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

Strong public-key cryptography is often considered to be too computationally expensive for small devices if not accelerated by cryptographic hardware. We revisited this statement and implemented elliptic curve point multiplication for 160-bit, 192-bit, and 224-bit NIST/SECG curves over GF(p) and RSA-1024 and RSA-2048 on two 8-bit microcontrollers. To accelerate multiple-precision multiplication, we propose a new algorithm to reduce the number of memory accesses. Implementation and analysis led to three observations: 1. Public-key cryptography is viable on small devices without hardware acceleration. On an Atmel ATmega128 at 8 MHz we measured 0.81s for 160-bit ECC point multiplication and 0.43s for a RSA-1024 operation with exponent e = 2 16 +1. 2. The relative performance advantage of ECC point multiplication over RSA modular exponentiation increases with the decrease in processor word size and the increase in key size. 3. Elliptic curves over fields using pseudo-Mersenne primes as standardized by NIST and SECG allow for high performance implementations and show no performance disadvantage over optimal extension fields or prime fields selected specifically for a particular processor architecture.

Comparing elliptic curve cryptography and RSA on 8-bit CPUs

Strong public-key cryptography is often considered to be too computationally expensive for small devices if not accelerated by cryptographic hardware. We revisited this statement and implemented elliptic curve point multiplication for 160-bit, 192-bit, and 224-bit NIST/SECG curves over GF(p) and RSA-1024 and RSA-2048 on two 8-bit microcontrollers. To accelerate multiple-precision multiplication, we propose a new algorithm to reduce the number of memory accesses.

/pdf/comparing-elliptic-curve-cryptography-and-rsa-on-8-bit-cpus-25yrgr22sg.pdf

Comparing Elliptic Curve Cryptography and RSA on 8-Bit CPUs

Internet of Things (IoT) is playing a more and more important role after its showing up, it covers from traditional equipment to general household objects such as WSNs and RFID. With the great potential of IoT, there come all kinds of challenges. This paper focuses on the security problems among all other challenges. As IoT is built on the basis of the Internet, security problems of the Internet will also show up in IoT. And as IoT contains three layers: perception layer, transportation layer and application layer, this paper will analyze the security problems of each layer separately and try to find new problems and solutions. This paper also analyzes the cross-layer heterogeneous integration issues and security issues in detail and discusses the security issues of IoT as a whole and tries to find solutions to them. In the end, this paper compares security issues between IoT and traditional network, and discusses opening security issues of IoT.

https://csi.dgist.ac.kr/uploads/Seminar/1407_IoT_SSH.pdf

Security of the Internet of Things: perspectives and challenges

In this paper, we quantify the energy cost of authentication and key exchange based on public-key cryptography on an 8-bit microcontroller platform. We present a comparison of two public-key algorithms, RSA and elliptic curve cryptography (ECC), and consider mutual authentication and key exchange between two untrusted parties such as two nodes in a wireless sensor network. Our measurements on an Atmel ATmega128L low-power microcontroller indicate that public-key cryptography is very viable on 8-bit energy-constrained platforms even if implemented in software. We found ECC to have a significant advantage over RSA as it reduces computation time and also the amount of data transmitted and stored.

Energy analysis of public-key cryptography for wireless sensor networks

Sizzle: A standards-based end-to-end security architecture for the embedded Internet

Since its proposal by Victor Miller [17] and Neal Koblitz [15] in the mid 1980s, Elliptic Curve Cryptography (ECC) has evolved into a mature public-key cryptosystem. Offering the smallest key size and the highest strength per bit, its computational efficiency can benefit both client devices and server machines. We have designed a programmable hardware accelerator to speed up point multiplication for elliptic curves over binary polynomial fields GF(2m). The accelerator is based on a scalable architecture capable of handling curves of arbitrary field degrees up to m = 255. In addition, it delivers optimized performance for a set of commonly used curves through hard-wired reduction logic. A prototype implementation running in a Xilinx XCV2000E FPGA at 66.4 MHz shows a performance of 6987 point multiplications per second for GF(2163). We have integrated ECC into OpenSSL, today's dominant implementation of the secure Internet protocol SSL, and tested it with the Apache web server and open-source web browsers.

/pdf/an-end-to-end-systems-approach-to-elliptic-curve-2ou87ucasp.pdf

Sheueling Chang Shantz

Papers

Comparing elliptic curve cryptography and RSA on 8-bit CPUs

Comparing Elliptic Curve Cryptography and RSA on 8-Bit CPUs

Energy analysis of public-key cryptography for wireless sensor networks

Sizzle: A standards-based end-to-end security architecture for the embedded Internet

An End-to-End Systems Approach to Elliptic Curve Cryptography