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"Computer security -- Mathematics"
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Security of Block Ciphers
A comprehensive evaluation of information security analysis spanning the intersection of cryptanalysis and side-channel analysis
* Written by authors known within the academic cryptography community, this book presents the latest developments in current research
* Unique in its combination of both algorithmic-level design and hardware-level implementation; this all-round approach - algorithm to implementation – covers security from start to completion
* Deals with AES (Advanced Encryption standard), one of the most used symmetric-key ciphers, which helps the reader to learn the fundamental theory of cryptanalysis and practical applications of side-channel analysis
eBook
The mathematics of secrets : cryptography from caesar ciphers to digital encryption
The Mathematics of Secrets takes readers on a tour of the mathematics behind cryptography--the science of sending secret messages. Joshua Holden shows how mathematical principles underpin the ways that different codes and ciphers operate, as he focuses on both code making and code breaking. He discusses the majority of ancient and modern ciphers currently known, beginning by looking at substitution ciphers, built by substituting one letter or block of letters for another. Explaining one of the simplest and historically well-known ciphers, the Caesar cipher, Holden establishes the key mathematical idea behind the cipher and discusses how to introduce flexibility and additional notation. He explores polyalphabetic substitution ciphers, transposition ciphers, including one developed by the Spartans, connections between ciphers and computer encryption, stream ciphers, ciphers involving exponentiation, and public-key ciphers, where the methods used to encrypt messages are public knowledge, and yet, intended recipients are still the only ones who are able to read the message. Only basic mathematics up to high school algebra is needed to understand and enjoy the book.
Book
Introduction to Cryptography with Open-Source Software
This text illustrates algorithms and cryptosystems using examples and the open-source computer algebra system of Sage. It enables students to run their own programs and develop a deep and solid understanding of the mechanics of cryptography. The author, a noted educator in the field, covers the methods, algorithms, and applications of modern cryptographic systems. He provides a highly practical learning experience by progressing at a gentle pace, keeping mathematics at a manageable level, and including numerous end-of-chapter exercises.
eBook
The golden ticket
The P-NP problem is the most important open problem in computer science, if not all of mathematics.The Golden Ticketprovides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. In this informative and entertaining book, Lance Fortnow traces how the problem arose during the Cold War on both sides of the Iron Curtain, and gives examples of the problem from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. But difficulty also has its advantages. Hard problems allow us to safely conduct electronic commerce and maintain privacy in our online lives.
The Golden Ticketexplores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of the P-NP problem.
eBook
Secret history : the story of cryptology
\"Codes are a part of everyday life, from the ubiquitous Universal Price Code (UPC) to postal zip codes. They need not be intended for secrecy. They generally use groups of letters (sometimes pronounceable code words) or numbers to represent other words or phrases. There is typically no mathematical rule to pair an item with its representation in code. A few more examples will serve to illustrate the range of codes\"-- Provided by publisher.
Book
Numerical algorithms for personalized search in self-organizing information networks
This book lays out the theoretical groundwork for personalized search and reputation management, both on the Web and in peer-to-peer and social networks. Representing much of the foundational research in this field, the book develops scalable algorithms that exploit the graphlike properties underlying personalized search and reputation management, and delves into realistic scenarios regarding Web-scale data.
Sep Kamvar focuses on eigenvector-based techniques in Web search, introducing a personalized variant of Google's PageRank algorithm, and he outlines algorithms--such as the now-famous quadratic extrapolation technique--that speed up computation, making personalized PageRank feasible. Kamvar suggests that Power Method-related techniques ultimately should be the basis for improving the PageRank algorithm, and he presents algorithms that exploit the convergence behavior of individual components of the PageRank vector. Kamvar then extends the ideas of reputation management and personalized search to distributed networks like peer-to-peer and social networks. He highlights locality and computational considerations related to the structure of the network, and considers such unique issues as malicious peers. He describes the EigenTrust algorithm and applies various PageRank concepts to P2P settings. Discussion chapters summarizing results conclude the book's two main sections.
Clear and thorough, this book provides an authoritative look at central innovations in search for all of those interested in the subject.
eBook
Digital privacy and security using Windows : a practical guide
\"This book teaches you how to secure your online identity and personal devices, encrypt your digital data and online communications, protect cloud data and Internet of Things (IoT), mitigate social engineering attacks, keep your purchases secret, and conceal your digital footprint ... The book helps you build a robust defense from electronic crime and corporate surveillance. It covers general principles of digital privacy and how to configure and use various security applications to maintain your privacy, such as TOR, VPN, and BitLocker. You will learn to encrypt email communications using Gpg4win and Thunderbird.\"--Page 4 of cover.
Book
On the algebraic degree of iterated power functions
New symmetric primitives are being designed to address a novel set of design criteria. Instead of being executed on regular processors or smartcards, they are instead intended to be run in abstract settings such as multi-party computations or zero-knowledge proof systems. This implies in particular that these new primitives are described using operations over large finite fields. As the number of such primitives grows, it is important to better understand the properties of their underlying operations. In this paper, we investigate the algebraic degree of one of the first such block ciphers, namely MiMC. It is composed of many iterations of a simple round function, which consists of an addition and of a low-degree power permutation applied to the full state, usually
x
↦
x
3
. We show in particular that, while the
univariate
degree increases predictably with the number of rounds, the
algebraic
degree (a.k.a multivariate degree) has a much more complex behaviour, and simply stays constant during some rounds. Such
plateaus
slightly slow down the growth of the algebraic degree. We present a full investigation of this behaviour. First, we prove some lower and upper bounds for the algebraic degree of an arbitrary number of iterations of MiMC and of its inverse. Then, we combine theoretical arguments with simulations to prove that the upper bound is tight for up to 16,265 rounds. Using these results, we slightly improve the higher-order differential attack presented at Asiacrypt 2020 to cover one or two more rounds. More importantly, our results provide some precise guarantees on the algebraic degree of this cipher, and then on the minimal complexity for a higher-order differential attack.
Journal Article