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」

This paper presents new speed records for 128-bit secure elliptic-curve Diffie---Hellman key-exchange software on three different popular microcontroller architectures. We consider a 255-bit curve proposed by Bernstein known as Curve25519, which has also been adopted by the IETF. We optimize the X25519 key-exchange protocol proposed by Bernstein in 2006 for AVR ATmega 8-bit microcontrollers, MSP430X 16-bit microcontrollers, and for ARM Cortex-M0 32-bit microcontrollers. Our software for the AVR takes only 13,900,397 cycles for the computation of a Diffie---Hellman shared secret, and is the first to perform this computation in less than a second if clocked at 16 MHz for a security level of 128 bits. Our MSP430X software computes a shared secret in 5,301,792 cycles on MSP430X microcontrollers that have a 32-bit hardware multiplier and in 7,933,296 cycles on MSP430X microcontrollers that have a 16-bit multiplier. It thus outperforms previous constant-time ECDH software at the 128-bit security level on the MSP430X by more than a factor of 1.2 and 1.15, respectively. Our implementation on the Cortex-M0 runs in only 3,589,850 cycles and outperforms previous 128-bit secure ECDH software by a factor of 3.

/pdf/high-speed-curve25519-on-8-bit-16-bit-and-32-bit-44gp8mlns4.pdf

High-speed Curve25519 on 8-bit, 16-bit, and 32-bit microcontrollers

For most of the time since they were proposed, it was widely believed that hyperelliptic curve cryptosystems (HECC) carry a substantial performance penalty compared to elliptic curve cryptosystems (ECC) and are, thus, not too attractive for practical applications. Only quite recently improvements have been made, mainly restricted to curves of genus 2. The work at hand advances the state-of-the-art considerably in several aspects. First, we generalize and improve the closed formulae for the group operation of genus 3 for HEC defined over fields of characteristic two. For certain curves we achieve over 50% complexity improvement compared to the best previously published results. Second, we introduce a new complexity metric for ECC and HECC defined over characteristic two fields which allow performance comparisons of practical relevance. It can be shown that the HECC performance is in the range of the performance of an ECC; for specific parameters HECC can even possess a lower complexity than an ECC at the same security level. Third, we describe the first implementation of a HEC cryptosystem on an embedded (ARM7) processor. Since HEC are particularly attractive for constrained environments, such a case study should be of relevance.

/pdf/hyperelliptic-curve-cryptosystems-closing-the-performance-2agm5edwke.pdf

Hyperelliptic Curve Cryptosystems: Closing the Performance Gap to Elliptic Curves

In order to protect FPGA designs against IP theft and related issues such as product cloning, all major FPGA manufacturers offer a mechanism to encrypt the bitstream used to configure the FPGA. From a mathematical point of view, the employed encryption algorithms, e.g., AES or 3DES, are highly secure. However, recently it has been shown that the bitstream encryption feature of several FPGA product lines is susceptible to side-channel attacks that monitor the power consumption of the cryptographic module. In this paper, we present the first successful attack on the bitstream encryption of the Altera Stratix II FPGA. To this end, we reverse-engineered the details of the proprietary and unpublished Stratix II bitstream encryption scheme from the Quartus II software. Using this knowledge, we demonstrate that the full 128-bit AES key of a Stratix II can be recovered by means of side-channel analysis with 30,000 measurements, which can be acquired in less than three hours. The complete bitstream of a Stratix II that is (seemingly) protected by the bitstream encryption feature can hence fall into the hands of a competitor or criminal - possibly implying system-wide damage if confidential information such as proprietary encryption schemes or keys programmed into the FPGA are extracted. In addition to lost IP, reprogramming the attacked FPGA with modified code, for instance, to secretly plant a hardware trojan, is a particularly dangerous scenario for many security-critical applications.

Side-channel attacks on the bitstream encryption mechanism of Altera Stratix II: facilitating black-box analysis using software reverse-engineering

This paper presents a side-channel analysis of the bitstream encryption mechanism provided by Xilinx Virtex FPGAs. This work covers our results analyzing the Virtex-4 and Virtex-5 family showing that the encryption mechanism can be completely broken with moderate effort. The presented results provide an overview of a practical real-world analysis and should help practitioners to judge the necessity to implement side-channel countermeasures. We demonstrate sophisticated attacks on off-the-shelf FPGAs that go far beyond schoolbook attacks on 8-bit AES S-boxes. We were able to perform the key extraction by using only the measurements of a single power-up. Access to the key enables cloning and manipulating a design, which has been encrypted to protect the intellectual property and to prevent fraud. As a consequence, the target product faces serious threats like IP theft and more advanced attacks such as reverse engineering or the introduction of hardware Trojans. To the best of our knowledge, this is the first successful attack against the bitstream encryption of Xilinx Virtex-4 and Virtex-5 reported in open literature.

Black-Box side-channel attacks highlight the importance of countermeasures: an analysis of the xilinx virtex-4 and virtex-5 bitstream encryption mechanism

The authors propose a new block cipher, DESL (DES lightweight extension), which is strong, compact and efficient. Due to its low area constraints DESL is especially suited for RFID (radiofrequency identification) devices. DESL is based on the classical DES (data encryption standard) design, however, unlike DES it uses a single S-box repeated eight times. This approach makes it possible to considerably decrease chip size requirements. The S-box has been highly optimized in such a way that DESL resists common attacks, i.e., linear and differential cryptanalysis, and the Davies-Murphy-attack. Therefore DESL achieves a security level which is appropriate for many applications. Furthermore, we propose a light-weight implementation of DESL which requires 45% less chip size and 86% less clock cycles than the best AES implementations with regard to RFID applications. Compared to the smallest DES implementation published, our DESL design requires 38% less transistors. Our 0.18mum DESL implementation requires a chip size of 7392 transistors (1848 gate equivalences) and is capable to encrypt a 64-bit plaintext in 144 clock cycles. When clocked at 100 kHz, it draws an average current of only 0.89muA. These hardware figures are in the range of the best eSTREAM streamcipher candidates, comprising DESL as a new alternative for ultra low-cost encryption

Christof Paar

Papers

High-speed Curve25519 on 8-bit, 16-bit, and 32-bit microcontrollers

Hyperelliptic Curve Cryptosystems: Closing the Performance Gap to Elliptic Curves

Side-channel attacks on the bitstream encryption mechanism of Altera Stratix II: facilitating black-box analysis using software reverse-engineering

Black-Box side-channel attacks highlight the importance of countermeasures: an analysis of the xilinx virtex-4 and virtex-5 bitstream encryption mechanism

New Light-Weight Crypto Algorithms for RFID