An Efficient and Authentication Signcryption Scheme Based on Elliptic Curves

The signcryption is a relatively new cryptographic technique that is supposed to fulfill the functionalities of encryption and digital signature in a single logical step. Several signcryption schemes are proposed throughout the years, each of them having its own problems and limitations. In this paper, the security of a recent signcryption scheme, i.e. Hwang et al.'s scheme is analyzed, and it is proved that it involves several security flaws and shortcomings. Several devastating attacks are also introduced to the mentioned scheme whereby it fails all the desired and essential security attributes of a signcryption scheme.

With ever growing popularity, wireless communication system also vulnerable to various security attacks. To provide high level security, many cryptographic solutions have been proposed. One such solution is signcryption, where authenticity and confidentiality provided by single logical step. Therefore, signcryption scheme helps to reduce computational cost, but it is not feasible for resource constraint environments. Because, most of the existing approaches were based on El-Gamal, bilinear pairing, Rivest-Shamir-Adleman (RSA), and Elliptic curve Cryptography (ECC). They consume more energy due to their increased key size. Hence, the new signcryption approach is proposed based on Hyper Elliptic Curve Cryptosystem (HECC) whose key size is much lesser than ECC. It significantly reduces the cost of computation and communication overhead by half the amount of ECC which suits well for resource constraint environments. Further, the proposed scheme attains necessary security features along with forward secrecy and public verifiability. On the other hand, the security of the approach is validated through an automated protocol validation tool – AVISPA.

Signcryption is a cryptographic method that fulfills both the functions of secure encryption and digital signature with less cost.To transmit secure and authenticated message in wireless sensor networks,an efficient signcryption scheme with forward secrecy based on elliptic curve,which was presented by HWANG,was modified and it was implemented in TinyOS,which is called TinySignCrypt.Compared with other schemes,the experimental results in the MICA2 platform show TinySignCrypt has better performance in terms of communication and computation load.

Signcryption is a cryptographic technique that provides both confidentiality and authenticity of data during public transmission in many modern applications like Internet -of -Things (IoT), Wireless Sensor Networks (WSNs) etc. The functionalities of encryption and Signature can achieve simultaneously through the signcryption with lower computational cost and communication overheads than those of traditional sign-then-encrypt approach. Many signcryption schemes have been constructed by various researchers in different cryptographic frameworks. Certificateless cryptography is one of the recent public key cryptography which eliminates the key escrow problem and complex certificate management problemsin identity based cryptography and traditional public key cryptography respectively. Providing the security and efficiency in many modern applications including IoT and WSNs is a crucial task. In this paper, we proposed new signcryption scheme in certificateless cryptography. This scheme supports the property of public verifiability and is secure against various types of adversaries in the random oracle model with the assumption that the Computational Diffie-Hellman Problem (CDHP) and the Elliptic Curve Discrete Logarithmic Problems (ECDLP) are hard. Due to pairing-free environment the proposed scheme is computationally more efficient than the existing public verifiable signcryption schemes.

An addition law for an elliptic curve is complete if it is defined for all possible pairs of input points on the elliptic curve. In Elliptic Curve Cryptography (ECC), a complete addition law provides a natural protection against side-channel attacks which are based on Simple Power Analysis (SPA). Montgomery curves are a specific family of elliptic curves that play a crucial role in ECC because of its well-known Montgomery ladder, particularly in the Elliptic Curve Diffie-Hellman Key Exchange (ECDHKE) protocol and the Elliptic Curve factorization Method (ECM). However, the complete addition law for Montgomery curves, as stated in the literature, has a computational cost of 14M+ 2D, where M,D denote the costs of a field multiplication and a field multiplication by a constant, respectively. The lack of a competitive complete addition law has led implementers towards twisted Edwards curves, which offer a complete addition law at a lower cost of 8M+ 1D for appropriately chosen curve constants.In this paper, we introduce extended Montgomery coordinates as a novel representation for points on Montgomery curves. This coordinate system enables us to define birational multiplication-free maps between the extended twisted Edwards coordinates and extended Montgomery coordinates. Using this map, we can transfer the complete addition laws from twisted Edwards curves to Montgomery curves without incurring additional multiplications or squarings. In addition, we employ a technique known as scaling to refine the addition laws for twisted Edwards curves, which results in having i) Complete addition laws with the costs varying between 8M+1D and 9M+1D for a broader range of twisted Edwards curves, ii) Incomplete addition laws for twisted Edwards curves with the cost of 8M. Consequently, by leveraging our birational multiplication-free maps, we present complete addition laws for Montgomery curves with the cost of 8M+1D. This shows a significant improvement for complete addition law for Montgomery curves by reducing the computational cost by 6M+ 1D. This improvement makes Montgomery curves a more attractive option for applications where an efficient complete addition law is essential.

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

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

Signcryption schemes offer the possibility to simultaneously sign and encrypt a message.In order to guarantee the authentication of both signer and receiver in the most efficient way during the signcryption, certificate based solutions have been proposed in literature.We first compare into detail three recently proposed certificate based signcryption systems relying on the elliptic curve discrete logarithm problem and without the usage of compute intensive pairing operations.Next, we demonstrate how the performance of these certificate based systems can be improved by using the Elliptic Curve Qu Vanstone (ECQV) implicit certificates.What is more, generalized signcryption schemes are easily derived from these schemes and the anonymity feature of sender and receiver is already inherently included or can be very efficiently obtained without a significant additional cost.

A Signcryption proposed by Yuliang Zheng in 1997 is a hybrid public key primitive that combines a digital signature and an encryption. It provides more efficient method than a straightforward composition of a signature scheme with an encryption scheme. In a mobile communication environment, the authenticated key agreement protocol should be designed to have lower computational complexity and memory requirements. Therefore, in this paper, our proposed method that efficient authenticated key exchange protocol using Signcryption scheme and based on EC using Signcryption in mobile and wireless network. And we analyze computational cost and security requirements of proposed protocol.

Blind signcryption schemes are the extension of signcryption schemes. They are used to protect the privacy and identity of the sender from other users, especially in electronic voting and electronic cash payment systems. A number of blind signcryption schemes are introduced over the years and some of them are proved to be insecure. In this Letter, the authors analysed a recently proposed blind signcryption scheme based on elliptic curves and proved it is insecure. Their analysis showed that the proposed scheme is unable to provide the claimed security attributes of message integrity, authentication, unforgeability, and signer non‐repudiation. After successful cryptanalysis, they introduced a modified version of this scheme to overcome the security flaws and weakness.

Signcryption was first proposed by Zheng and there after several signcryption schemes have been formulated. The broadcast scheme for Zheng does not offer non repudiation using public verification. A latest research by Elkamchouchi et. al proposed a new signcryption scheme for the broadcast environment. The scheme is known as Signcryption Multiple-Recipients Variant (SMRV). From the detail analysis of the scheme, it is observed that confidentiality of the information is lost when the parameters are sent to the third party for verification. Thus the scheme violates the basic property of security. Upon further analysis it is seen that the computational cost of the scheme can be reduced by eliminating few unnecessary steps which do not strengthen the security of the scheme but introduces an extra computational cost. In this paper an efficient and improved signcryption scheme for the broadcast environment is presented. The presented scheme is more efficient than Zheng's and Elkamchouchi et. al scheme in terms of computational cost. The scheme offers non repudiation through public verification and confidentiality of the information is also ensured.

An efficient CPPA scheme for intelligent transportation networks

In this paper, a Modular Fractional Chaotic Sine Map (MFC-SM) has been introduced to achieve high Lyapunov exponent values and completely chaotic behavior of the bifurcation diagram for high level security. The proposed MFC-SM is compared with the conventional non MFC-SM and it has an excellent chaotic analysis. In addition, the randomness test results indicate that the proposed MFC-SM shows better performance and satisfy all randomness tests. Due to the excellent chaotic properties and good randomization results for the proposed MFC-SM, it is used to be cooperated with the biometric digital identity to achieve dynamic chaotic biometric digital identity. Also, for real time image encryption, both Discrete Wavelet Transform (DWT)partial image encryption and Isomorphic Elliptic Curve (IEC)key exchange are used. In addition, the biometric digital identity is extracted from the user fingerprint image as fingerprint minutia data incorporated with the proposed MFC-SM and hence, a new Dynamic Fractional Chaotic Biometric Digital IdentityIEC (DFC-BID-IEC) has been introduced. Dynamic Fractional Chaotic Key Generator (DFC-KG) is used to control the key schedule for all encryption and decryption processing. The encryption process consists of the confusion and diffusion steps. In the confusion step, the 2D Arnold Cat Map (ACM) is used with secret parameters taken from DFC-KG. Also, the diffusion step is based on the dynamic chaotic self-invertible secret key matrix which can be generated from the proposed MFC-SM. The IEC key exchange secret parameters are generated based on Elliptic Curve Diffie?Hellman(ECDH) key exchange and the isomorphism parametre. Statistical analysis, differential analysis and key sensitivity tests are performed to estimate the security strengths of the proposed DFC-BID-IEC system. The experimental results show that the proposed algorithm is robust against common signal processing attacks and provides a high security level and high speed for image encryption application.

There are many threats from virus, hacker, electronic eavesdropper, and electronic deceiver in the network. The growth of the computer system and network makes the organizations and personal users to depend on the information that circulate in these systems more and more. This makes us be aware of that protecting the data and resources from leak, insuring the reliability of data and information, and protecting the system from suffering the hit from network are very important.Submit a cryptography that is affirmative by people to reach the demand on the safety of SET system. The algorithm submitted is public, and everyone can use and to verify its safety, using Elliptic Curve Cryptography to execute the key exchange and encryption decryption, and making sure its performance of SET is better while the safety of SET is same as before, and the overload of compute and transmission is yet lower.

This paper discusses parallelization of elliptic curve cryptography hardware accelerators using elliptic curves over binary fields F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2m</sub> . Elliptic curve point multiplication, which is the operation used in every elliptic curve cryptosystem, is hierarchical in nature, and parallelism can be utilized in different hierarchy levels as shown in many publications. However, a comprehensive analysis on the effects of parallelization has not been previously presented. This paper provides tools for evaluating the use of parallelism and shows where it should be used in order to maximize efficiency. Special attention is given for a family of curves called Koblitz curves because they offer very efficient point multiplication. A new method where the latency of point multiplication is reduced with parallel field arithmetic processors is introduced. It is shown to outperform the previously presented multiple field multiplier techniques in the cases of Koblitz curves and generic curves with fixed base points. A highly efficient general elliptic curve cryptography processor architecture is presented and analyzed. Based on this architecture and analysis on the effects of parallelization, a few designs are implemented on an Altera Stratix II field-programmable gate array (FPGA).