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The classified mathematical papers of A. A. Albert: a glimpse into the application of mathematics to cryptologic problems during the 1950s and 1960s

Abraham Adrian Albert “A cubed” (1905–1972) was an algebraist best known academically for his study of associative and non-associative algebras. By the 1940s he had also developed an interest in cryptology and its relationship to mathematics. Throughout the following two decades, Albert would participate in several mathematics programs to study and advise on cryptanalysis. In particular, Albert’s work with the National Security Agency (NSA) set a framework for the development of cryptology as a mathematical discipline. This research aims to present a timeline for and the breadth of Albert’s promotion of cryptology in the post-WWII American mathematical community and to examine, for the first time, reports Albert authored under contract with the NSA. In doing so, we hope to better understand the relationship between the NSA and academic mathematicians at the time of writing. The reports, released in 2020 by the NSA in response to a 2010 Freedom of Information Act request, have been arranged by the author into eleven collections based on content. Each collection will be introduced with their ideas and results given in a roughly chronological order. These collections span ideas in group theory, field theory, matrix algebra, and geometry, most often with application to cryptological systems.

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Side-channel attack–resistant PRESENT cipher by versatile key scheduling and compact S-box utilizing optimized three-phase logic design

The most widely used technology at the moment is the Internet of Things (IoT), which is expanding at a rapid pace because it allows us to remotely control and manage a variety of smart devices and relieves us from our demanding daily routines. Technology is also vulnerable to security breaches, as evidenced by the rise in cybercrimes and identity theft. More so than any other known IoT security breach, side-channel analysis is extremely insecure. A current issue for lightweight IoT applications is differential power analysis, a kind of side-channel analysis that is very accurate in obtaining the secret key. As a result, developing a safe style takes more time and effort. PRESENT is an easy-to-use, low-power encryption algorithm that is based on Advanced Encryption Standard (AES) and is utilized in IoT devices like RFID tags and access cards. Even with the plethora of countermeasures proposed in the last ten years, none are able to keep up with the IoT’s rapid expansion. A clever combination of masking and hiding techniques could stop several security breaches. Masked three-phase dual rail pre-charge logic is a new hybrid countermeasure that thwarts combined side-channel attacks and is suggested as a means of attaining the necessary degree of security. The hybrid design utilized in PRESENT resulted in an increase in complexity and required more work in terms of area and power. Consequently, more PRESENT optimization techniques are applied. Additionally, for PRESENT hardware implementation, a flexible key scheduling structure with parallel input and output is proposed. Using the Cadence Virtuoso simulation tool with 180-nm technology, a secured structure combining optimized algorithm and secured logic is designed, and the outcomes are analyzed. Normalized energy deviation (NED)/normalized standard deviation (NSD) analysis and Pearson correlation are used to analyze safety. The simulation results for the gates show that our proposed logic has the lowest values of NED and NSD at the assigned frequencies. When compared with side-channel analysis, the outcomes have shown to be both safe and effective. In comparison to earlier designs, the suggested system’s area and power consumption are cut by 67% and 64%, respectively.

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