanalysis, Eric Crockett

Mathematical Sciences Technical Reports (MSTR)

Cryptographic algorithms are based on a wide variety of difficult problems in mathematics. One of these problems is finding a solution to a system of multivariate quadratic equations (MQ). A generalization of this problem is to find a solution to a system of higher order non-linear equations. Both of these problems are NP-hard over any field. Many cryptosystems such as AES, Serpent, Toyocrypt, and others can be reduced to some form of the MQ problem. In this paper we analyze the relinearization and XL algorithms for solving overdetermined systems of non-linear equations, as well as two variations of the XL …

Cryptography Using Steganography: New Algorithms And Applications, Jonathan Blackledge

Articles

Developing methods for ensuring the secure exchange of information is one of the oldest occupations in history. With the revolution in Information Technology, the need for securing information and the variety of methods that have been developed to do it has expanded rapidly. Much of the technology that forms the basis for many of the techniques used today was originally conceived for use in military communications and has since found a place in a wide range of industrial and commercial sectors. This has led to the development of certain industry standards that are compounded in specific data processing algorithms together …

On The Applications Of Deterministic Chaos For Encrypting Data On The Cloud, Jonathan Blackledge, Nikolai Ptitsyn

Conference papers

Cloud computing is expected to grow considerably in the future because it has so many advantages with regard to sale and cost, change management, next generation architectures, choice and agility. However, one of the principal concerns for users of the Cloud is lack of control and above all, data security. This paper considers an approach to encrypting information before it is ‘place’ on the Cloud where each user has access to their own encryption algorithm, an algorithm that is based on a set of Iterative Function Systems that outputs a chaotic number stream, designed to produce a cryptographically secure cipher. …

Statistical Investigation Of Structure In The Discrete Logarithm, Andrew Hoffman

Mathematical Sciences Technical Reports (MSTR)

The absence of an efficient algorithm to solve the Discrete Logarithm Problem is often exploited in cryptography. While exponentiation with a modulus is extremely fast with a modern computer, the inverse is decidedly not. At the present time, the best algorithms assume that the inverse mapping is completely random. Yet there is at least some structure, and to uncover additional structure that may be useful in constructing or refining algorithms, statistical methods are employed to compare modular exponential mappings to random mappings. More concretely, structure will be defined by representing the mappings as functional graphs and using parameters from graph …