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」

General-purpose communication systems such as GSM and UMTS have been in the focus of security researchers for over a decade now. Recently also technologies that are only used under more specific circumstances have come into the spotlight of academic research and the hacker scene alike. A striking example of this is recent work [Driessen et al. 2012] that analyzed the security of the over-the-air encryption in the two existing ETSI satphone standards GMR-1 and GMR-2. The firmware of handheld devices was reverse-engineered and the previously unknown stream ciphers A5-GMR-1 and A5-GMR-2 were recovered. In a second step, both ciphers were cryptanalized, resulting in a ciphertext-only attack on A5-GMR-1 and a known-plaintext attack on A5-GMR-2.In this work, we extend the aforementioned results in the following ways: First, we improve the proposed attack on A5-GMR-1 and reduce its average-case complexity from 232 to 221 steps. Second, we implement a practical attack to successfully record communications in the Thuraya network and show that it can be done with moderate effort for approximately d5,000. We describe the implementation of our modified attack and the crucial aspects to make it practical. Using our eavesdropping setup, we recorded 30 seconds of our own satellite-to-satphone communication and show that we are able to recover Thuraya session keys in half an hour (on average). We supplement these results with experiments designed to highlight the feasibility of also eavesdropping on the satphone's emanations.The purpose of this article is threefold: Develop and demonstrate more practical attacks on A5-GMR-1, summarize current research results in the field of GMR-1 and GMR-2 security, and shed light on the amount of work and expertise it takes from setting out to analyze a complex system to actually break it in the real world.

An experimental security analysis of two satphone standards

For classical fault analysis, a transient fault is required to be injected during runtime, e.g., only at a specific round. Instead, Persistent Fault Analysis (PFA) introduces a powerful class of fault attacks that allows for a fault to be present throughout the whole execution. One limitation of original PFA as introduced by Zhang et al. at CHES'18 is that the adversary needs know (or brute-force) the faulty values prior to the analysis. While this was addressed at a follow-up work at CHES'20, the solution is only applicable to a single faulty value. Instead, we use the potency of Statistical Fault Analysis (SFA) in the persistent fault setting, presenting Statistical Persistent Fault Analysis (SPFA) as a more general approach of PFA. As a result, any or even a multitude of unknown faults that cause an exploitable bias in the targeted round can be used to recover the cipher's secret key. Indeed, the undesired faults in the other rounds that occur due the persistent nature of the attack converge to a uniform distribution as required by SFA. We verify the effectiveness of our attack against LED and AES.

SPFA: SFA on Multiple Persistent Faults

The HyperElliptic Curve Cryptosystem (HECC) was quite extensively studied during the recent years. In the open literature one can find results on how to improve the group operations of HECC as well as teh implementations for various types of processors. There have also been some efforts to implement HECC on hardware devices, like for instance FPGAs. Only one of these works, however, deals with the inversion-free formulae to compute the group operations of HECC.

We present inversion-free group operations for the HEC y2 + xy = x5 + f1x + f0 and we target characteristic-two fields. The reason is that of allowing a fair comparison with hardware architectures using the affine case presented in [BBWP04]. In the main part of the paper we use these results to investigate various hardware architectures for a HECC VLSI coprocessor. If area constraints are not considered, scalar multiplication can be performed in 19,769 clock cycles using three field multipliers (of type D = 32), one field adder and one field squarer, where D indicates the digit-size of the multiplier. However, the optimal solution in terms of latency and area uses two multipliers (of type D = 4), one addition and one squaring. The main finding of the present contribution is that coprocessors based on the inversion-free formulae should be preferred compared to those using group operations containing inversion. This holds despite the fact that one field inversion in the affine HECC group operation is traded by up to 24 field multiplications in the inversion-free case.

Performance of HECC coprocessors using inversion-free formulae

A collision timing attack which exploits the data-dependent timing characteristics of combinational circuits is demonstrated. The attack is based on the correlation collision attack presented at CHES 2010, and the timing attributes of combinational circuits when implementing complex functions, e.g., S-boxes, in hardware are exploited by the help of the scheme used in another CHES 2010 paper namely fault sensitivity analysis. Similarly to other side-channel collision attacks, our approach avoids the need for a hypothetical model to recover the secret materials. The results when attacking all 14 AES ASIC cores of the SASEBO LSI chips in three different process technologies, 130nm, 90nm, and 65nm, are presented. Successfully breaking the DPA-protected and the fault attack protected cores indicates the strength of the attack.

/pdf/collision-timing-attack-when-breaking-42-aes-asic-cores-1gkxw1p2qy.pdf

Collision Timing Attack when Breaking 42 AES ASIC Cores.

A design methodology is proposed to implement instructionset extensions for cryptographic processors and hardware accelerators with the aim to improve their potential robustness against Differential Power Analysis (DPA) attacks. The approach has a high-level component that is based on identifying the critical units and functions in a design with respect to DPA resistance, and a gate-level component that is based on implementing the critical units using an inherently DPA-resistant circuit design style. Our methodology can be used to automatically identify and to isolate the DPAcritical nodes, as well as to map them onto a robust cell library that is compatible with conventional deep-submicron CMOS technologies.

Christof Paar

Papers

An experimental security analysis of two satphone standards

SPFA: SFA on Multiple Persistent Faults

Performance of HECC coprocessors using inversion-free formulae

Collision Timing Attack when Breaking 42 AES ASIC Cores.

Design of Low-Power DPA-Resistant Cryptographic Functional Units