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Efficient implementation of elliptic curves on sensor nodes
Abstract
The deployment of cryptography on sensor networks is a challenging task, given the limited computational power and the resource-constrained nature of the sensoring devices. Because of its lower processing requirement and storage overhead, elliptic curve cryptography has been proposed as an ideal public key system for this scenario. This paper presents an efficient implementation of binary elliptic curves on the MICAz Mote, a common sensor in real-world installations. The implementation focus on the standardized NIST-K163, NIST-B163, NIST-K233 and NIST-B233 curves.
Supplementary resource (1)
... Como resultados obtidos decorrentes desta etapa, pode-se citar os trabalhos [84,85,86] que implementam curvas elípticas em microcontroladores AVR ATmega128 de 8 bits: Os dois primeiros aprimoram o estado-da-arte de implementações de criptografia de curvas elípticas em redes de sensores sem fio. Nós sensores representam um extremo no espectro de arquiteturas modernas, por terem recursos particularmente limitados e natureza descartável. ...
O advento da criptografia assimétrica ou de chave pública possibilitou a aplicação de criptografia em novos cenários, como assinaturas digitais e comércio eletrônico, tornando-a componente vital para o fornecimento de confidencialidade e autenticação em meios de comunicação. Dentre os métodos mais eficientes de criptografia assimétrica, a criptografia de curvas elípticas destaca-se pelos baixos requisitos de armazenamento para chaves e custo computacional para execução. A descoberta relativamente recente da criptografia baseada em emparelhamentos bilineares sobre curvas elípticas permitiu ainda sua flexibilização e a construção de sistemas criptográficos com propriedades inovadoras, como sistemas baseados em identidades e suas variantes. Porém, o custo computacional de criptossistemas baseados em emparelhamentos ainda permanece significativamente maior do que os assimétricos tradicionais, representando um obstáculo para sua adoção, especialmente em dispositivos com recursos limitados.
As contribuições deste trabalho objetivam aprimorar o desempenho de criptossistemas baseados em curvas elípticas e emparelhamentos bilineares e consistem em: (i) implementação eficiente de corpos binários em arquiteturas embarcadas de 8 bits (microcontroladores presentes em sensores sem fio); (ii) formulação eficiente de aritmética em corpos binários para conjuntos vetoriais de arquiteturas de 64 \emph{bits} e famílias mais recentes de processadores Desktop dotadas de suporte nativo à multiplicação em corpos binários; (iii) técnicas para implementação serial e paralela de curvas elípticas binárias e emparelhamentos bilineares simétricos e assimétricos definidos sobre corpos primos ou binários. Estas contribuições permitiram obter significativos ganhos de desempenho e, conseqüentemente, uma série de recordes de velocidade para o cálculo de diversos algoritmos criptográficos relevantes em arquiteturas modernas que vão de sistemas embarcados de 8 bits a processadores com 8 cores.
... Our C language implementation uses RELIC, which stands for "RELIC is an Efficient LIbrary for Cryptography" [30] and was designed for use in constrained devices. This library has been optimized for elliptic curve arith- metic operations [6,40] and is coded in both C and Assembly languages. RELIC is flexible in the sense that users can fine-tune security (e.g., the size of the curves) and performance (e.g., the usage of pre-computation tables) parameters before compilation to the target platform. ...
Despite the continuous growth in the number of smartphones around the globe, Short Message Service (SMS) still remains as one of the most popular, cheap and accessible ways of exchanging text messages using mobile phones. Nevertheless, the lack of security in SMS prevents its wide usage in sensitive contexts such as banking and health-related applications. Aiming to tackle this issue, this paper presents SMSCrypto, a framework for securing SMS-based communications in mobile phones. SMSCrypto encloses a tailored selection of lightweight cryptographic algorithms and protocols, providing encryption, authentication and signature services. The proposed framework is implemented both in Java (target at JVM-enabled platforms) and in C (for constrained SIM Card processors) languages, thus being suitable for a wide range of scenarios. In addition, the signature model adopted does not require an on-line infrastructure and the inherent overhead found in the Public Key Infrastructure (PKI) model, facilitating the development of secure SMS-based applications. We evaluate the proposed framework on a real phone and on SIM Card-comparable microcontroller.
... It was assumed that asymmetric keys require too much communication overhead and processing cost to use in WSNs. Recently though, Elliptic Curve Cryptography has lowered the code and communication overhead required for asymmetric cryptography [9], making it a viable alternative for WSNs. Additionally, through the use of specialized encryption chips, the energy cost of encryption can be significantly lowered [10]. ...
Wireless Sensor Networks are becoming federated and mobile environments. These new capabilities pose a lot of new possibilities and challenges. One of these challenges is to create a secure environment to allow multiple trusted companies to share and merge their sensor network infrastructure. The most basic need for a secure environment is the deployment of key material. However, most current day research assumes pre-shared secrets between the sensor nodes of most, if not all, companies in a federation. These solutions are often not scalable nor mobile enough to meet realistic business requirements. Additionally, most key deployment protocols totally omit any connectivity with back-end infrastructure. This paper proposes a novel deployment protocol for the MAnagement of Secret keYs (MASY). MASY allows secure deployment of a key to a sensor node when it enters a previously unknown network. By off-loading the trust creation process to the resource-rich back-end infrastructure, the burden on the sensor nodes remains very limited.
In this article we present the fastest known implementation of a modular multi- plication for a 160-bit standard compliant elliptic curve (secp160r1) for 8-bit micro controller which are typically used in WSNs. The major part (77%) of the processing time for an elliptic curve operation such as ECDSA or EC Diffie-Hellman is spent on modular multiplication. We present an optimized arithmetic algorithm which significantly speed up ECC schemes. The reduced processing time also yields a significantly lower energy consumption of ECC schemes. With our implementation results we can show that a 160-bit modular multiplication can be performed in 0.39 ms on an 8-bit AVR processor clocked at 7.37 MHz. This brings the vision of asymmetric cryptography in the field of WSNs with all its benefits for key-distribution and authentication a step closer to reality.
This paper describes an algorithm for computing elliptic scalar multiplications on non-supersingular elliptic curves defined
over GF(2m). The algorithm is an optimized version of a method described in [1], which is based on Montgomery’s method [8]. Our algorithm is easy to implement in both hardware and software, works for any elliptic curve over GF(2m), requires no precomputed multiples of a point, and is faster on average than the addition-subtraction method described in
draft standard IEEE P1363. In addition, the method requires less memory than projective schemes and the amount of computation
needed for a scalar multiplication is fixed for all multipliers of the same binary length. Therefore, the improved method
possesses many desirable features for implementing elliptic curves in restricted environments.
In this paper we describe an efficient algorithm for multiplication in F2m, where the field elements of F2m are represented in standard polynomial basis. The proposed algorithm can be used in practical software implementations of
elliptic curve cryptography. Our timing results, on several platforms, show that the new method is significantly faster than
the “shift-and-add” method
- A Jerome
Jerome A. Solinas. Efficient Arithmetic on Koblitz Curves.
Designs, Codes and Cryptography, 19(2-3):195-249,
2000.