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」

Numerous contactless smartcards (and the corresponding RFID readers) are compatible with NFC, e.g., Mifare cards and the governmental ID card in Germany called nPA. NFC-enabled smartphones and other NFC objects such as door locks have become widespread. Existing and future applications of the up-and-coming technology require a secure way of assigning and transporting user rights, e.g., for opening and starting a car or access control to a building. In this paper, we propose a scheme that securely identifies a customer on a website and creates a (personalized) credential containing the booked access permissions. This credential is safely transported via the Internet to the user’s smartphone and finally grants access to an NFC-enabled object. In our proof-of-concept implementation, an application on a commercial smartphone is used for communicating with a web server of a car rental agency. During the booking process, the phone operates as an RFID reader to interrogate the nPA of the user and utilizes the security mechanisms of the nPA, including the PACE protocol, for identifying the customer. After having obtained the credential, the smartphone emulates a Mifare DESFire card that is read by the NFC door lock of a rental car to verify the validity of the access permission. We discuss security issues and limitations of our approach.

Rights Management with NFC Smartphones and Electronic ID Cards: A Proof of Concept for Modern Car Sharing

Efficient implementation of block ciphers is critical towards achieving both high security and high-speed processing. Numerous block ciphers have been proposed and implemented, using a wide and varied range of functional operations. Existing microprocessor architectures do not provide this broad range of support. However, the advent of intellectual property (IP) microprocessor cores presents the opportunity to augment existing datapaths and instruction sets to add acceleration modules. Therefore, we will present a hardware architecture that achieves efficient implementation of generalized Galois Field fixed field constant multiplication, a core operation of Rijndael, chosen by the National Institute of Standards and Technology (NIST) as the Advanced Encryption Standard (AES) Advanced Encryption Algorithm in October of 2000. A detailed discussion of the architecture will be provided and an analysis of system performance and resource utilization will be performed to demonstrate the efficiency versus other implementations.

Efficient Implementation of Galois Field Fixed Field Constant Multiplication

On the Security and Efficiency of Real-World Lightweight Authentication Protocols

Gate camouflaging is a known security enhancement technique that tries to thwart reverse engineering by hiding the functions of gates or the connections between them. A number of works on SAT-based attacks have shown that it is often possible to reverse engineer a circuit function by combining a camouflaged circuit model and the ability to have oracle access to the obfuscated combinational circuit. Especially in small circuits it is easy to reverse engineer the circuit function in this way, but SAT-based reverse engineering techniques provide no guarantees of recovering a circuit that is gate-by-gate equivalent to the original design. In this work we show that an attacker who doesn't know gate functions or connections of an aggressively camouflaged circuit cannot learn the correct gate-level schematic even if able to control inputs and probe all combinational nodes of the circuit. We then present a stronger attack that extends SAT-based reverse engineering with fault analysis to allow an attacker to recover the correct gate-level schematic. We analyze our reverse engineering approach on an S-Box circuit.

SAT-based reverse engineering of gate-level schematics using fault injection and probing

This contribution describes new GF(p) multipliers, for p>2, specially suited for GF(p/sup m/) multiplication. We construct truth tables whose inputs are the bits of the multiplicand and multiplier and whose output are the bits that represent the modular product. However, contrary to previous approaches, we do not represent the elements of GF(p) in the normal binary positional system. Rather, we choose a representation which minimizes the resulting Boolean function. We obtain improvements of up to 35% in area when compared to previous approaches for small odd prime fields. We report transistor counts for all multipliers with p<2/sup 5/ which we obtained through the SIS sequential circuit synthesis program.

Christof Paar

Papers

Rights Management with NFC Smartphones and Electronic ID Cards: A Proof of Concept for Modern Car Sharing

Efficient Implementation of Galois Field Fixed Field Constant Multiplication

On the Security and Efficiency of Real-World Lightweight Authentication Protocols

SAT-based reverse engineering of gate-level schematics using fault injection and probing

Area efficient GF(p) architectures for GF(p/sup m/) multipliers