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」

When complex functions, for example, substitution boxes of block ciphers, are realized in hardware, timing attributes of the underlying combinational circuit depend on the input/output changes of the function. These characteristics can be exploited by the help of a relatively new scheme called fault sensitivity analysis. A collision timing attack which exploits the data-dependent timing characteristics of combinational circuits is demonstrated in this paper. The attack is based on an also recently published correlation collision attack, which avoids the need for a hypothetical timing model for the underlying combinational circuit to recover the secret materials. The target platforms of our proposed attack are 14 AES ASIC cores of the SASEBO LSI chips in three different process technologies, 13 nm, 90 nm, and 65 nm. Successfully breaking all cores including the DPA-protected and fault attack protected cores indicates the strength of the attack.

One Attack to Rule Them All: Collision Timing Attack versus 42 AES ASIC Cores

The field of lightweight cryptography has developed significantly over recent years and many impressive implementation results have been published. However these results are often concerned with a core computation and when it comes to a real implementation there can be significant hidden overheads. In this paper we consider the case of CRYPTOGPS and we outline a full implementation that has been fabricated in ASIC. Interestingly, the implementation requirements still remain within the typically-cited limits for on-the-tag cryptography.

Lightweight cryptography and RFID: tackling the hidden overheads

Cryptographic algorithms are used in a large variety of different applications to ensure security services. It is, thus, very interesting to investigate various implementation platforms. Hyperelliptic curve schemes are cryptographic primitives to which a lot of attention was recently given due to the short operand size compared to other algorithms. They are specifically interesting for special-purpose hardware. This paper provides a comprehensive investigation of high-efficient HEC architectures.

We propose a genus-2 hyperelliptic curve cryptographic coprocessor using affine coordinates. We implemented a special class of hyperelliptic curves, namely using the parameter h(x)=x and f=x5+f1x+f0 and the base field GF(289). In addition, we only consider the most frequent case in our implementation and assume that the other cases are handled, e.g. by the protocol.

We provide three different implementations ranging from high speed to moderate area. Hence, we provide a solution for a variety of applications. Our high performance HECC coprocessor is 78.5% faster than the best previous implementation and our low area implementation utilizes only 22.7% of the area that the smallest published design uses. Taking into account both area and latency, our coprocessor is an order of magnitude more efficient than previous implementations. We hope that the work at hand provides a step towards introducing HEC systems in practical applications.

Hyperelliptic curve coprocessors on a FPGA

Cryptographic algorithms are constantly evolving to meet security needs, and modular arithmetic is an integral part of these algorithms, especially in the case of public-key cryptosystems. To achieve optimal system performance while maintaining physical security, it is desirable to implement cryptographic algorithms in hardware. However, many public- key cryptographic algorithms require the implementation of modular arithmetic, specifically modular multiplication, for operands of 1024 bits in length. Additionally, algorithm agility is required to support algorithm independent protocols, a feature of most modern security protocols. Reprogrammability, particularly in-system reprogrammability, is critical in enabling the switching between cryptographic algorithms required for algorithm independent protocols. Field Programmable Gate Arrays (FPGAs) are a viable option for achieving this goal. Ideally, the targeted FPGA will have been designed with the architectural requirements for wide-operand modular arithmetic in mind in an effort to maximize system performance. This contribution investigates existing FPGA architectures with respect to modular multiplication. It also proposes a new FPGA architecture optimized for the wide-operand additions required for modular multiplication.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Toward an FPGA architecture optimized for public-key algorithms

Since the introduction of the first side-channel analyses in academia about 15 years ago, several physical attacks have been presented that exploit side-channel leakages to break implementations of cryptographic algorithms. This article deals with the same physical property of electronic devices, but focuses on the art of tailoring it for constructive uses. More precisely, two scenarios, i.e., hardware Trojans and IP watermarking, are illustrated in which the designer of an electronic circuit can add functionality by considering side channels as part of the available design space. Both applications use the same concept, i.e., deliberately leaking a secret through a side channel while keeping the introduced side channel hidden from adversaries and attackers. This article provides a broad overview of the existing works for both applications and should serve as a comprehensible introduction to the underlying field of research. This includes many subtle details that have not been discussed in literature yet, including existing shortcomings and possible improvements to the existing works. The solutions summarized in this article provide general guidelines for theorists and practitioners to use side channels constructively to achieve designs that are robust against detection and removal. Furthermore, we present an entirely new design of a Trojan side-channel. This architecture demonstrates the potential of a Trojan side-channel that is neatly tailored to the targeted implementation. The new design removes all non-invasive starting points a third party could use to analyze or get access to the secret-channel.

Christof Paar

Papers

One Attack to Rule Them All: Collision Timing Attack versus 42 AES ASIC Cores

Lightweight cryptography and RFID: tackling the hidden overheads

Hyperelliptic curve coprocessors on a FPGA

Toward an FPGA architecture optimized for public-key algorithms

Side channels as building blocks