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 appli- cations 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 importantduring the design of the cipher and at 1570 GE, the hardware requirements for present are competitive with today's leading compact stream ciphers. 1

/pdf/small-footprint-block-cipher-design-how-far-can-you-go-1rx8izxyhl.pdf

Small-Footprint Block Cipher Design - How far can you go?

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.

Physical security bounds against tampering

The discipline of reverse engineering integrated circuits (ICs) is as old as the technology itself. It grew out of the need to analyze competitor’s products and detect possible IP infringements. In recent years, the growing hardware Trojan threat motivated a fresh research interest in the topic. The process of IC reverse engineering comprises two steps: netlist extraction and specification discovery. While the process of netlist extraction is rather well understood and established techniques exist throughout the industry, specification discovery still presents researchers with a plurality of open questions. It therefore remains of particular interest to the scientific community. In this paper, we present a survey of the state of the art in IC reverse engineering while focusing on the specification discovery phase. Furthermore, we list noteworthy existing works on methods and algorithms in the area and discuss open challenges as well as unanswered questions. Therefore, we observe that the state of research on algorithmic methods for specification discovery suffers from the lack of a uniform evaluation approach. We point out the urgent need to develop common research infrastructure, benchmarks, and evaluation metrics.

https://link.springer.com/content/pdf/10.1007/s13389-021-00268-5.pdf

A survey of algorithmic methods in IC reverse engineering

Authentication and message integrity are essential building blocks for protocols of many security related verification processes like data origin authentication for valid software updates or device authentication. Critical embedded devices like a brake control unit in a car must only accept updates from valid issuers. At the same time it is essential for security and commercial reasons to prove the authenticity of the device to other integrated systems to prevent product counterfeiting. The most widely used algorithms for digital signatures, RSA and ECDSA, depend on finite field engines. Many embedded devices are powered by 8-bit microprocessors. On this platform the finite field engines either require costly coprocessors, or the implementations become very large and very slow. Hence the need for better methods is highly visible. One alternative to RSA and ECDSA is the Merkle signature scheme which provides digital signatures using hash functions only, without relying on any number theoretic assumptions. In this paper, we present an implementation of the Merkle signature scheme on an 8-bit microprocessor. Our results prove that the Merkle signature scheme can provide very good timings and a higher degree of security compared to previous implementations of RSA and ECDSA, while maintaining a smaller code size.

Efficient Hash-Based Signatures on Embedded Devices

In contrast to software reverse engineering, there are hardly any tools available that support hardware reversing. Therefore, the reversing process is conducted by human analysts combining several complex semi-automated steps. However, countermeasures against reversing are evaluated solely against mathematical models. Our research goal is the establishment of cognitive obfuscation based on the exploration of underlying psychological processes. We aim to identify problems which are hard to solve for human analysts and derive novel quantification metrics, thus enabling stronger obfuscation techniques.

https://dl.acm.org/doi/pdf/10.1145/3287624.3288741

Christof Paar

Papers

Small-Footprint Block Cipher Design - How far can you go?

Physical security bounds against tampering

A survey of algorithmic methods in IC reverse engineering

Efficient Hash-Based Signatures on Embedded Devices

Towards cognitive obfuscation: impeding hardware reverse engineering based on psychological insights