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In this paper, we propose an energy-efficient design of architecture for digit-serial multiplication over generic GF( 2 m ), which could be used for different fields as and when required and to enhance the security by changing the fields. An efficient input scheduling scheme is proposed to reduce the required number of input pins and a digit extraction circuit for digit-serial multiplication. Besides, to reduce the dynamic power consumption, we have proposed a simple technique using an array of m AND gates that minimizes the output bit-switching. To study the impact of digit size, the digit-serial multipliers for m = 163 and 233 are synthesised by Xilinx Vivado for FPGA implementation. It is found that the required number of slices, power consumption, and energy per multiplication increase while the computational delay falls with the increase in digit size. Therefore, larger digit sizes could be considered only when fast multiplication is necessary. The array of AND gates for output bit control helps in reducing the dynamic power consumption and energy per multiplication, respectively, by 50.4% and 57.7% for m = 163 and 49.8 % and 51.8 % , for m = 233 , on average, for different digit sizes over the conventional least-significant-digit-first design. [ABSTRACT FROM AUTHOR]

A new fractional difference equation two‐dimensional triangle function combination discrete chaotic map (2D‐TFCDM) based on Caputo derivative is proposed. Using the bifurcation diagram, the maximum Lyapunov exponent, and the phase diagram, the numerical solutions of the fractional difference equations are obtained, and the chaotic behavior is observed numerically. After encrypting the key with elliptic curve cryptosystem, the fractional map is developed as an encryption algorithm and applied to color image encryption. Finally, the proposed encryption system is systematically analyzed from five main aspects, and the results show that the proposed encryption system has a good encryption effect. [ABSTRACT FROM AUTHOR]

With the development of wireless communication technology and the popularization of intelligent terminals, more and more cryptographic algorithms are applied to IoT devices to ensure the security of communication and data.Among them, the SM2 elliptic curve public key cryptography proposed by the State Cryptography Administration is an elliptic curve public key cryptography algorithm developed domestically, which has the advantages of high security and short key.SM2 has been widely deployed in various communication systems and is used in essential parts such as identity authentication and key negotiation.However, since SM2 involves large integer operations on finite fields, the computational cost is high, and its execution on a low-power embedded platform seriously affects the user experience.Therefore, an efficient implementation scheme of SM2 algorithm for low-power embedded platform was proposed for ARM-m series processors.Specifically, Thumb-2 instruction set was adopted to handle carry and save addressing cycles, basic operations such as modulo addition and sub-traction of large integers were optimized, and the number of available registers on the platform was combined to build efficient basic operations.Besides, based on the short multiplication and accumulation instruction cycle of ARM-m series processors, the implementation of Montgomery multiplication was optimized, and an efficient modular multiplication scheme was designed in combination with the CIOS algorithm.The scheme was no longer limited to Mersenne primes, and greatly improved the speed and flexibility of modular multiplication.Based on the theoretical analysis and experimental test, the window length selection method of the multiple point-scalar multiplication wNAF sliding window method on the embedded platform was given.The experimental test results show that the proposed scheme can effectively improve the computational efficiency of the SM2 algorithm on the resource-constrained low-power embedded platform.Without pre-calculation, the test signature speed can reach 0.204s/time, the signature verification speed is 0.388s/time, the encryption speed is 0.415s/time, and the decryption speed is 0.197s/time.

Recently, an encryption scheme (Abdelfatah IEEE Access 8:3875–3890, 2020) based on chaotic and enhanced elliptic curve cryptography was proposed. The author uses a pixel grouping method as an essential stage for the entire encryption scheme. This Pixel grouping method is carried out so that the execution speed is enhanced. However, there exists a condition during the pixel grouping stage that makes the method futile while decrypting. Upon pixel grouping, if the large integer turns out to be equal or larger than the modulo prime parameter P of the elliptic curve, precise decrypted values cannot be obtained. In this paper, the flaw is avoided by using the inverse modulo operator if the large integer is greater than or equal to P. Experimental analysis to prove the conditions is shown in this paper. Moreover, a new method is added to circumvent such conditions. [ABSTRACT FROM AUTHOR]

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The last decade witnessed rapid increase in multimedia and other applications that require transmitting and protecting huge amount of data streams simultaneously. For such applications, a high-performance cryptosystem is compulsory to provide necessary security services. Elliptic curve cryptosystem (ECC) has been introduced as a considerable option. However, the usual sequential implementation of ECC and the standard elliptic curve (EC) form cannot achieve required performance level. Moreover, the widely used Hardware implementation of ECC is costly option and may be not affordable. This research aims to develop a high-performance parallel software implementation for ECC. To achieve this, many experiments were performed to examine several factors affecting ECC performance including the projective coordinates, the scalar multiplication algorithm, the elliptic curve (EC) form, and the parallel implementation. The ECC performance was analyzed using the different factors to tune-up them and select the best choices to increase the speed of the cryptosystem. Experimental results illustrated that parallel Montgomery ECC implementation using homogenous projection achieves the highest performance level, since it scored the shortest time delay for ECC computations. In addition, results showed that NAF algorithm consumes less time to perform encryption and scalar multiplication operations in comparison with Montgomery ladder and binary methods. Java multi-threading technique was adopted to implement ECC computations in parallel. The proposed multithreaded Montgomery ECC implementation significantly improves the performance level compared to previously presented parallel and sequential implementations. [ABSTRACT FROM AUTHOR]

In this paper, a novel fractional quantum logistic map (FQLM) based on fractional difference is proposed and image encryption algorithm based on it are exploited. First, the FQLM is proposed and its dynamical behaviors are observed with bifurcation diagram, phase portraits and largest Lyapunov exponent plots. After that, the ECC is utilized to cover up the encryption keys and the FQLM is used for the permutation and diffusion process of image encryption. Finally, the cryptosystem is used in image encryption and the algorithm is analyzed in four respects, showing a distinct advantage of the proposed cryptosystem over some of existing ones. [ABSTRACT FROM AUTHOR]

We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gröbner basis algorithms.

Image encryption based on elliptic curve cryptosystem and reducing its complexity is still being actively researched. Generating matrix for encryption algorithm secret key together with Hilbert matrix will be involved in this study. For a first case we will need not to compute the inverse matrix for the decryption processing cause the matrix that be generated in encryption step was self invertible matrix. While for the second case, computing the inverse matrix will be required. Peak signal to noise ratio (PSNR), and unified average changing intensity (UACI) will be used to assess which case is more efficiency to encryption the grayscale image. [ABSTRACT FROM AUTHOR]

Summary: From the last decade, every developing nations are focusing on the smart cities. Smart city will provide all necessary services, ie, water management, waste management, traffic management, and health services, to its citizens effectively. A new paradigm in the smart vehicles is able to form a network called vehicular ad hoc network (VANET). There is a wireless enabled roadside unit (RSU) through which the vehicle drivers can effectively exchange the important traffic data and take proper driving decisions. Each roadside unit is capable of managing some vehicles, which can form a group. There are many schemes available for data transmission in VANET group but they are less secured. In this paper, we propose an intelligent conditional privacy preserving scheme for vehicular ad hoc networks using elliptic curve cryptography. The security analysis showed that the proposed scheme is intelligent, efficient, and easily deployable. [ABSTRACT FROM AUTHOR]

In order to address the problem of elliptic curve cryptosystem (ECC) for the expensive cost in scalar multiplication and the vulnerability to the power analysis attacks,a pseudo 4D projective coordinate-based multi-base scalar multiplication was proposed to optimize group operation layer and scalar multiplication operation layer,which aimed at increasing the performance of ECC and resisting common power analysis attacks.Experimental results show that compared with the state-of-the-art algorithms,the proposed algorithm decreases 5.71% of point doubling cost,3.17% of point tripling cost,and 8.74% of point quintupling cost under discrete group operations.When the key length is 160 bit,the proposed algorithm decreases 36.32% of point tripling cost,17.42% of point quintupling cost,and 8.70% of the system cost under continuous group operations.The analyzing of power consumption wave shows that the proposed algorithm can resist SPA and DPA attack.

Instant messaging (IM) systems can be considered the most frequently used applications in mobile social networks. Nowadays, people are becoming increasingly concerned about data security and privacy protection with IM applications. Therefore, a comprehensive enhanced secure IM scheme was proposed in this paper, which is based on the elliptic curve cryptosystem and the advanced encryption standard algorithm. An offline key agreement process between users was designed under the computational Diffie-Hellman (CDH) assumption by updating the ephemeral key periodically. The proposed scheme supports denial of replaying attack and denial of forgery attack by utilizing timestamps and the elliptic curve digital signature algorithm. It supports multiple types of messages (such as document and multimedia messages) and prevents privacy leakage by storing sent and received messages with ciphertext. We proved the security of the proposed scheme under the elliptic curve discrete logarithm assumption and the CDH assumption. The comparison results of the proposed scheme with other schemes and the results of an experiment show that it is a comprehensive secure scheme with high security and good practicability.practicability.

Smart home based on Internet of things (IoT) is rapidly emerging as an exciting research and industry field. However, security and privacy have been critical issues due to the open feature of wireless communication channel. As a step towards this direction, Shuai et al. proposed an anonymous authentication scheme for smart home environment using Elliptic curve cryptosystem. They provided formal proof and heuristic analysis and argued that their scheme is secure against various attacks including de-synchronization attack, mobile device loss attack and so on, and provides user anonymity and untraceability. However, this paper shows that Shuai et al.‘s scheme does not provide user anonymity nor untraceability, which are very important features for the contemporary IoT network environment. [ABSTRACT FROM AUTHOR]

Mobile communications (e.g., emails, Snapchat and Facebook) over a wireless connection is a norm in our Internet-connected society. Ensuring the security of communications between devices is an ongoing challenge. A number of authenticated key exchange (AKE) protocols have been proposed to verify the authenticity of a user and the integrity of messages sent over an insecure wireless communication channel. Recently, Tsai et al. proposed two AKE protocols designed for wireless network systems. In this paper, we demonstrate that their protocols are vulnerable to off-line password guessing attacks through presenting concrete attacks, contrary to their claims.

With the progressive development of a wide range of applications, interconnect things and internet of things (IoT) became an imperative required trend by industries and academicians. IoT became a base infrastructure for remote access or control depending on internet protocol (IP) networks, especially after the COVID-19 pandemic. The huge application domain’s infrastructure, which depends on IoT, requires a trusted connection to guarantee security and privacy while transferring data. This paper proposes a hybrid identity authentication pipeline that integrates three schemes, namely, an elliptic curve cryptography (ECC) scheme is integrated with the Ong, Schnorr, and Shamir (OSS) signature scheme and chaotic maps. The latter satisfies both security and guarantee criteria. The novelty of the proposal is in using chaotic mapping and a cyclic group to deduce a substitution box (S-Box) and a reversible matrix as a portion of the OSS signature equation. The ECC-based security part is an efficient public key cryptography mechanism with less computational cost, which makes it the most convenient to be used in IoT devices for authentication and privacy. The strength of the proposed scheme relies on combining the discrete logarithm problem (DLP) and integer factorization problem (IFP). The proposed approach was simulated using Lab-View and compared with other state-of-the art schemes. Extensive simulation results and analysis of the security and time rendering results confirmed its durability against different types of attacks, such as linear and differential attacks.

Nowadays it is vital to have a robust mechanism that can identify people, objects, animals, and living beings, for example, for agricultural, health and national security purposes. Some drawbacks occur when very many objects need to be identified, and the tool is unable to support all of them. Even if the mechanism could tag them all, it is also important that the labels or codewords not resemble each other, to be able to detect and correct errors. To solve this problem, this article proposes an MDS (Maximum Distance Separable) code C with length 11 and dimension 7 over the finite field F 2 10 . Furthermore, we construct a subcode of C with capacity for 327 different identifiers. Concretely we consider the set of all codewords with entries belonging to the subfield of F 2 10 isomorphic to F 2 5 . A decoding algorithm and an encryption method using elliptic curves cryptography for the codewords are also proposed. [ABSTRACT FROM AUTHOR]

A Koblitz curve Ea is defined over field F2m. Let τ =(-1)1-a+√-7/2 where a ∈ {0, 1} denotes the Frobenius endomorphism from the set E(F2m) to itself. It can be used to improve the performance of computing scalar multiplication on Koblitz Curves. In this paper, another version of formula for τm = rm + smτ where rm and sm are integers is introduced. Through this approach, we discover an alternative method to find the number of points through the curve Ea. [ABSTRACT FROM AUTHOR]

In this work, we retake an old idea that Koblitz presented in his landmark paper (Koblitz, in: Proceedings of CRYPTO 1991. LNCS, vol 576, Springer, Berlin, pp 279–287, 1991), where he suggested the possibility of defining anomalous elliptic curves over the base field F 4 . We present a careful implementation of the base and quadratic field arithmetic required for computing the scalar multiplication operation in such curves. We also introduce two ordinary Koblitz-like elliptic curves defined over F 4 that are equipped with efficient endomorphisms. To the best of our knowledge, these endomorphisms have not been reported before. In order to achieve a fast reduction procedure, we adopted a redundant trinomial strategy that embeds elements of the field F 4 m , with m a prime number, into a ring of higher order defined by an almost irreducible trinomial. We also suggest a number of techniques that allow us to take full advantage of the native vector instructions of high-end microprocessors. Our software library achieves the fastest timings reported for the computation of the timing-protected scalar multiplication on Koblitz curves, and competitive timings with respect to the speed records established recently in the computation of the scalar multiplication over binary and prime fields. [ABSTRACT FROM AUTHOR]

The Internet of Things (IoT) is an information carrier based on the Internet and traditional telecommunications network, which enables all ordinary physical objects that can be independently addressed to form an interconnected network. User authentication protocol is an essential technology for security and privacy in the IoT environment. This paper analyzes the security of Mirsaraei et al.'s three-factor authentication scheme for IoT environments (Mirsaraei et al., 2022 [31]), and finds that the scheme cannot provide users with untraceability, perfect forward secrecy or the resistance of key compromise impersonation attack. The article improves Mirsaraei et al.'s scheme and proposes a three-factor authentication protocol with perfect forward secrecy using elliptic curve cryptosystem, which retains the general process of Mirsaraei et al.'s scheme. The formal security analysis of the proposed protocol is carried out by ROR (Real-or-Random) model, and the formal security verification of the proposed protocol is implemented by Proverif tool. The cryptoanalysis results demonstrate that the proposed protocol makes up for the shortcomings of Mirsaraei et al.'s scheme in security and can resist more malicious attacks as opposed to recent schemes. Moreover, the performance analysis using MIRACL (Multiprecision Integer and Rational Arithmetic C/C++ Library) shows that, the proposed protocol has great advantages over analogical three-factor authentication schemes in terms of computational overhead and communication overhead. • This paper find the security defects of Mirsaraei et al.'s scheme and improve it. • The proposed scheme provides excellent computational and communication cost. • The proposed scheme provides perfect forward secrecy. • Formal security analyses demonstrate the security of the proposed scheme. [ABSTRACT FROM AUTHOR]

With a trusted-third-party (TTP)-based key exchange protocol, when a user would like to transmit a message to another user, the transmitted data are encrypted by a session key exchanged between the two ends of the corresponding connection with the help of the TTP. Up to present, due to the assistance of a TTP, this type of protocols has performed well in protecting messages delivered between two authorized users. Even this, inflexibility, unreliability, and inefficiency problems still exist in these previously proposed protocols. Therefore, in this paper, a multi-key exchange protocol, named the TTP-based high-efficient multi-key exchange protocol (THMEP), is proposed to provide users with a secure and efficient protocol, which employs the elliptic curve cryptography, a 2-D operation, and a current time encryption key, to exchange their session keys. The proposed protocol not only effectively hides important encryption parameters, but also achieves fully mutual authentication between a user and his/her trusted server. It can resist known-key, impersonation, replay, eavesdropping, and forgery attacks. Besides, the THMEP generates 40 session keys in a key exchange process, meaning the proposed protocol can support 40 sessions simultaneously. It also shortens the processing time, which is 3.78 times faster than that of a specific previous study. Its security level and performance are higher than those of the compared state-of-the-art protocols. In other words, the THMEP is very suitable for IoT applications.