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」

Heute bedrohen Risiken wie Produktpiraterie und Industriespionage Technologiekonzerne mehr denn je. Weder wertvoll aufgebautes Know-How noch kostspielige Eigenentwicklungen durfen in die Hande der Konkurrenz geraten. Uber Gewinner und Verlierer dieses Wettkampfs entscheidet haufig, ob die Schutzmechanismen der verwendeten Baugruppen halten, was die Hersteller versprechen. In diesem Beitrag untersuchen wir am Beispiel von Xilinx Bauelementen, wie sich die Bitstromverschlusselung zum Schutz der FPGA Konfiguration in der Praxis bewahrt. Wir zeigen, wie sich mittels Seitenkanalanalyse sogar mit dem hochsicheren AES-256 geschutzte Inhalte entschlusseln lassen.

Praktische Angriffe auf die Bitstromverschlüsselung von Xilinx FPGAs

In this paper, we investigate physical-layer security (PLS) methods for proximity-based group-key establishment and proof of location. Fields of application include secure car-to-car communication, privacy-preserving and secure distance evidence for healthcare, or location-based feature activation. Existing technologies do not solve the problem satisfactorily due to communication restrictions, e.g., ultra-wideband (UWB) based time of flight measurements, or trusted hardware, e.g., using global navigation satellite system (GNSS) positioning data.We introduce PLS as a possible solution candidate. It is information-theoretically secure, thereby also post-quantum resistant, and has the potential to run on resource-constrained devices with low latency. We use wireless channel properties of satellite-to-earth links, demonstrate the first feasibility study using off-the-shelf hardware testbeds, and present first evaluation results and future directions for research.

Keys from the Sky: A First Exploration of Physical-Layer Security Using Satellite Links

In diesem Kapitel erlernen Sie


eine kurze Zusammenfassung der Geschichte der asymmetrischen Kryptografie,


die Vor- und Nachteile der asymmetrischen Kryptografie,


Grundlagen der Zahlentheorie, die fur das Verstandnis von asymmetrischen Algorithmen notwendig sind. Insbesondere wird der erweiterte euklidische Algorithmus eingefuhrt.

Einführung in die asymmetrische Kryptografie

The security of FPGAs is a crucial topic, as any vulnerability within the hardware can have severe consequences, if they are used in a secure design. Since FPGA designs are encoded in a bitstream, securing the bitstream is of the utmost importance. Adversaries have many motivations to recover and manipulate the bitstream, including design cloning, IP theft, manipulation of the design, or design subversions e.g., through hardware Trojans. Given that FPGAs are often part of cyber-physical systems e.g., in aviation, medical, or industrial devices, this can even lead to physical harm. Consequently, vendors have introduced bitstream encryption, offering authenticity and confidentiality. Even though attacks against bitstream encryption have been proposed in the past, e.g., side-channel analysis and probing, these attacks require sophisticated equipment and considerable technical expertise. In this paper, we introduce novel low-cost attacks against the Xilinx 7-Series (and Virtex-6) bitstream encryption, resulting in the total loss of authenticity and confidentiality. We exploit a design flaw which piecewise leaks the decrypted bitstream. In the attack, the FPGA is used as a decryption oracle, while only access to a configuration interface is needed. The attack does not require any sophisticated tools and, depending on the target system, can potentially be launched remotely. In addition to the attacks, we discuss several countermeasures.

Christof Paar

Papers

Praktische Angriffe auf die Bitstromverschlüsselung von Xilinx FPGAs

Keys from the Sky: A First Exploration of Physical-Layer Security Using Satellite Links

Einführung in die asymmetrische Kryptografie

The Unpatchable Silicon: A Full Break of the Bitstream Encryption of Xilinx 7-Series FPGAs