There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

1. The Advanced Encryption Standard Process.- 2. Preliminaries.- 3. Specification of Rijndael.- 4. Implementation Aspects.- 5. Design Philosophy.- 6. The Data Encryption Standard.- 7. Correlation Matrices.- 8. Difference Propagation.- 9. The Wide Trail Strategy.- 10. Cryptanalysis.- 11. Related Block Ciphers.- Appendices.- A. Propagation Analysis in Galois Fields.- A.1.1 Difference Propagation.- A.l.2 Correlation.- A. 1.4 Functions that are Linear over GF(2).- A.2.1 Difference Propagation.- A.2.2 Correlation.- A.2.4 Functions that are Linear over GF(2).- A.3.3 Dual Bases.- A.4.2 Relationship Between Trace Patterns and Selection Patterns.- A.4.4 Illustration.- A.5 Rijndael-GF.- B. Trail Clustering.- B.1 Transformations with Maximum Branch Number.- B.2 Bounds for Two Rounds.- B.2.1 Difference Propagation.- B.2.2 Correlation.- B.3 Bounds for Four Rounds.- B.4 Two Case Studies.- B.4.1 Differential Trails.- B.4.2 Linear Trails.- C. Substitution Tables.- C.1 SRD.- C.2 Other Tables.- C.2.1 xtime.- C.2.2 Round Constants.- D. Test Vectors.- D.1 KeyExpansion.- D.2 Rijndael(128,128).- D.3 Other Block Lengths and Key Lengths.- E. Reference Code.

The Design of Rijndael: AES - The Advanced Encryption Standard

After two decades of research and development, elliptic curve cryptography now has widespread exposure and acceptance. Industry, banking, and government standards are in place to facilitate extensive deployment of this efficient public-key mechanism. Anchored by a comprehensive treatment of the practical aspects of elliptic curve cryptography (ECC), this guide explains the basic mathematics, describes state-of-the-art implementation methods, and presents standardized protocols for public-key encryption, digital signatures, and key establishment. In addition, the book addresses some issues that arise in software and hardware implementation, as well as side-channel attacks and countermeasures. Readers receive the theoretical fundamentals as an underpinning for a wealth of practical and accessible knowledge about efficient application. Features & Benefits: * Breadth of coverage and unified, integrated approach to elliptic curve cryptosystems * Describes important industry and government protocols, such as the FIPS 186-2 standard from the U.S. National Institute for Standards and Technology * Provides full exposition on techniques for efficiently implementing finite-field and elliptic curve arithmetic* Distills complex mathematics and algorithms for easy understanding* Includes useful literature references, a list of algorithms, and appendices on sample parameters, ECC standards, and software toolsThis comprehensive, highly focused reference is a useful and indispensable resource for practitioners, professionals, or researchers in computer science, computer engineering, network design, and network data security.

https://cdn.preterhuman.net/texts/cryptography/Hankerson,%20Menezes,%20Vanstone.%20Guide%20to%20elliptic%20curve%20cryptography%20(Springer,%202004)(ISBN%20038795273X)(332s)_CsCr_.pdf

Guide to Elliptic Curve Cryptography

National Institute of Standards and Technology における超伝導研究及び生活

The objective of this paper is to give a comprehensive introduction to applied cryptography with an engineer or computer scientist in mind. The emphasis is on the knowledge needed to create practical systems which supports integrity, confidentiality, or authenticity. Topics covered includes an introduction to the concepts in cryptography, attacks against cryptographic systems, key use and handling, random bit generation, encryption modes, and message authentication codes. Recommendations on algorithms and further reading is given in the end of the paper. This paper should make the reader able to build, understand and evaluate system descriptions and designs based on the cryptographic components described in the paper.

[서평]「Applied Cryptography」

This chapter discusses building blocks for implementing popular public key cryptosystems, like RSA, Diffie-Hellman Key Exchange (DHKE) and Elliptic Curve Cryptography (ECC) Therefore, we briefly introduce field-based arithmetic on which most of recently established public key cryptosystems rely As most popular fields, we give examples for architecture implementing efficient arithmetic operations over prime and binary extension fields for use in cryptographic applications

Modular Integer Arithmetic for Public Key Cryptography

This paper presents intermediate results of our investigations into the potential of analog hardware for the purpose of solving linear equation (LES) systems which are of quadratic form and binary. Based on the assumption that we can efficiently solve binary LES over the rationals with sufficient precision, we present a generic method to map a rational solution to a solution which solves the equation system over $\mathbb{F}_2$. We show that, in order to perform this mapping, we only need to look at two bits of the binary expansion of each of the elements of the rational solution vector.

http://www5.rz.rub.de:8032/imperia/md/content/wolf/waifi_driessen.pdf

Solving binary linear equation systems over the rationals and binaries

Pervasive networks with low-cost embedded 8-bit processors are set to change our day-to-day life Public-key cryptography provides crucial functionality to assure security which is often an important requirement in pervasive applications However, it has been the hardest to implement on constraint platforms due to its very high computational requirements This contribution describes a proof-of-concept implementation for an extremely low-cost instruction set extension using reconfigurable logic, which enables an 8-bit micro-controller to provide full size elliptic curve cryptography (ECC) capabilities Introducing full size public-key security mechanisms on such small embedded devices will allow new pervasive applications We show that a standard compliant 163-bit point multiplication can be computed in 0113 sec on an 8-bit AVR micro-controller running at 4 Mhz with minimal extra hardware, a typical representative for a low-cost pervasive processor Our design not only accelerates the computation by a factor of more than 30 compared to a software-only solution, it also reduces the code-size, data-RAM and power requirements

Reconfigurable instruction set extension for enabling ECC on an 8-bit processor

We present a design for a Wi-Fi user-authentication token that tunnels data through the SSID field, packet timing, and packet length. Previous attempts to build an online-banking transaction-signing token have been only moderately successful, due in large part to usability problems. Average consumers, especially in the United States, are simply unwilling to transcribe strings of digits from PC to token and back again. In a departure from previous work, our token communicates using point-to-point side-channels in Wi-Fi that allow two devices to directly exchange messages – even if one is also connected to an access point. The result is a token that can authenticate transactions using only one touch by the user. The increased usability means more transactions can be authenticated, reducing fraud and driving more banking business online.

One-touch financial transaction authentication

We consider the problem of an active adversary physically manipulating computations of a cryptographic device that is implemented in circuitry. Which kind of circuit based security can ever be guaranteed if all computations are vulnerable towards fault injection? In this paper, we define physical security parameters against tampering adversaries. Therefore, we present an adversarial model with a strong focus on fault injection techniques based on radiation and particle impact. Physical implementation strategies to counteract tampering attempts are discussed.

/pdf/physical-security-bounds-against-tampering-4jalqifspj.pdf

Christof Paar

Papers

Modular Integer Arithmetic for Public Key Cryptography

Solving binary linear equation systems over the rationals and binaries

Reconfigurable instruction set extension for enabling ECC on an 8-bit processor

One-touch financial transaction authentication

Physical security bounds against tampering