An efficient scalar multiplication algorithm for ECC in WSNs

Wireless sensor networks facilitate real-time data processing in many applications such as intrusion detection and military surveillance. These applications inherently demand a high level of security. Public key cryptographic techniques such as Elliptic Curve Cryptography (ECC) provide a flexible interface to ensure security, requiring no pre-distribution of keys. However, ECC is very compute-intensive, owing to the computationally complex elliptic curve point multiplication operation. This work presents a technique to speed up the elliptic curve point multiplication operation, achieving a cost reduction of about 48% over the double and add algorithm and about 40% over the width-w Non Adjacent Form (NAF) algorithm. Additionally, results of its software implementation are also presented, simulating the specifications of MEMSIC's wireless sensor network development kit. Finally, we conclude that the timing results obtained from the software implementation conform to the theoretical results.

Wireless Sensor Networks (WSNs), comprising of tiny nodes with limited energy, computational and communication resources, are being widely used in various application areas ranging from pollution and weather monitoring to military. Even though every application may not require data to be exchanged in a secure manner, few WSN applications may have certain security requirements. The data is encrypted by a sender and sent over the wireless links and the same is decrypted at the receiver. To meet this purpose, symmetric key cryptographic (SKC) algorithms may be used. Such SKC primitives require keys to be made available before carrying out the data transfer between the nodes. Alternately, Public Key Cryptographic techniques, such as RSA algorithm can be considered. Even though, RSA is a popular algorithm providing good security level, it is computationally intensive involving large key sizes. The RSA can not be used in WSNs, as the nodes have limited resources. Presently, it is infeasible to implement the RSA algorithm using any of the WSN nodes commercially available. Elliptic curve cryptography (ECC), another public key cryptographic (PKC) algorithm providing same level of security with smaller key size requirements, can be used as an alternative in order to provide security in WSN applications. ECC encryption and decryption use domain parameters, which includes the Generator point to be published. In most of the outdoor WSN applications, the deployment of the nodes is random and the nodes could be captured and an attacker could launch man-in-middle (MIM) attack, and break the public key thereby leading to security breach in the network. A technique to overcome such an attack is proposed in this work and the same is compared with two other similar approaches.

Wireless Sensor Networks (WSN's) are resource constrained networks, demanding energy efficient cryptographic algorithms in order to extend security to them. When compared with the popular RSA algorithm, Elliptic Curve Cryptography (ECC) offers similar level of security with smaller key size requirements. An efficient implementation of ECC heavily relies on the scalar multiplication operation. An efficient method for the elliptic curve point multiplication operation is proposed and its resource requirements are compared with binary and non-adjacent form (NAF) techniques. While comparing these, addition and doubling operations are considered. The proposed scalar multiplication technique makes use of both affine and projective coordinate systems while carrying out addition and doubling operations. The number of computations required to perform these operations is compared and an appropriate coordinate system is chosen for each of the operations.

With hardware support and software optimization, Public Key Cryptography (PKC) has been announced feasible on micro sensors recently [1][2][22][23]. A number of experiments proved that the Elliptic Curve Cryptography (ECC) is more suitable for resource constraint motes compared with RSA [2][3]. But even ECC based protocols still cost too much energy. In this paper, we propose C4W, an identity-based public key infrastructure specially designed for wireless sensor networks (WSNs), in which all nodes can generate others' ECC public keys directly from their identities. Without certificates, no energy will be consumed for certificates communication and verification, which makes C4W especially energy efficient. C4W uses a protocol without certificates to realize mutual authentication and key agreement. Compared with a simplified SSL (SSSL) protocol using an abbreviated certificate, C4W consumes lower than 35% energy, and the communication consumption of C4W is only 28.5% of that consumed by SSSL. Furthermore, the energy analysis of C4W illuminates that the expensive public key computational cost is almost neglectable compared with the heavy communication consumption in a large-scale WSNs, which gives the asymmetric key management in WSNs a bright future.

The elliptic curve cryptography is almost used in the literature to develop the public key cryptosystems. A new general-purpose symmetric key cryptosystem using elliptic prime curves is proposed in this paper. For a given prime number P, there are many elliptic prime curves on which each point in the quadrant (0,0) to (P-1,P-1) lays. The set of minimum number of eligible elliptic prime curves for a given prime number P constitutes a lookup table that is the secret key of the proposed cryptosystem. The sender can pick up one eligible elliptic curve for each 2n-bit plaintext block. The sender sends two integers cipher for each 2n-bit plaintext block with encryption rate = 0.8. Moreover, a small prime number can be used efficiently with high security and good robustness against brute force attack.

Data transfer between components, continuous device monitoring, and other features are possible with an IoT-based energy management system. Due to its lightweight, compact, and expandable characteristics, the Message Queuing Telemetry Transport protocol (MQTT) has recently played an important role in IoT. Since the MQTT protocol cannot provide security between the publishing house and the subscription service, cryptographic techniques can be enforced. This work implements a public-key encryption system-based Elliptic Curve Cryptography (ECC) technique to secure data from Publisher's end to the Subscriber's end. The data from the Raspberry plane is sent to the MQTT publisher with elliptical curve encryption built-in feature. The message/text is converted into cipher text and conveyed through the topic within the MQTT protocol to the subscribed Broker. The subscriber decrypts the cipher text using the elliptical curve cryptography technique with the secret key. This protects data, personal privacy, and safety in a more efficient and convenient way. ECC and MQTT protocols implemented in this work proved to be worthy for both burst mode and continuous data transmissions when compared to the conventional cryptographic techniques.

Wireless sensor networks (WSNs) use sensors to monitor phenomena such as temperature, humidity, groundwater levels and transmit this information to a base station using wireless channels. WSNs find applications in military, ecological, and health-related areas. A hybrid wireless sensor network includes two networks: an ad hoc wireless network and a wireless sensor network. The nodes in the ad hoc network act as base stations conducting surveillance on the WSN. In this dissertation, we focus on the key management issues in hybrid wireless sensor networks. The key management issues in hybrid wireless sensor networks can be divided into three categories according to which layer they affect: ad hoc network layer, wireless sensor network layer, and integrated cross layer. At the ad hoc network layer, we propose two elliptic curve discrete logarithm problem (ECDLP) based schemes for secure group communication (SGC). Unlike the vast majority of secure group communication protocols using the discrete logarithm problem (DLP) based Diffie-Hellman as the basic key agreement protocol, our solutions use the ECDLP-based Diffie-Hellman protocol. We also extend our research on secure group communication to the wireless sensor network layer. We formally define the grouping and secure group communication problems in WSNs. We further propose and evaluate four centralized group rekeying (CGK) schemes for SGC in WSNs. Our proposed key management protocol at the integrated cross layer, mKeying, includes two schemes, a key distribution scheme, KeyDist, supporting multiple base stations in the network, and a centralized key revocation scheme, KeyRev, for removing compromised sensor nodes from the sensor network. Through these protocols for key distribution, key revocation, and group communication, we present an integrated approach to provide security in hybrid wireless sensor networks.

Wireless Sensor Networks (WSNs) are used in many applications in military, environmental, and health-related areas. These applications often include the monitoring of sensitive information such as enemy movement on the battlefield or the location of personnel in a building. Security is important in WSNs. However, WSNs suffer from many constraints, including low computation capability, small memory, limited energy resources, susceptibility to physical capture, and the use of insecure wireless communication channels. These constraints make security in WSNs a challenge. In this paper, we try to explore security issue in WSN. First, the constraints, security requirements and attacks with their corresponding countermeasures in WSNs are explained. Individual sensor nodes are subject to compromised security. An adversary can inject false reports into the networks via compromised nodes. Furthermore, an adversary can create a Gray hole by compromised nodes. If these two kinds of attacks occur simultaneously in a network, some of the existing methods fail to defend against those attacks. The Ad-hoc On Demand Distance (AODV) Vector scheme for detecting Gray-Hole attack and Statistical En-Route Filtering is used for detecting false report. For increasing security level, the Elliptic Curve Cryptography (ECC) algorithm is used. Simulations results obtain so far reduces energy consumption and also provide greater network security to some extent.

A promising direction for constructing cryptographically stable pseudo-random sequence generators is an application of transformations in a group of points of elliptic and hypereliptic curves. This will allow building evidence-stable crypto algorithms, the problem of finding the private key in which is associated with solving a theoretically complex elliptic curve discrete logarithm problem. This paper proposes a method for generating pseudo-random sequences of the maximal period using transformations on elliptic curves. This method consists in the application of recurrent transformations with sequential formation of elements of points group of elliptic curves. This allows providing the maximum period of pseudo-random sequences with the reduction of the problem of finding the private key to the solution of the theoretically complex elliptic curve discrete logarithm problem. The block diagram of the device for generating pseudo-random sequences and the scheme for generating the internal states of the generator are given. We also present the results of statistical testing of some generators, which show that the generated sequences are indistinguishable in a statistical sense from truly random ones.KeywordsPseudo-random sequencesElliptic curvesMaximum period

Elliptic curve cryptosystem (ECC) was proposed by Miller [10] and Koblitz [9] which relies on the difficulty of elliptic curve discrete logarithmic problem (ECDLP). It is gaining wide acceptance as an alternative to the conventional public key cryptosystem such as RSA [24], DSA [25], DH [26]. Also it is noted that the wireless sensor networks (WSN) based on the rapid progress of wireless communications and embedded micro electro mechanical systems technologies are becoming important part in our daily life. The security of the WSN becomes one of the major concerns in its applications. Even ECC prominently offers great potential benefits for WSN security there is still a lot of work needs to be done due to WSN has very restraint running conditions such as limited energy source, capability of computing, etc. It is well known that scalar multiplication operation in ECC accounts for about 80% of key calculation time on wireless sensor network motes. In this paper we present an optimized dynamic window based on our previous research works. The whole quality of service (QoS) has been improved under this algorism in particularly the power consuming is more efficiently. The simulation results showed that the average calculation time, due to fuzzy conditions decreased from previous 26 to current 9 as a whole the calculation time, decreased by approximately 18% in comparison to our previous algorithms in an ECC wireless sensor network [23].

The reach of algebraic curves in cryptography goes far beyond elliptic curve or public key cryptography yet these other application areas have not been systematically covered in the literature. Addressing this gap, Algebraic Curves in Cryptography explores the rich uses of algebraic curves in a range of cryptographic applications, such as secret sh

Elliptic curve cryptography is a public key cryptosystem based on the elliptic curve discrete logarithm problem. The reason for the attractiveness of ECC is that there is no sub-exponential algorithm known to solve the elliptic curve discrete logarithm problem. This leads to lower memory requirements, lower computation requirements and higher security than other public key cryptosystems. This project describes an implementation of a micro coded elliptic curve processor using FPGA technology. This processor implements optimal normal basis field operations. The design is generated by a parameterized module generator which can accommodate arbitrary n and also produce field multipliers with different speed/area tradeoffs. The control part of the processor is micro coded, enabling curve operations to be incorporated into the processor hence reducing the chip's I/O requirements. The micro coded approach also facilitates rapid development and algorithmic optimization. for example, projective and affine coordinates were supported using different sets of micro codes. The design was successfully tested on a Xilinx Spartan -II kit device. Elliptic curve processor is particularly suitable for recourse limited devices because of its lower requirements of memory and computation. It is applicable to be implanted into smart cards, cellular phones and other hand-held devices so that secure communication can be provided. For based on implement the FPGA Using Verilog HDL.

Elliptic curves cryptography was introduced independently by Victor Miller (Miller, 1986) and Neal Koblitz (Koblitz, 1987(Koblitz, ) in 1985. .At that time elliptic curve cryptography was not actually seen as a promising cryptographic technique.As time progress and further research and intensive development done especially on the implementation side, elliptic curve cryptography is now being implemented widely.Elliptic curves cryptography offers smaller key size, bandwidth savings and faster in implementations when compared to the RSA (Rivest-Shamir-Adleman) cryptography which based its security on the integer factorization problem.The most interesting feature of the elliptic curves is the group structure of the points generated by the curves, where points on the elliptic curves form a group.The security of elliptic curves cryptography relies on the elliptic curves discrete logarithm problem.The elliptic curve discrete logarithm problem is analogous to the ordinary algebraic discrete logarithm problem, l = g x , where given the l and g, it is infeasible to compute the x.Elliptic curve discrete logarithm problem deals with solving for n the relation P = nG.Given the point P and the point G, then it is very hard to find the integer n.To implement the discrete logarithm problem in elliptic curve cryptography, the main task is to compute the order of group of the curves or in other words the number of points on the curve.Computation to find the number of points on a curve, has given rise to several point counting algorithms.The Schoof and the SEA (Schoof-Elkies-Atkin) point counting algorithms will be part of the discussion in this chapter.This chapter is organized as follows: Section 2, gives some preliminaries on elliptic curves, and in section 3, elliptic curve discrete logarithm problem is discussed.Some relevant issues on elliptic curve cryptography is discussed in section 4, in which the Diffie-Hellman key exchange scheme, ElGamal elliptic curve cryptosystem and elliptic curve digital signature scheme are discussed here accompanied with some examples.Section 5 discussed the two point counting algorithms, Schoof algorithm and the SEA (Schoof-Elkies-Atkin) algorithm.Following the discussion in section 5, section 6 summaries some similarities and the differences between these two algorithms.Section 7 gives some brief literature on these two point counting algorithms.Finally, section 8 is the concluding remarks for this chapter. Elliptic curvesElliptic curves obtained their name from their relation to elliptic integrals that arise from the computation of the arc length of ellipses (Lawrence & Wade, 2006).Elliptic curves are www.intechopen.com Cryptography and Security in Computing1 1 2 3 4 2 2 4 Fig. 1.1. 2(1 ) (1 ) yx x x   www.intechopen.com

Wireless Sensor Networks (WSN) are becoming an increasingly popular technology for data collection. Since data is of significant importance in the current era, security of the data is essentially indispensable. Because the nodes deployed are usually on an unattended environment, security of the data communicated between the wireless sensor nodes is of utmost importance. A secure established connection between two nodes in a WSN promises a number of preventive measures against different threats but the main issue is to establish the secure connection between any two nodes in a wireless sensor network. With limited resources on a wireless sensor node in mind, this research focuses on establishing Symmetric-Pairwise keys between any two WSN nodes using Public-Key Cryptography (pkc) — which in this case is Elliptic Curve Cryptography.

Elliptic curve cryptography (ECC) is an emerging and efficient cryptography technique which can be applied in various fields of application such as sensor network, network security, authentication, signature verification and in the different applications of the internet of things (IOT). ECC is lightweight, efficient and more secure compare to any other public key cryptography. Different methods have been proposed in the literature to convert input message to elliptic curve point but all of them lack in security, scalability and computationally inefficient for large input size. So, a scalable and computationally efficient algorithm is highly required. In this paper, we propose two different algorithms for input message to elliptic curve point conversion which will reduce communication cost and computational cost of encryption and decryption. The experimental result also shows that the proposed algorithms give better performance and best suitable for large size input text compared to any other existing algorithms.