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」

The distinct advantage of SRAM-based field programmable gate arrays (FPGA) is their flexibility for configuration changes. However, this opens up the threat of theft of Intellectual Property (IP) since the system configuration is stored in easy-to-access Flash memory. To prevent this, high-end FPGAs have already been extended with symmetric-key decryption engines used to load an encrypted version of the configuration that cannot simply be copied and used without knowledge of the secret key. However, such protection systems based on straightforward use of symmetric cryptography are not well-suited with respect to business and licensing processes, since they are lacking a convenient scheme for key transport and installation. We propose a new protection scheme for the IP of circuits in configuration bit files that provides a significant improvement to the current unsatisfying situation. It uses both public-key and symmetric cryptography, but does not burden FPGAs with the usual overhead of public-key cryptography: While it needs hard-wired symmetric cryptography, the public-key functionality is moved into a temporary configuration bit stream for a one-time setup procedure. This approach requires only very few modifications to current FPGA technology. Using five basic stages, the new protection scheme allows new accounting models for volume licensing of IP, with automated key installation on FPGAs taking place at the customer's site.

/pdf/dynamic-intellectual-property-protection-for-reconfigurable-386v7t3h12.pdf

Dynamic Intellectual Property Protection for Reconfigurable Devices

We present the first simple power analysis (SPA) of software implementations of KeeLoq . Our attack drastically reduces the efforts required for a complete break of remote keyless entry (RKE) systems based on KeeLoq . We analyze implementations of KeeLoq on microcontrollers and exploit timing vulnerabilities to develop an attack that allows for a practical key recovery within seconds of computation time, thereby significantly outperforming all existing attacks: Only one single measurement of a section of a KeeLoq decryption is sufficient to extract the 64 bit master key of commercial products, without the prior knowledge of neither plaintext nor ciphertext. We further introduce techniques for effectively realizing an automatic SPA and a method for circumventing a simple countermeasure, that can also be applied for analyzing other implementations of cryptography on microcontrollers.

Breaking KeeLoq in a Flash: On Extracting Keys at Lightning Speed

It is widely believed that genus four hyperelliptic curve cryptosystems (HECC) are not attractive for practical applications because of their complexity compared to systems based on lower genera, especially elliptic curves. Our contribution shows that for low cost security applications genus-4 hyperelliptic curves (HEC) can outperform genus-2 HEC and that we can achieve a performance similar to genus-3 HEC. Furthermore our implementation results show that a genus-4 HECC is an alternative cryptosystem to systems based on elliptic curves. In the work at hand we present for the first time explicit formulae for genus-4 HEC, resulting in a 60% speed-up compared to the best published results. In addition we implemented genus-4 HECC on a Pentium4 and an ARM microprocessor. Our implementations on the ARM show that for genus four HECC are only a factor of 1.66 slower than genus-2 curves considering group order ≃ 2 190 . For the same group order ECC and genus-3 HECC are about a factor of 2 faster than genus-4 curves on the ARM. The two most surprising results are: 1) for low cost security application, namely considering an underlying group of order 2 128 , HECC with genus 4 outperform genus-2 curves by a factor of 1.46 and has similar performance to genus-3 curves on the ARM and 2) when compared to genus-2 and genus-3, genus-4 HECC are better suited to embedded microprocessors than to general purpose processors.

Low cost security: Explicit formulae for genus-4 hyperelliptic curves

The McEliece public-key cryptosystem is based on the fact that decoding unknown linear binary codes is an NP-complete problem. The interest on implementing post-quantum cryptographic algorithms, e.g. McEliece, on microprocessor-based platforms has been extremely raised due to the increasing storage space of these platforms. Therefore, their vulnerability and robustness against physical attacks, e.g., state-of-the-art power analysis attacks, must be investigated. In this work, we address mainly two power analysis attacks on various implementations of McEliece on an 8-bit AVR microprocessor. To the best of our knowledge, this is the first time that such side-channel attacks are practically evaluated.

Practical power analysis attacks on software implementations of mceliece

This contribution is concerned with the question whether an adversary can automatically manipulate an unknown FPGA bitstream realizing a cryptographic primitive such that the underlying secret key is revealed. In general, if an attacker has full knowledge about the bitstream structure and can make changes to the target FPGA design, she can alter the bitstream leading to key recovery. However, this requires challenging reverse-engineering steps in practice. We argue that this is a major reason why bitstream fault injection attacks have been largely neglected in the past. In this paper, we show that malicious bitstream modifications are i) much easier to conduct than commonly assumed and ii) surprisingly powerful. We introduce a novel class of bitstream fault injection (BiFI) attacks which does not require any reverse-engineering. Our attacks can be automatically mounted without any detailed knowledge about either the bitstream format or the design of the crypto primitive which is being attacked. Bitstream encryption features do not necessarily prevent our attack if the integrity of the encrypted bitstream is not carefully checked. We have successfully verified the feasibility of our attacks in practice by considering several publicly available AES designs. As target platforms, we have conducted our experiments on Spartan-6 and Virtex-5 Xilinx FPGAs.

Christof Paar

Papers

Dynamic Intellectual Property Protection for Reconfigurable Devices

Breaking KeeLoq in a Flash: On Extracting Keys at Lightning Speed

Low cost security: Explicit formulae for genus-4 hyperelliptic curves

Practical power analysis attacks on software implementations of mceliece

Bitstream Fault Injections (BiFI)–Automated Fault Attacks Against SRAM-Based FPGAs