Elliptic Curve Digital Signature Research Articles

Digital Signature Standard Implementation Strategy by Optimizing Hash Functions Through Performance Optimization

Security method of data transmission process has been growing rapidly with the science of cryptography. Cryptography can provide security services that includes security aspects like confidentiality, data integrity, authentication and non-repudiation. Modern cryptography uses a key that must be kept secret to overcome the problem of cryptographic security. Problem in the use of the same key by two entities that communicate with each other in exchanging messages is a way to distribute the key. This problem can be overcome by using public-key cryptography, which allows users to communicate securely without a shared secret key. Digital signature is the application of public-key cryptography. When accessing important digital documents, it is necessary to verify the signature given. Implementation of digital signature always requires a hash function. Hash function used in this research namely SHA-256, SHA-384 and Tiger. Federal Information Processing Standards (FIPS) set the cryptographic standard for digital signatures is the Digital Signature Standard (DSS). Algorithms included in the DSS are the Digital Standard Algorithm (DSA), Ron Rives, Adi Shamir, and Leonard Adleman (RSA) and Elliptic Curve Digital Signature Algorithm (ECDSA). So it is necessary to test the best digital signature implementation strategy that can be used by optimizing the performance of the hash function. Performance testing of the three algorithms is done by making an application using a computer programming language C++. Implementation program using C++ class library for cryptographic scheme that is Crypto++ Library 5.6.0. Class libraries used in the classes functions for digital signatures. On the application of digital signatures generated, conducted tests is done by combining each hash function algorithm with each of the DSS in order to compare their performance in terms of time and memory usage. Against the test results are then analyzed using statistical tests. The result shows that pair of Tiger hash function and DSA algorithm is the best combination.

Analysing the Security Aspects of IoT using Blockchain and Cryptographic Algorithms

Technological advancement is a never-ending field that shows its evolution from time to time. In 1832, with the invention of the electromagnetic telegraph, the era of the Internet of Things (IoT) began. Within the time of 190 years, this technological domain has revolutionized IoT and made it omnipresent. However, with this evolved and omnipresent nature of IoT, many drawbacks, privacy, interoperability, and security issues have also been generated. These different concerns should be tackled with some newer technologies rather than the conventional ones as somehow, they are only the generator of those issues. Outdated Security could be an appropriate issue of IoT along with the centralized point of failure. It also possesses more concerns and challenges to tackle. On the other side, there is a visible solution to address the challenges of IoT in this developing domain of technology. The visible approach is Blockchain which acted as the backbone in securing Bitcoin in 2008, which was created by the pseudo group named Satoshi Nakamoto. Blockchain has evolved from Blockchain 1.0 to Blockchain 4.0 as the latest one depicts its amalgamation with another component of Industry 4.0 i.e., Artificial Intelligence (AI). AI will give the ability to think logically and like humans. In addition to this SMART solution, there is also an advanced cryptographical technique known as the Elliptic Curve Digital Signature Algorithm (ECDSA) which can enhance the security spectrum of IoT if applied appropriately. This paper produces a vision to enhance and optimize the security of IoT using a network peer-to-peer technology Blockchain along with advanced cryptography.

Multi-Functional Resource-Constrained Elliptic Curve Cryptographic Processor

With the rising data evolution, the demand for secured communications over networks is rising immensely. Elliptic Curve Cryptography (ECC) provides an attractive solution to fulfill the requirements of modern network applications. Many proposals published over the year over different variants of ECC satisfied some of the issues. Nevertheless, modern network applications such as Internet-of-Thing (IoT) and Software-Defined Networking (SDN) put the requirements on various aspects and can only be solved by different ECC algorithms. Looking at this point of view, an efficient architecture that could combine multiple ECC algorithms becomes an urgent request. In addition, even though many investigations of ECC on Field-Programmable Gate Arrays (FPGA), an efficient architecture that could be well-deployed on Application-Specific Integrated Circuit (ASIC) needs to get more study. Therefore, this paper proposes an area-efficient ECC hardware design that could integrate multiple ECC algorithms. The proposed design is deployed on both ASIC and FPGA platforms. Four well-known ECC-based Digital Signature Algorithms (DSAs), which are the Edwards-curve Digital Signature Algorithm (EdDSA) with Curve25519, Elliptic Curve Digital Signature Algorithm (ECDSA) with National Institute of Standards and Technology (NIST) Curve P-256, P-384, and P-521, are implemented. Furthermore, the design supports all DSA schemes: public-key generation, signature generation, and verification. We also provide optimized calculation flows for modular multiplication, modular inversion, point addition, point doubling, and Elliptic Curve Point Multiplication (ECPM) for two different elliptic curves: the NIST curve and Edward curve, on a unique architecture. The calculation processes are designed in projective coordinates and optimized in time and space to achieve a high level of parallelism. The proposed ECC processor could run up to 102-MHz on ASIC 180-nm and 109.7-MHz on Xilinx Virtex-7. In terms of area, The processor occupies 377,471 gates with 4.87- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$mm^{2}$ </tex-math></inline-formula> on the ASIC platform and 11,401 slices on the FPGA platform. The experimental results show that our combinational design achieves area-efficient even when compared with other single-functional architecture on both ASIC and FPGA.

A Blockchain-Based Architecture for Securing Industrial IoTs Data in Electric Smart Grid

There are numerous internet-connected devices attached to the industrial process through recent communication technologies, which enable machine-to-machine communication and the sharing of sensitive data through a new technology called the industrial internet of things (IIoTs). Most of the suggested security mechanisms are vulnerable to several cybersecurity threats due to their reliance on cloud-based services, external trusted authorities, and centralized architectures; they have high computation and communication costs, low performance, and are exposed to a single authority of failure and bottleneck. Blockchain technology (BC) is widely adopted in the industrial sector for its valuable features in terms of decentralization, security, and scalability. In our work, we propose a decentralized, scalable, lightweight, trusted and secure private network based on blockchain technology/smart contracts for the overhead circuit breaker of the electrical power grid of the Al-Kufa/Iraq power plant as an industrial application. The proposed scheme offers a double layer of data encryption, device authentication, scalability, high performance, low power consumption, and improves the industry’s operations; provides efficient access control to the sensitive data generated by circuit breaker sensors and helps reduce power wastage. We also address data aggregation operations, which are considered challenging in electric power smart grids. We utilize a multi-chain proof of rapid authentication (McPoRA) as a consensus mechanism, which helps to enhance the computational performance and effectively improve the latency. The advanced reduced instruction set computer (RISC) machines ARM Cortex-M33 microcontroller adopted in our work, is characterized by ultra-low power consumption and high performance, as well as efficiency in terms of real-time cryptographic algorithms such as the elliptic curve digital signature algorithm (ECDSA). This improves the computational execution, increases the implementation speed of the asymmetric cryptographic algorithm and provides data integrity and device authenticity at the perceptual layer. Our experimental results show that the proposed scheme achieves excellent performance, data security, real-time data processing, low power consumption (70.880 mW), and very low memory utilization (2.03% read-only memory (RAM) and 0.9% flash memory) and execution time (0.7424 s) for the cryptographic algorithm. This enables autonomous network reconfiguration on-demand and real-time data processing.

An Efficient Authenticated Elliptic Curve Cryptography Scheme for Multicore Wireless Sensor Networks

The need to ensure the longevity of Wireless Sensor Networks (WSNs) and secure their communication has spurred various researchers to come up with various WSN models. Prime among the methods for extending the life span of WSNs is the clustering of Wireless Sensors (WS), which reduces the workload of WS and thereby reduces its power consumption. However, a drastic reduction in the power consumption of the sensors when multicore sensors are used in combination with sensors clustering has not been well explored. Therefore, this work proposes a WSN model that employs clustering of multicore WS. The existing Elliptic Curve Cryptographic (ECC) algorithm is optimized for parallel execution of the encryption/decryption processes and security against primitive attacks. The Elliptic Curve Diffie-Helman (ECDH) was used for the key exchange algorithm, and the Elliptic Curve Digital Signature Algorithm (ECDSA) was used to authenticate the communicating nodes. Security analysis of the model and comparative performance analysis with the existing ones were demonstrated. The security analysis results reveal that the proposed model meets the security requirements and resists various security attacks. Additionally, the projected model is scalable, energy-conservative, and supports data freshness. The results of comparative performance analysis show that the proposed WSN model can efficiently leverage multiprocessors and/or many cores for quicker execution and conserves power usage.

A Secure Hardware Implementation for Elliptic Curve Digital Signature Algorithm

Since the end of the 1990s, cryptosystems implemented on smart cards have had to deal with two main categories of attacks: side-channel attacks and fault injection attacks. Countermeasures have been developed and validated against these two types of attacks, taking into account a well-defined attacker model. This work focuses on small vulnerabilities and countermeasures related to the Elliptic Curve Digital Signature Algorithm (ECDSA) algorithm. The work done in this paper focuses on protecting the ECDSA algorithm against fault-injection attacks. More precisely, we are interested in the countermeasures of scalar multiplication in the body of the elliptic curves to protect against attacks concerning only a few bits of secret may be sufficient to recover the private key. ECDSA can be implemented in different ways, in software or via dedicated hardware or a mix of both. Many different architectures are therefore possible to implement an ECDSA-based system. For this reason, this work focuses mainly on the hardware implementation of the digital signature ECDSA. In addition, the proposed ECDSA architecture with and without fault detection for the scalar multiplication have been implemented on Xilinx field programmable gate arrays (FPGA) platform (Virtex-5). Our implementation results have been compared and discussed. Our area, frequency, area overhead and frequency degradation have been compared and it is shown that the proposed architecture of ECDSA with fault detection for the scalar multiplication allows a trade-off between the hardware overhead and the security of the ECDSA.

Attack Detection Using a Lightweight Blockchain Based Elliptic Curve Digital Signature Algorithm in Cyber Systems

Cyber-physical systems (CPSs) are highly susceptible to malicious cyberattacks due to their reliance on communication networks. For this reason, many different attack detection techniques have been developed to guarantee the safety of CPSs. This article introduces BlockChain (BC) to address CPS issues such as data security and privacy. Additionally, BC is not well suited for CPS due to its high computing complexity, limited scalability, significant bandwidth overhead, and latency. To meet the requirements of CPS, a light-weight blockchain-based signature algorithm (LWBSA) model is developed in this work. The concept's resource constraints are alleviated by having a single centrally managed manager generate shared keys for outward-bound data transmission requests. The LWBSA paradigm provided herein produces an overlay network where extremely equipped resources can merge into a community BC, hence ensuring both dedicated privileges. Lightweight consensus, the elliptic curve digital signature algorithm (ECDSA), and distributed throughput management (DTM) are the three optimizations implemented in the ELIB model discussed here. Extensive simulation is carried out to examine the implications of different situations on processing time, energy usage, and overhead. The experimental outcomes show that the LWBSA achieves the best possible performance across a wide variety of measures.

Implementation of Boneh - Lynn - Shacham short digital signature scheme using Weil bilinear pairing based on supersingular elliptic curves

One option for a digital signature solution for devices with low memory and low bandwidth transmission over channels uses a short digital signature scheme based on Weil bilinear pairing aimed at short processing times, fast computation, and convenient deployment on applications. The computational technique of non-degenerate bilinear pairings uses supersingular elliptic curves over a finite field Fpl (where p is a sufficiently large prime number) and has the advantage of being able to avoid Weil-descent, Menezes-Okamoto-Vanstone (MOV) attacks, and attacks by the Number Field Sieve algorithm. Compared to Elliptic Curve Digital Signature Algorithm (ECDSA) digital signature schemes, generating a digital signature for a Boneh-Lynn-Shacham (BLS) scheme using Weil bilinear pairing on a supersingular elliptic curve is simple. In this study, the authors replace non-degenerate bilinear pairing calculations on a supersingular elliptic curve with a Weil pairing with PεE(Fp ), QεE(Fp1) and a higher security multiplier α=12 in the BLS short digital signature scheme. The execution time of the BLS short digital signature program showed improvement compared to the commercial ECDSA digital signature scheme.

Empirical Evaluation of ECC Batch Verification Algorithms of Digital Signature in Wireless Sensor Network

Wireless sensor network (WSN) is an emerging topic in wireless communication where various sensor nodes are connected over the internet for data exchange. Exchanging the information over the WSN is very critical; therefore, it requires authentication and security mechanisms to ensure integrity and confidentiality. To avoid unauthorized use of WSN, the authentication through a digital signature turns into an essential task in WSN. Verification of individual signature is taking too much time and it is not suitable for wireless sensor network. Digital signature verification time can be reduced by using batch verification techniques in WSN. Therefore, the goal of this research is to examine and analyze the different type of batch verification algorithm based on Elliptic Curve Cryptography (ECC). With respect to security, the entire algorithm is identical to the standard Elliptic Curve Digital Signature Algorithm (ECDSA) verification algorithm. These algorithms are effectively limited to small batch sizes.

Secure Data Transmission in Internet of Medical Things Using RES-256 Algorithm

In this article, the concept of cryptographic algorithms is used as an efficient access control mechanism for Internet of Medical Things-based health care system. The algorithms, such as Rivest Cipher (RC6), are used to generate the key value, and elliptic curve digital signature algorithm will encrypt the key value from RC6 and the encrypted output is send to secure hash algorithm (SHA256) for hashing process based on cipher value which improves data integrity. Furthermore, these high-security algorithms are used to provide availability and confidentiality to protect sensitive information from implantable devices and strengthen the health care systems through enhanced services. Comprehensive experimental analysis and simulation results indicate that the proposed scheme is more secure against various known attacks, such as denial of service, router attack, and sensor attacks. This proposed system has better resistance protocols in analyzing the safety of patients.

Lightweight Authentication Model for IoT Environments Based on Enhanced Elliptic Curve Digital Signature and Shamir Secret Share

Lightweight Authentication Model for IoT Environments Based on Enhanced Elliptic Curve Digital Signature and Shamir Secret Share

Speeding-Up Elliptic Curve Cryptography Algorithms

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.

How Not to Handle Keys: Timing Attacks on FIDO Authenticator Privacy

This paper presents a timing attack on the FIDO2 (Fast IDentity Online) authentication protocol that allows attackers to link user accounts stored in vulnerable authenticators, a serious privacy concern. FIDO2 is a new standard specified by the FIDO industry alliance for secure token online authentication. It complements the W3C WebAuthn specification by providing means to use a USB token or other authenticator (which holds the secret authenticating material and implements FIDO protocols) as a second factor during the authentication process. From a cryptographic perspective, the protocol is a simple challenge-response where the elliptic curve digital signature algorithm is used to sign challenges. To protect the privacy of the user the token uses unique key pairs per service. To accommodate for small memory, tokens use various techniques that make use of a special parameter called a key handle sent by the service to the token with which the token can securely produce an authentication key (through generation or decryption). We identify and analyse a vulnerability in the way the processing of key handles is implemented that allows attackers to remotely link user accounts on multiple services. We show that for vulnerable authenticators there is a difference between the time it takes to process a key handle for a different service but correct authenticator, and for a different authenticator but correct service. This difference can be used to perform a timing attack allowing an adversary to link user’s accounts across services. We present several real world examples of adversaries that are in a position to execute our attack and can benefit from linking accounts. We found that two of the eight hardware authenticators we tested were vulnerable despite FIDO level 1 certification, indicating a not insignificant problem. This vulnerability cannot be easily mitigated on authenticators because, for security reasons, they usually do not allow firmware updates. In addition, we show that due to the way existing browsers implement the WebAuthn standard, the attack can be executed remotely. However, we discuss countermeasures that can be implemented by browser providers to mitigate the remote form of the attack.

A flexible and lightweight privacy-preserving handshake protocol based on DTLShps for IoT

Anonymous authentication is widely studied for preserving the privacy of IoT devices . Although attribute-based signature (ABS) schemes can show identity attributes flexibly, letting the private key be generated by someone else is not safe. The computational overhead of traditional anonymous credential schemes based on zero-knowledge proofs (ZKP) is heavy for resource-constrained IoT devices. DTLShps, a lightweight handshake protocol based on software-defined networking (SDN), brings a new thought to verify certificates for resource-constrained IoT devices without anonymous functions. In this article, a lightweight privacy-preserving handshake protocol is designed based on DTLShps to flexibly present attributes of anonymous certificates for resource-constrained IoT devices. An authorization code is designed to represent the authorization status of each identity attribute defined in the X.509 standard. The IoT device cooperating with the CA can flexibly show arbitrary identity attributes to its peer by the authorization code. Only one signing operation of the elliptic curve digital signature algorithm (ECDSA) is needed to grant the authorization on the IoT device with the cooperation of the controller. The security of the proposed scheme is validated by the BAN logic and the tool Scyther. The performance evaluation shows that the computational delay on the IoT device and overall handshake delay is effectively reduced compared with the existing anonymous certificate schemes.

Reinforced securing of data leakage in Mobile Ad hoc Network (MANET) by hybrid mechanism of identity based encryption (IBE)

In Mobile Ad hoc Network (MANET), private data leakage that involves user’s private keys may become a threat to the computing systems security. It is essential that usual requirement of traditional cryptographic patterns or mechanisms have been performed for enduring several leakage attacks. However, the attacker can track and crack the cryptographic security due to the performance of continuous leakage attacks, which assist in introducing leakage resilience cryptography. But, still there are certain issues such as data loss, data failure system, data affecting and system break that are not yet resolved. As a result, various bounded-leakage models have been created for Identity Based Encryption (IBE) constructions that fail to fulfill their stated security under continuous-leakage assaults. This paper has introduced a hybrid mechanism of security to resolve the above listed issues by focusing in avoiding continuous leakage resilient through modified IBE schemes using Adaptive Chosen Cipher-text Attacks (ACCA) with Elliptical Curve Digital Signature Algorithm (ECDSA).

A unique secure multimodal biometrics-based user anonymous authenticated key management protocol (SMUAAKAP) based on block chain mechanism for generic HIoTNs

The concept of blockchain has sparked hopes in the field of communication security between IoT devices. In blockchain, all network nodes need to verify its legitimacy before accepting and recording it. Users of HIoTNs (Hierarchical IoT Networks) want to get real-time data from specific sensors in a specific implementation. Users need authentications at GNs for obtaining their required services. On successful authentications, parties on either sides of communication can create secret session keys for safe communications. Critical issues like this in HIoTNs are addressed in this work by its novel proposed multimodal-biometrics based lightweight user authentications. The scheme based on block chain technologies is called SMUAAKMPs (Secure Multimodal Biometrics-based User Anonymous Authenticated Key Management Protocols). ECDSAs (Elliptic Curve Digital Signature Algorithms) are utilised for devices and GNs, to generate public and private keys. In addition, multimodal biometric verifications are executed using fuzzy commitment approaches. The fuzzy commitment technique is then used to validate the biometric authentication using the segmented face. This work's detailed security analyses use ROR (Real-Or-Random) models where formal security verifications are done by software verification tool AVISPAs (Automated Validation of Internet Security Protocols and Applications). Informal security analyses show that the proposed SMUAAKMPs withstand multiple known attacks. The system also provides improved safety and functionalities at reduced costs in computations and communications when compared to UABKMPs, UAKMPs, and SMBUAKEPs.

A New Certificateless Signcryption Scheme for Securing Internet of Vehicles in the 5G Era

The application of digital signature technology to the Internet of vehicles (IoV) is affected by its network and communication environment. In the 5G era, the influx of a large number of intelligent devices into the mobile Internet requires a low transmission delay and power consumption as well as high-security requirements. To the best of our knowledge, a well-designed solution in which signcryption technology is used has not been proposed in the IoV research area. Motivated by the fact, a certificateless signcryption scheme based on the elliptic curve digital signature algorithm, in which pseudonym and timestamp mechanism are also considered, has been designed in this paper. We prove that the scheme proposed by us can be reduced to solving the difficulty of the computational Diffie–Hellman problem with a standard model, showing that the scheme meets requirements on both security and efficiency, which provides a comparative analysis with the state-of-the-art schemes in terms of security analysis, computational cost, and communication cost, demonstrating that the scheme proposed by us is suitable to be deployed in the IoV environment, which is of the characteristics of high-speed vehicle movement.

Holistic Research on Blockchain’s Consensus Protocol Mechanisms with Security and Concurrency Analysis Aspects of CPS

In the present era, the consensus for blockchain is of three types: consortium/permissioned, decentralized/permissionless, and somewhat decentralized. Presently, security and privacy of blockchain scenarios are in four directions: auditability and transparency, accountability and nonrepudiation, contract privacy, and transactional privacies. Blockchain works on multilayered architectures with its consensus mechanisms. In this paper, important mechanisms of various consensus protocols for application specific usage are analyzed. In general, these consensus mechanisms have four groups of properties; all are examined and discussed. Moreover, the security analysis is shown. Furthermore, the paper examines the elliptic curve digital signature algorithm (ECDSA), which is in use by the cryptocurrencies along with many blockchain-based systems. Moreover, a variant of ECDSA (vECDSA) is also considered. In particular, ECDSA and vECDSA are compared in this research. In addition, modeling and analysis aspects related to the security and concurrency aspects of CPS are discussed. In particular, Petri-net-based models of CPS are considered, especially in terms of liveness and boundedness properties of the system.

Attacks Against White-Box ECDSA and Discussion of Countermeasures

This paper deals with white-box implementations of the Elliptic Curve Digital Signature Algorithm (ECDSA): First, we consider attack paths to break such implementations. In particular, we provide a systematic overview of various fault attacks, to which ECDSA white-box implementations are especially susceptible. Then, we propose different mathematical countermeasures, mainly based on masking/blinding of sensitive variables, in order to prevent or at least make such attacks more difficult. We also briefly mention some typical implementational countermeasures and their challenges in the ECDSA white-box scenario. Our work has been initiated by the CHES challenge WhibOx Contest 2021, which consisted of designing and breaking white-box ECDSA implementations, so called challenges. We illustrate our results and findings by means of the submitted challenges and provide a comprehensive overview which challenge could be solved in which way. Furthermore, we analyze selected challenges in more details.

Combining Elliptic Curve Cryptography and Blockchain Technology to Secure Data Storage in Cloud Environments

Many encryption strategies have been applied to ensure data confidentiality and improve cloud security. The most recent cryptosystems are based on homomorphic (HE), attribute-based (ABE), and hybrid encryption. However, most of them suffer from numerous drawbacks: high time consumption, encrypted message size, and some vulnerabilities. Hence, a secure method is highly required to get a satisfying security level while keeping the computational complexity reduced. This paper outlines a novel technique that combines elliptic curve cryptography (ECC) and Blockchain technology. The data is first encoded using the Elliptic Curve Integrated Encryption Scheme, then signed using signed using the Elliptic Curve Digital Signature Algorithm, and finally confirmed by the blockchain network before being stored in the cloud. The performance evaluation results prove that the proposed system is highly resistant to man-in-the-middle and replay attacks and performs better than a set of existing solutions in terms of cryptography cost, encryption/decryption time, and algortithm complexity.