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」

In this paper we propose a new block cipher, DESL (DES Lightweight), which is based on the classical DES (Data Encryption Standard) design, but unlike DES it uses a single S-box repeated eight times. On this account we adapt well-known DES S-box design criteria, such that they can be applied to the special case of a single S-box. Furthermore, we show that DESL is resistant against certain types of the most common attacks, i.e., linear and differential cryptanalyses, and the Davies-Murphy attack. Our hardware implementation results of DESL are very promising (1848 GE), therefore DESL is well suited for ultra-constrained devices such as RFID tags.

/pdf/new-lightweight-des-variants-knthjeayev.pdf

New Lightweight DES Variants

The technical analysis used in determining which of the potential Advanced Encryption Standard candidates was selected as the Advanced Encryption Algorithm includes efficiency testing of both hardware and software implementations of candidate algorithms. Reprogrammable devices such as field-programmable gate arrays (FPGAs) are highly attractive options for hardware implementations of encryption algorithms, as they provide cryptographic algorithm agility, physical security, and potentially much higher performance than software solutions. This contribution investigates the significance of FPGA implementations of the Advanced Encryption Standard candidate algorithms. Multiple architectural implementation options are explored for each algorithm. A strong focus is placed on high-throughput implementations, which are required to support security for current and future high bandwidth applications. Finally, the implementations of each algorithm will be compared in an effort to determine the most suitable candidate for hardware implementation within commercially available FPGAs.

An FPGA-based performance evaluation of the AES block cipher candidate algorithm finalists

In recent years, hardware Trojans have drawn the attention of governments and industry as well as the scientific community. One of the main concerns is that integrated circuits, e.g., for military or critical-infrastructure applications, could be maliciously manipulated during the manufacturing process, which often takes place abroad. However, since there have been no reported hardware Trojans in practice yet, little is known about how such a Trojan would look like, and how difficult it would be in practice to implement one.

In this paper we propose an extremely stealthy approach for implementing hardware Trojans below the gate level, and we evaluate their impact on the security of the target device. Instead of adding additional circuitry to the target design, we insert our hardware Trojans by changing the dopant polarity of existing transistors. Since the modified circuit appears legitimate on all wiring layers (including all metal and polysilicon), our family of Trojans is resistant to most detection techniques, including fine-grain optical inspection and checking against "golden chips". We demonstrate the effectiveness of our approach by inserting Trojans into two designs -- a digital post-processing derived from Intel's cryptographically secure RNG design used in the Ivy Bridge processors and a side-channel resistant SBox implementation -- and by exploring their detectability and their effects on security.

/pdf/stealthy-dopant-level-hardware-trojans-2r20357yk6.pdf

Stealthy dopant-level hardware trojans

We introduce multi-channel attacks, i.e., side-channel attacks which utilize multiple side-channels such as power and EM simultaneously. We propose an adversarial model which combines a CMOS leakage model and the maximum-likelihood principle for performing and analyzing such attacks. This model is essential for deriving the optimal and very often counter-intuitive techniques for channel selection and data analysis. We show that using multiple channels is better for template attacks by experimentally showing a three-fold reduction in the error probability. Developing sound countermeasures against multi-channel attacks requires a rigorous leakage assessment methodology. Under suitable assumptions and approximations, our model also yields a practical assessment methodology for net information leakage from the power and all available EM channels in constrained devices such as chip-cards. Classical DPA/DEMA style attacks assume an adversary weaker than that of our model. For this adversary, we apply the maximum-likelihood principle to such design new and more efficient single and multiple-channel DPA/DEMA attacks.

Christof Paar

Papers

New Lightweight DES Variants

An FPGA-based performance evaluation of the AES block cipher candidate algorithm finalists

Stealthy dopant-level hardware trojans

Cryptographic Hardware and Embedded Systems - CHES 2003

Cryptographic Hardware and Embedded Systems — CHES 2000