Entropy in Dimension One

This paper completely classifies which numbers arise as the topological entropy associated to postcritically finite self-maps of the unit interval. Specifically, a positive real number h is the topological entropy of a postcritically finite self-map of the unit interval if and only if exp(h) is an algebraic integer that is at least as large as the absolute value of any of the conjugates of exp(h); that is, if exp(h) is a weak Perron number. The postcritically finite map may be chosen to be a polynomial all of whose critical points are in the interval (0,1). This paper also proves that the weak Perron numbers are precisely the numbers that arise as exp(h), where h is the topological entropy associated to ergodic train track representatives of outer automorphisms of a free group.Comment: 38 pages, 15 figures. This paper was completed by the author before his death, and was uploaded by Dylan Thurston. A version including endnotes by John Milnor will appear in the proceedings of the Banff conference on Frontiers in Complex Dynamic

Effects of Architecture on Information Leakage of a Hardware Advanced Encryption Standard Implementation

Side-channel analysis (SCA) is a threat to many modern cryptosystems. Many countermeasures exist, but are costly to implement and still do not provide complete protection against SCA. A plausible alternative is to design the cryptosystem using architectures that are known to leak little information about the cryptosystem\u27s operations. This research uses several common primitive architectures for the Advanced Encryption Standard (AES) and assesses the susceptibility of the full AES system to side-channel attack for various primitive configurations. A combined encryption/decryption core is also evaluated to determine if variation of high-level architectures affects leakage characteristics. These different configurations are evaluated under multiple measurement types and leakage models. The results show that different hardware configurations do impact the amount of information leaked by a device, but none of the tested configurations are able to prevent exploitation

Set It and Forget It! Turnkey ECC for Instant Integration

Historically, Elliptic Curve Cryptography (ECC) is an active field of applied cryptography where recent focus is on high speed, constant time, and formally verified implementations. While there are a handful of outliers where all these concepts join and land in real-world deployments, these are generally on a case-by-case basis: e.g.\ a library may feature such X25519 or P-256 code, but not for all curves. In this work, we propose and implement a methodology that fully automates the implementation, testing, and integration of ECC stacks with the above properties. We demonstrate the flexibility and applicability of our methodology by seamlessly integrating into three real-world projects: OpenSSL, Mozilla's NSS, and the GOST OpenSSL Engine, achieving roughly 9.5x, 4.5x, 13.3x, and 3.7x speedup on any given curve for key generation, key agreement, signing, and verifying, respectively. Furthermore, we showcase the efficacy of our testing methodology by uncovering flaws and vulnerabilities in OpenSSL, and a specification-level vulnerability in a Russian standard. Our work bridges the gap between significant applied cryptography research results and deployed software, fully automating the process

Design and Cryptanalysis of a Customizable Authenticated Encryption Algorithm

It is common knowledge that encryption is a useful tool for providing confidentiality. Authentication, however, is often overlooked. Authentication provides data integrity; it helps ensure that any tampering with or corruption of data is detected. It also provides assurance of message origin. Authenticated encryption (AE) algorithms provide both confidentiality and integrity / authenticity by processing plaintext and producing both ciphertext and a Message Authentication Code (MAC). It has been shown too many times throughout history that encryption without authentication is generally insecure. This has recently culminated in a push for new authenticated encryption algorithms. There are several authenticated encryption algorithms in existence already. However, these algorithms are often difficult to use correctly in practice. This is a significant problem because misusing AE constructions can result in reduced security in many cases. Furthermore, many existing algorithms have numerous undesirable features. For example, these algorithms often require two passes of the underlying cryptographic primitive to yield the ciphertext and MAC. This results in a longer runtime. It is clear that new easy-to-use, single-pass, and highly secure AE constructions are needed. Additionally, a new AE algorithm is needed that meets stringent requirements for use in the military and government sectors. This thesis explores the design and cryptanalysis of a novel, easily customizable AE algorithm based on the duplex construction. Emphasis is placed on designing a secure pseudorandom permutation (PRP) for use within the construction. A survey of state of the art cryptanalysis methods is performed and the resistance of our algorithm against such methods is considered. The end result is an algorithm that is believed to be highly secure and that should remain secure if customizations are made within the provided guidelines