An Improved Group Key Agreement Based on Elliptic Curve

Elliptic curve digital signature algorithm (ECDSA) is elliptic curve analogue of digital signature algorithm. This paper presents implementation of ECDSA on NIST recommended Elliptic curves in binary fields of size 163 bits. The work involved implementation of different modules of ECDSA on reconfigurable hardware platform (Xilinx xc6vlx240T-1ff1156). The private key generation and binary weight calculation (used in scalar multiplication) is done in software using Microblaze (soft core of Xilinx). The private key along with the other global parameters for ECDSA are passed from Microblaze to the programmable logic of FPGA where final signature generation and verification is performed. Two implementations have been done based on different word sizes in Montgomery multiplication over binary fields. The first implementation requires 0.367 ms with 11040 slices for signature generation and 0.393 ms with 12846 slices for signature verification at a clocking frequency of 100 MHz. The second implementation requires 0.615 ms with 8773 slices for signature generation and 0.672 ms with 9967 slices for signature verification at the same clocking frequency. These implementations are faster compared to other implementations reported in literature for binary curves.

Elliptic curve cryptosystems (ECCs) are becoming more popular because of the reduced number of key bits required in comparison to other cryptosystems (for example, a 160 bit ecc has roughly the same security as 1024 bit RSA). ECCs are especially suited to smart cards because of the limited memory and computational power available on these devices. This paper discusses an optimized implementation of the elliptic curve Digital Signature Algorithm implemented over the field $GF(p)$ on a Motorola smart card. Algorithms for point addition, point doubling and scalar multiplication are compared according to their timings. The effects of different memory usage, code size and speed tradeoffs which were considered during the implementation are discussed. Also, optimized point addition and doubling algorithms are presented.

In this paper, we describe the design and implementation of a new security protocol based on Elliptic Curve Cryptosystems (ECC) for securing Wireless Sensor Networks (WSNs). Some public-key-based protocols such as TinyPK and EccM 2.0 have already been proposed in response. However, they exhibit poor performance. Moreover, they are vulnerable to man-in-the-middle attacks. We propose a cluster-based Elliptic Curve Diffie-Hellman (ECDH) and Elliptic Curve Digital Signature Algorithm (ECDSA) for efficiency and security during the pairwise key setup and broadcast authentication phases, respectively. We have implemented our protocol on 8-bit, 7.3828-MHz MICAz mote. The experimental results indicate the feasibility of our protocol for WSNs.

Background: Today’s developing era data and information security plays an important role in unsecured communication between Internet of Things (IoT) elements. As the technologies are developing huge amount of information are exchanged with each other which increases the demand of a secure encryption standards. Objectives: To protect the information transmission between nodes in the perceptual layer of IoT, security is to be enhanced such that the Men in Middle (MIM) attack of information by intruders in the communication link is not possible. Methods/Statistical analysis: The security method is implemented using the concept of symmetric, asymmetric and hash algorithms between the sender and receiver. Elliptic Curve Cryptography (ECC) is performed for encrypting and sharing the Advanced Encryption Standard (AES) secret key between the sender and receiver. Elliptic Curve digital signature are added with the encrypted data for validation in transmission. Secured Hash Algorithm (SHA) is considered for generating Elliptical Curve Digital Signature Algorithm (ECDSA). All the algorithms are combined to enhance the security. Findings: Elliptic Curve Cryptography is generally applied for encrypting and sharing the secret key between the sender and receiver when Advanced Encryption Standard is used for encryption/decryption of data. A highly efficient architectures for asymmetric key encryption is applied with symmetric key encryption for encrypting the data transmitted between the devices present in the perceptual layers in the IoT. Due to security issues NIST selected SHA-3 Keccak-f[1600] algorithm. An authentication process based on ECC is applied to perceptual layer involving initialization and authentication phase apart from encryption and signature generation. Sender combines the encrypted data and key with signature together before transmitting to the receiver. The receiver verifies the signature and decrypts the key and obtains original information. Hence it is very difficult for the man in middle to access the information exchanged between the Perceptual Layer devices. Application/Improvements: This generally doesn’t require an innovative technique but an approach to develop the method implemented successfully in the perceptual layer of Internet of Things. The key is encrypted and decrypted using a novel ECC algorithm with improved ECDSA.

Recently, a fast and secure hash function SFHA - 256 has been proposed and claimed as more secure and as having a better performance than the SHA - 256. In this paper an improved version of SFHA - 256 is proposed and analyzed using two parameters, namely the avalanche effect and uniform deviation. The experimental results and further analysis ensures the performance of the newly proposed and improved SFHA-256. From the analysis it can be concluded that the newly proposed algorithm is more secure, efficient, and practical.

This paper concentrates on the hardware implementation of efficient and re- configurable elliptic curve digital signature algorithm (ECDSA) that is suitable for verifying transactions in Blockchain related applications. Despite ECDSA architecture being computationally expensive, the usage of a dedicated stand-alone circuit enables speedy execution of arithmetic operations. The prototype put forth supports N-bit elliptic curve cryptography (ECC) group operations, signature generation and verification over a prime field for any elliptic curve. The research proposes new hardware framework for modular multiplication and modular multiplicative inverse which is adopted for group operations involved in ECDSA. Every hardware design offered are simulated using modelsim register transfer logic (RTL) simulator. Field programmable gate array (FPGA) implementation of var- ious modules within ECDSA circuit is compared with equivalent existing techniques that is both hardware and software based to highlight the superiority of the suggested work. The results showcased prove that the designs implemented are both area and speed efficient with faster execution and less resource utilization while maintaining the same level of security. The suggested ECDSA structure could replace the software equivalent of digital signatures in hardware blockchain to thwart software attacks and to provide better data protection.

Recent works have shown the usefulness of network and application layer protocols that connect low-power sensor nodes directly to multiple applications and users on the Internet. We propose a security solution for this scenario. While previous works have provided security support for various communication patterns in sensor networks, such as among nodes, from nodes to a base station, and from users to nodes, the security of communication from sensor nodes to multiple users has not been sufficiently addressed. Specifically, we explore this design space and develop a security solution, named Secure Tiny Web Service, for efficient authentication of data sent by a resource-constrained sensor node to multiple users, using digital signatures. We investigate the resource overheads in communication and computation of four suitable signature schemes—the Elliptic Curve Digital Signature Algorithm, the (elliptic curve) Schnorr signature, and the Boneh–Lynn–Shacham and Zhang–Safavi-Naini–Susilo short signature schemes. We implement these schemes on two popular sensor node architectures (based on AVR ATmega128L and MSP430 processors with 802.15.4 radios) and experimentally characterize relevant trade-offs.

This article examines digital signature as a critical security measure for authentication and verification in electronic transactions, distinguishing them from simpler e-signatures by their use of advanced cryptographic techniques. Digital signature leverage asymmetric cryptography to provide higher security, with various standardised algorithms, such as the Digital Signature Algorithm (DSA) and Rivest- Shamir-Adleman (RSA), forming the foundation of secure systems today. The paper outlines the evolution of digital and electronic signature, from early telegraph-based approvals to the modern applications that facilitate secure digital contracts and communications. Key digital signature algorithms are analysed in detail, highlighting their strengths and weaknesses, including RSA, DSA, Elliptic Curve Digital Signature Algorithm (ECDSA), and Edwards-Curve Digital Signature Algorithm (EdDSA). Additionally, the article addresses the technical and implementation challenges of digital signature algorithms, such as high computational demands, complexities in key management, and difficulties in secure implementation. It concludes with an exploration of future trends, such as the development of efficient and quantum-resistant algorithms, improvements in cryptographic hardware, and new strategies to simplify secure key management. This comprehensive overview provides insights into both current digital signature practices and emerging solutions poised to enhance security and efficiency in an evolving digital landscape.

Cheque Truncation System (CTS) is a technique of preventing tangible movement of cheque by substituting it with a digital image, with an aim for secure and faster clearance. For the first time re-watermarking is applied for authenticating transactions in CTS. Methodology for the proposed approach splits the host image (Ih) into two layers (L). In L1 cheque details are fused with two image color channels to form a composite message (Cm). Secure hash algorithm (SHA-512) is applied to Cm to generate a unique message digest (Md). Elliptic Curve Digital Signature Algorithm (ECDSA) is applied to Md to create a digital signature. The signature is embedded by exploiting Human Visual System (HVS) color channel sensitivity in equally parted mode. In L2, joint secret is established to form key using Elliptic Curve Diffie Hellman Protocol (ECDHP). Advanced Encryption Standard (AES) is applied to user details intricate in the transaction. Encrypted contents are then inserted in L2 by applying Discrete Cosine Transform (DCT). Experimental results state solution to integrity concerns by using ECDSA with SHA-512, reaction to security issues by AES and the response to key distribution problem by ECDHP. An effective semi-blind CTS is perceived with PSNR between 59-60 dB.

In recent decades there has been an increasing interest in Elliptic curve cryptography (ECC) and, especially, the Elliptic Curve Digital Signature Algorithm (ECDSA) in practice. The rather recent developments of emergent technologies, such as blockchain and the Internet of Things (IoT), have motivated researchers and developers to construct new cryptographic hardware accelerators for ECDSA. Different types of optimizations (either platform dependent or algorithmic) were presented in the literature. In this context, we turn our attention to ECC and propose a new method for generating ECDSA moduli with a predetermined portion that allows one to double the speed of Barrett’s algorithm. Moreover, we take advantage of the advancements in the Artificial Intelligence (AI) field and bring forward an AI-based approach that enhances Schoof’s algorithm for finding the number of points on an elliptic curve in terms of implementation efficiency. Our results represent algorithmic speed-ups exceeding the current paradigm as we are also preoccupied by other particular security environments meeting the needs of governmental organizations.

Elliptic curve cryptosystems proved to be well suited for securing systems with constrained resources like embedded and portable devices. In a fault-based attack, errors are induced during the computation of a cryptographic primitive, and the results are collected to derive information about the secret key safely stored in the device. We introduce a novel attack methodology to recover the secret key employed in implementations of the Elliptic Curve Digital Signature Algorithm. Our attack exploits the information leakage induced when altering the execution of the modular arithmetic operations used in the signature primitive and does not rely on the underlying elliptic curve mathematical structure, thus being applicable to all standardized curves. We provide both a validation of the feasibility of the attack, even employing common off-the-shelf hardware to perform the required computations, and a low-cost countermeasure to counteract it.

The concept of public key cryptography was first introduced by Diffie and Hellman in 1976 using discrete logarithm problem as base of difficulty. In 1985, T. ElGamal proposed public key cryptosystem scheme based on discrete logarithm problem. Elliptic curve cryptosystems were first proposed in 1985 independently by Neil Koblitz and Victor Miller. Elliptic curve cryptosystems are unique in using elliptic curve groups for arithmetic. This cryptosystem is based on discrete logarithm problem in the group of points of an elliptic curve defined over a finite field. The discrete logarithm problem in an elliptic curve group appears to be much harder than the discrete logarithm problem in other groups. Hence elliptic curves cryptosystem can match the security of other cryptosystems while using smaller key. In this paper we will discuss a VLSl implementation of elliptic curves cryptosystem for ElGamal encryption scheme.

In this paper we have implemented the ECDSA (Elliptic Curve Digital Signature Algorithm) technique to provide security in HWMP (Hybrid Wireless Mesh Protocol). The motivation behind the use of ECDSA is that it is integrated into the IEEE P802.11s/D4.0 standard. We have used the ECDSA technique to secure control message in HWMP, namely PREQ (Path Request) and PREP (Path Reply). In these Control messages, we are interested only by mutable fields (i.e. fields that change during control packet exchange). Simulation results show that the ECDSA-HWMP does not too much a long overhead compared to the orignal HWMP.

ABSTRACTBecause wireless sensor network (WSN), which is composed of a large number of low‐cost and resource‐constrained devices, communicates on the basis of wireless protocols such as IEEE 802.15.4, ZigBee, and DASH‐7, it is easily vulnerable to eavesdropping, illegal modification, privacy infringement and denial‐of‐service attacks. These attacks destroy the data integrity, confidentiality, and authentication of the basic WSN security requirements and then the reliability and security of the WSN‐based applications are deteriorated. There have been many research efforts to make secure WSN environments. Among these efforts, TinyECC is one of outstanding works. It provides several security protocols such as Elliptic Curve Diffie–Hellman, Elliptic Curve Digital Signature Algorithm, and Elliptic Curve Integrated Encryption Scheme, based on the Elliptic Curve Cryptography (ECC). TinyECC is basically a well‐written TinyOS‐based code and is optimized to resource‐constrained environments. The Barrett reduction, hybrid multiplication, and several optimization techniques are also used for high performance even with low‐energy consumption. However, the hybrid multiplication technique used in TinyECC is known to be not suitable for 16‐bit processor, MSP430, which is a familiar processor for sensor node. This is due to the fact that the MSP 430 processor does not provide enough number of registers for hybrid multiplication techniques. Because the multiplication operation over the finite field is a major operation of the ECC, it causes a high latency of multiplication operations and eventually degrades the performance of the ECC operation. In this paper, we propose a novel multiplication operation based on the cached operands and reordered partial products. The proposed method shows that the latency of the polynomial multiplication, which is the core operation of the ECC, is 6% smaller than previously known results. Copyright © 2012 John Wiley & Sons, Ltd.

Elliptic curve cryptography is a relatively new public-key cryptography mechanism which has been becoming more popular in recent years. Its usage has been increasing in various fields using different cryptographic protocols, such as Elliptic Curve Diffie-Hellman (ECDH), Elliptic Curve Digital Signature Algorithm (ECDSA) and the ElGamal encryption scheme. Several attacks have been developed to solve the elliptic curve discrete logarithm problem. One of the most practical generic attacks is the Pollard's Rho algorithm, which originates as an algorithm for prime factorisation. This paper will attempt to provide a statistical insight on how various factors, namely the private-public key pairs and parameters within the sequence used in Pollard's Rho algorithm, may affect the performance speed of the algorithm. This will be done using the ANOVA statistical test. which shows that from the perspective of the initial values and addends of the sequences, the Pollard's Rho algorithm is "random" enough.