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

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 Simon and Speck families of block ciphers were designed specifically to offer security on constrained devices, where simplicity of design is crucial. However, the intended use cases are diverse and demand flexibility in implementation. Simplicity, security, and flexibility are ever-present yet conflicting goals in cryptographic design. This paper outlines how these goals were balanced in the design of Simon and Speck.

The SIMON and SPECK lightweight block ciphers

At IEEE Security & Privacy 2015, Bos, Costello, Naehrig, and Stebila proposed an instantiation of Peikert's ring-learning-with-errors-based (Ring-LWE) key-exchange protocol (PQCrypto 2014), together with an implementation integrated into OpenSSL, with the affirmed goal of providing post-quantum security for TLS. In this work we revisit their instantiation and stand-alone implementation. Specifically, we propose new parameters and a better suited error distribution, analyze the scheme's hardness against attacks by quantum computers in a conservative way, introduce a new and more efficient error-reconciliation mechanism, and propose a defense against backdoors and all-for-the-price-of-one attacks. By these measures and for the same lattice dimension, we more than double the security parameter, halve the communication overhead, and speed up computation by more than a factor of 8 in a portable C implementation and by more than a factor of 27 in an optimized implementation targeting current Intel CPUs. These speedups are achieved with comprehensive protection against timing attacks.

/pdf/post-quantum-key-exchange-a-new-hope-3pmodym9j1.pdf

Post-quantum key exchange: a new hope

The market for RFID technology has grown rapidly over the past few years. Going along with the proliferation of RFID technology is an increasing demand for secure and privacy-preserving applications. In this context, RFID tags need to be protected against physical attacks such as Differential Power Analysis (DPA) and fault attacks. The main obstacles towards secure RFID are the extreme constraints of passive tags in terms of power consumption and silicon area, which makes the integration of countermeasures against physical attacks even more difficult than for other types of embedded systems. In this paper we propose a fresh re-keying scheme that is especially suited for challenge-response protocols such as used to authenticate tags. We evaluate the resistance of our scheme against fault and side-channel analysis, and introduce a simple architecture for VLSI implementation. In addition, we estimate the cost of our scheme in terms of area and execution time for various security/performance trade-offs. Our experimental results show that the proposed re-keying scheme provides better security (and does so at less cost) than state-of-the-art countermeasures.

/pdf/fresh-re-keying-security-against-side-channel-and-fault-12c6zf5m73.pdf

Fresh re-keying: security against side-channel and fault attacks for low-cost devices

In this paper we introduce an open framework for the benchmarking of lightweight block ciphers on a multitude of embedded platforms. Our framework is able to evaluate execution time, RAM footprint, as well as (binary) code size, and allows a user to define a custom “figure of merit” according to which all evaluated candidates can be ranked. We used the framework to benchmark various implementations of 13 lightweight ciphers, namely AES, Fantomas, HIGHT, LBlock, LED, Piccolo, PRESENT, PRINCE, RC5, Robin, Simon, Speck, and TWINE, on three different platforms: 8-bit ATmega, 16-bit MSP430, and 32-bit ARM. Our results give new insights to the question of how well these ciphers are suited to secure the Internet of Things (IoT). The benchmarking framework provides cipher designers with a tool to compare new algorithms with the state-of-the-art and allows standardization bodies to conduct a fair and comprehensive evaluation of a large number of candidates.

/pdf/triathlon-of-lightweight-block-ciphers-for-the-internet-of-1nqcnibfi0.pdf

Triathlon of Lightweight Block Ciphers for the Internet of Things.

Secure communication over public networks like the Internet requires the use of cryptographic algorithms as basic building blocks. Most cryptographic workloads pose a considerable burden on devices like PDAs, cell phones, and sensor nodes, which are limited in processing power, memory and energy. In this paper we present an approach to increase the efficiency of 32-bit processors for handling symmetric cryptographic algorithms with the help of instruction set extensions. We propose a number of custom instructions to support the Advanced Encryption Standard (AES). Using the SPARC V8-compatible Leon2 embedded processor, we evaluate the effects of the extensions on performance and code size of AES, as well as on silicon area. With a moderate increase in silicon area, AES performance can be improved by a factor of nearly 10, while code size is reduced significantly and implementation flexibility is retained. We also show that our approach is very beneficial for implementation in superscalar processors and that it can compete with the performance of previously proposed cryptographic processors and instruction set extensions.

/pdf/instruction-set-extensions-for-efficient-aes-implementation-6czy91qjko.pdf

Instruction set extensions for efficient AES implementation on 32-bit processors

In this paper, we introduce a framework for the benchmarking of lightweight block ciphers on a multitude of embedded platforms Our framework is able to evaluate the execution time, RAM footprint, as well as binary code size, and allows one to define a custom “figure of merit” according to which all evaluated candidates can be ranked We used the framework to benchmark implementations of 19 lightweight ciphers, namely AES, Chaskey, Fantomas, HIGHT, LBlock, LEA, LED, Piccolo, PRESENT, PRIDE, PRINCE, RC5, RECTANGLE, RoadRunneR, Robin, Simon, SPARX, Speck, and TWINE, on three microcontroller platforms: 8-bit AVR, 16-bit MSP430, and 32-bit ARM Our results bring some new insights into the question of how well these lightweight ciphers are suited to secure the Internet of things The benchmarking framework provides cipher designers with an easy-to-use tool to compare new algorithms with the state of the art and allows standardization organizations to conduct a fair and consistent evaluation of a large number of candidates

/pdf/triathlon-of-lightweight-block-ciphers-for-the-internet-of-3zoj5ur11f.pdf

Triathlon of Lightweight Block Ciphers for the Internet of Things

We present, for the first time, a general strategy for designing ARX symmetric-key primitives with provable resistance against single-trail differential and linear cryptanalysis. The latter has been a long standing open problem in the area of ARX design. The wide-trail design strategy (WTS), that is at the basis of many S-box based ciphers, including the AES, is not suitable for ARX designs due to the lack of S-boxes in the latter. In this paper we address the mentioned limitation by proposing the long trail design strategy (LTS) – a dual of the WTS that is applicable (but not limited) to ARX constructions. In contrast to the WTS, that prescribes the use of small and efficient S-boxes at the expense of heavy linear layers with strong mixing properties, the LTS advocates the use of large (ARX-based) S-Boxes together with sparse linear layers. With the help of the so-called long-trail argument, a designer can bound the maximum differential and linear probabilities for any number of rounds of a cipher built according to the LTS.

/pdf/design-strategies-for-arx-with-provable-bounds-sparx-and-lax-4nnqtmveuh.pdf

Johann Großschädl

Papers

Fresh re-keying: security against side-channel and fault attacks for low-cost devices

Triathlon of Lightweight Block Ciphers for the Internet of Things.

Instruction set extensions for efficient AES implementation on 32-bit processors

Triathlon of Lightweight Block Ciphers for the Internet of Things

Design Strategies for ARX with Provable Bounds: Sparx and LAX