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」

With the establishment of the AES the need for new block ciphers has been greatly diminished; for almost all block cipher applications the AES is an excellent and preferred choice. However, despite recent implementation advances, the AES is not suitable for extremely constrained environments such as RFID tags and sensor networks. In this paper we describe an ultra-lightweight block cipher, present . Both security and hardware efficiency have been equally important during the design of the cipher and at 1570 GE, the hardware requirements for present are competitive with today's leading compact stream ciphers.

/pdf/present-an-ultra-lightweight-block-cipher-33ym33ql7r.pdf

PRESENT: An Ultra-Lightweight Block Cipher

Cryptography is now ubiquitous moving beyond the traditional environments, such as government communications and banking systems, we see cryptographic techniques realized in Web browsers, e-mail programs, cell phones, manufacturing systems, embedded software, smart buildings, cars, and even medical implants Today's designers need a comprehensive understanding of applied cryptography After an introduction to cryptography and data security, the authors explain the main techniques in modern cryptography, with chapters addressing stream ciphers, the Data Encryption Standard (DES) and 3DES, the Advanced Encryption Standard (AES), block ciphers, the RSA cryptosystem, public-key cryptosystems based on the discrete logarithm problem, elliptic-curve cryptography (ECC), digital signatures, hash functions, Message Authentication Codes (MACs), and methods for key establishment, including certificates and public-key infrastructure (PKI) Throughout the book, the authors focus on communicating the essentials and keeping the mathematics to a minimum, and they move quickly from explaining the foundations to describing practical implementations, including recent topics such as lightweight ciphers for RFIDs and mobile devices, and current key-length recommendations The authors have considerable experience teaching applied cryptography to engineering and computer science students and to professionals, and they make extensive use of examples, problems, and chapter reviews, while the books website offers slides, projects and links to further resources This is a suitable textbook for graduate and advanced undergraduate courses and also for self-study by engineers

/pdf/understanding-cryptography-a-textbook-for-students-and-4dytdxglat.pdf

Understanding Cryptography: A Textbook For Students And Practitioners

We describe a new class of attacks on secure microcontrollers and smartcards. Illumination of a target transistor causes it to conduct, thereby inducing a transient fault. Such attacks are practical; they do not even require expensive laser equipment. We have carried them out using a flashgun bought second-hand from a camera store for $30 and with an $8 laser pointer. As an illustration of the power of this attack, we developed techniques to set or reset any individual bit of SRAM in a microcontroller. Unless suitable countermeasures are taken, optical probing may also be used to induce errors in cryptographic computations or protocols, and to disrupt the processor’s control flow. It thus provides a powerful extension of existing glitching and fault analysis techniques. This vulnerability may pose a big problem for the industry, similar to those resulting from probing attacks in the mid-1990s and power analysis attacks in the late 1990s. We have therefore developed a technology to block these attacks. We use self-timed dual-rail circuit design techniques whereby a logical 1 or 0 is not encoded by a high or low voltage on a single line, but by (HL) or (LH) on a pair of lines. The combination (HH) signals an alarm, which will typically reset the processor. Circuits can be designed so that singletransistor failures do not lead to security failure. This technology may also make power analysis attacks very much harder too.

Cryptographic Hardware and Embedded Systems - CHES 2002

This paper presents a block cipher that is optimized with respect to latency when implemented in hardware. Such ciphers are desirable for many future pervasive applications with real-time security needs. Our cipher, named PRINCE, allows encryption of data within one clock cycle with a very competitive chip area compared to known solutions. The fully unrolled fashion in which such algorithms need to be implemented calls for innovative design choices. The number of rounds must be moderate and rounds must have short delays in hardware. At the same time, the traditional need that a cipher has to be iterative with very similar round functions disappears, an observation that increases the design space for the algorithm. An important further requirement is that realizing decryption and encryption results in minimum additional costs. PRINCE is designed in such a way that the overhead for decryption on top of encryption is negligible. More precisely for our cipher it holds that decryption for one key corresponds to encryption with a related key. This property we refer to as α-reflection is of independent interest and we prove its soundness against generic attacks.

/pdf/prince-a-low-latency-block-cipher-for-pervasive-computing-3rf9hqsh69.pdf

Christof Paar

Papers

PRESENT: An Ultra-Lightweight Block Cipher

PRESENT: An Ultra-Lightweight Block Cipher

Understanding Cryptography: A Textbook For Students And Practitioners

Cryptographic Hardware and Embedded Systems - CHES 2002

PRINCE: a low-latency block cipher for pervasive computing applications