A Survey of Fast Scalar Multiplication on Elliptic Curve Cryptography for Lightweight Embedded Devices

Elliptic curve cryptography (ECC) is one of the most famous asymmetric cryptographic schemes which offers the same level of security with much shorter keys than the other widely used asymmetric cryptographic algorithm, Rivest, Shamir, and Adleman (RSA). In ECC, the main and most heavily used operation is the scalar multiplication kP, where the scalar value k is a private integer and must be secured. Various methods for fast scalar multiplication are based on the binary/ternary representation of the scalar. In this chapter, we present various methods to make fast scalar multiplication on ECC over prime field for lightweight embedded devices like wireless sensor network (WSN) and Internet of Things (IoT)

Cryptographic Key Distribution In Wireless Sensor Networks Using Bilinear Pairings

It is envisaged that the use of cheap and tiny wireless sensors will soon bring a third wave of evolution in computing systems. Billions of wireless senor nodes will provide a bridge between information systems and the physical world. Wireless nodes deployed around the globe will monitor the surrounding environment as well as gather information about the people therein. It is clear that this revolution will put security solutions to a great test. Wireless Sensor Networks (WSNs) are a challenging environment for applying security services. They differ in many aspects from traditional fixed networks, and standard cryptographic solutions cannot be used in this application space. Despite many research efforts, key distribution in WSNs still remains an open problem. Many of the proposed schemes suffer from high communication overhead and storage costs, low scalability and poor resilience against different types of attacks. The exclusive usage of simple and energy efficient symmetric cryptography primitives does not solve the security problem. On the other hand a full public key infrastructure which uses asymmetric techniques, digital signatures and certificate authorities seems to be far too complex for a constrained WSN environment. This thesis investigates a new approach to WSN security which addresses many of the shortcomings of existing mechanisms. It presents a detailed description on how to provide practical Public Key Cryptography solutions for wireless sensor networks. The contributions to the state-of-the-art are added on all levels of development beginning with the basic arithmetic operations and finishing with complete security protocols. This work includes a survey of different key distribution protocols that have been developed for WSNs, with an evaluation of their limitations. It also proposes Identity- Based Cryptography (IBC) as an ideal technique for key distribution in sensor networks. It presents the first in-depth study of the application and implementation of Pairing- Based Cryptography (PBC) to WSNs. This is followed by a presentation of the state of the art on the software implementation of Elliptic Curve Cryptography (ECC) on typical WSNplatforms. New optimized algorithms for performing multiprecision multiplication on a broad range of low-end CPUs are introduced as well. Three novel protocols for key distribution are proposed in this thesis. Two of these are intended for non-interactive key exchange in flat and clustered networks respectively. A third key distribution protocol uses Identity-Based Encryption (IBE) to secure communication within a heterogeneous sensor network. This thesis includes also a comprehensive security evaluation that shows that proposed schemes are resistant to various attacks that are specific to WSNs. This work shows that by using the newest achievements in cryptography like pairings and IBC it is possible to deliver affordable public-key cryptographic solutions and to apply a sufficient level of security for the most demanding WSN applications

Efficient and Secure ECDSA Algorithm and its Applications: A Survey

Public-key cryptography algorithms, especially elliptic curve cryptography (ECC)and elliptic curve digital signature algorithm (ECDSA) have been attracting attention frommany researchers in different institutions because these algorithms provide security andhigh performance when being used in many areas such as electronic-healthcare, electronicbanking,electronic-commerce, electronic-vehicular, and electronic-governance. These algorithmsheighten security against various attacks and the same time improve performanceto obtain efficiencies (time, memory, reduced computation complexity, and energy saving)in an environment of constrained source and large systems. This paper presents detailedand a comprehensive survey of an update of the ECDSA algorithm in terms of performance,security, and applications

Fast Scalar Multiplication on Elliptic Curve Cryptography in Selected Intervals Suitable For Wireless Sensor Networks

International audienceIn Wireless Sensor Networks (WSNs), providing a robust security mechanism with limited energy resources is very challenging because of sensor node's limited resources (computation, bandwidth, memory). Asymmetric-key can fulfill the requirement, but if the number of nodes is large, symmetric-key cryptography is the best natural method because of its scalability. Asymmetric-key cryptography is power-hungry; nevertheless, Elliptic Curve Cryptosystems (ECC) are feasible and more flexible for sensor nodes. Scalar multiplication is the most widely used operation on ECC. Various methods for fast scalar multiplication exist, but they are based on the binary/ternary representation of the scalar. In this paper, we present a novel technique to make fast scalar multiplication on Elliptic Curve Cryptosystems over prime field for light-weight embedded devices like sensor nodes. Our method significantly reduces the computation of scalar multiplication by an equivalent representation of points based on point order in a given interval. Since our technique can act as a support for most existing methods, after an analytical and efficiency analysis, we implement and evaluate its performance in different scenari

Implementation of ECC on FPGA using Scalable Architecture With equal Data and Key for WSN

Security of data transferred on the Wireless Sensor Network is of vital importance. In public key cryptography RSA algorithm has been used for a long time, but it does not meet the constraints of WSNs. Elliptic Curve Cryptography(ECC) has been employed recently because of its highest security for same length bit. ECC point multiplication operation is time consuming which affects the speed of encryption and decryption of data. Security in WSNs is addressed in our work, where a modified ECC is designed by performing the point multiplication using Montgomery multiplication technique that achieves considerable speed and with reduced area utilization. The ECC is first simulated on different FPGA devices, with key length 11, 112, 131 and 163 bits and the area-speed tradeoff is compared. ECC algorithm is implemented with software and hardware choosing Artix 7 XC7a100t-3csg324 FPGA which supports key lengths of 11, 112, 131 and 163 bits. When implemented on a Artix 7 FPGA, it completes 163 bit data encryption operation over GF(2163 ) in 1ms with the maximum frequency of 229MHz. The ECC algorithm is reconfigurable with low level to high level security with different bit key sizes. The proposed ECC algorithm modeled using VHDL and synthesized on Spartan 3 and 6, Virtex 4, 5 and 6 and Artix7 before the hardware implementation on Atrix 7. The design satisfies the needs of resource constrained devices by decreasing the encryption and decryption time to 1 ms with equal keylength and datasize, while device utilization is within 13%

Efficient software implementation of elliptic curves and bilinear pairings

Orientador: Júlio César Lopez HernándezTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: 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 embutidas de 8 bits (microcontroladores presentes em sensores sem fio); (ii) formulação eficiente de aritmética em corpos binários para conjuntos vetoriais de arquiteturas de 64 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 coresAbstract: The development of asymmetric or public key cryptography made possible new applications of cryptography such as digital signatures and electronic commerce. Cryptography is now a vital component for providing confidentiality and authentication in communication infra-structures. Elliptic Curve Cryptography is among the most efficient public-key methods because of its low storage and computational requirements. The relatively recent advent of Pairing-Based Cryptography allowed the further construction of flexible and innovative cryptographic solutions like Identity-Based Cryptography and variants. However, the computational cost of pairing-based cryptosystems remains significantly higher than traditional public key cryptosystems and thus an important obstacle for adoption, specially in resource-constrained devices. The main contributions of this work aim to improve the performance of curve-based cryptosystems, consisting of: (i) efficient implementation of binary fields in 8-bit microcontrollers embedded in sensor network nodes; (ii) efficient formulation of binary field arithmetic in terms of vector instructions present in 64-bit architectures, and on the recently-introduced native support for binary field multiplication in the latest Intel microarchitecture families; (iii) techniques for serial and parallel implementation of binary elliptic curves and symmetric and asymmetric pairings defined over prime and binary fields. These contributions produced important performance improvements and, consequently, several speed records for computing relevant cryptographic algorithms in modern computer architectures ranging from embedded 8-bit microcontrollers to 8-core processorsDoutoradoCiência da ComputaçãoDoutor em Ciência da Computaçã