Elliptic Curve Cryptosystem Research Articles

Cryptanalysis and Improvement of a Proxy Signcryption Scheme in the Standard Computational Model

Proxy signcryption is essential security primitive for emerging secure communication such as e-business, mobile agents, online voting, contract signing, and online auction. It combines the functionality of a proxy signature and encryption to achieve basic security features maintaining a low computational and communicational cost. Ming proposed Proxy Signcryption (PSC) scheme in the standard computational model, claimed it to be secured against: (1) Indistinguishable Chosen Ciphertext Attack (IND-CCA) under the Decisional Bi-linear Diffie-Hellman (DBDH) assumption (2) Existentially Unforgeable Chosen Message Attack (EUF-CMA) under the Computational Diffie Hellman (CDH) assumption. This paper first provides a security analysis to check the correctness and validity of the said PSC scheme. Furthermore, it proves PSC is vulnerable to the launched cryptanalysis attacks. It is established that the PSC is neither semantically secured against IND-CCA nor existentially secured against EUF-CMA in its defined security model. Secondly, we propose an improved new proxy signcryption scheme (N-PSC) based on Elliptic Curve Cryptosystem (ECC) without bi-linear pairing secure against IND-CCA and EUF-CMA for Type-1 adversary A 1 in the standard computational model. It is also proved that the new proposed N-PSC scheme achieves an extra security property of judge verification in case of signature dispute between the proxy correspondents, as well as it outperforms the existing states of the art schemes including the Ming scheme in terms of cost efficiency which makes the new proposed scheme suitable for scarce resources constraint proxy enabled communication applications.

Efficient and Provably Secure Anonymous User Authentication Scheme for Patient Monitoring Using Wireless Medical Sensor Networks

Wireless medical sensor networks (WMSNs) are playing an increasingly important role in smart healthcare applications. Since the data transmitted in WMSNs is closely related to patient's life and health, and considering the resource-constrain feature of the sensor node, constructing an authentication scheme for WMSNs is a formidable task. Recently, Soni et al. presented an elliptic curve cryptosystem based three-factor authentication scheme for WMSNs. However, we discover that their scheme suffers from serious vulnerabilities, such as sensor node capture attack, no forward secrecy, and the violation of three-factor security. To enhance the security and efficiency, we present a novel scheme using Rabin cryptosystem and chaotic maps. We use several widely-accepted security analysis methods to verify the correctness and security of our scheme. The Burrows-Abadi-Needham logic proof confirms the completeness of our scheme. The heuristic analysis indicates that our scheme is resistant to potential attacks and provides various security attributes like forward secrecy and three-factor security. Furthermore, we demonstrate that our scheme is provably secure in the random oracle model. Finally, the performance comparisons indicate that our scheme is superior to the related schemes both in security and efficiency and is more applicable to WMSNs owing to low overhead of the sensor node.

Microblaze-based parallel implementations of elliptic curve scalar multiplication over <i>F<SUB align="right">p</i> on FPGA

This paper presents flexible software/hardware parallel architectures for embedded elliptic curve cryptosystem (ECC) on FPGA as multi-processor system on programmable circuit (MPSoPC) design. The implementations perform elliptic curve scalar multiplication (ECSM) over arbitrary prime fields (Fp) using montgomery power ladder (MPL) algorithm and Chudnovsky projective system. Our aim is to achieve the best trade-off between flexibility, area and speed. In fact, the integration of multi Microblaze processors allows not only the flexibility of the overall system but also the exploitation of the parallelism in ECSM computation with several degrees. At the low abstraction level, the critical finite field operation which is Montgomery modular multiplication (MMM) is implemented in hardware Accelerator MMM (AccMMM) core based on the modified high radix-r (r = 232) MMM algorithm. The proposed architectures have been implemented in Xilinx Virtex-5 FPGA. The execution times for performing 256-bit and 521-bit ECSM are 19.98 ms and 81.42 ms, respectively.

A Combined Single Trace Attack on Global Shuffling Long Integer Multiplication and its Novel Countermeasure

Advanced collision-based single trace attacks which can be applied on simple power analysis resistant scalar multiplications become virtual threat on elliptic curve cryptosystems recently as their practical experimental results are increasingly reported in the literature. Since such attacks are based on detecting collisions of data dependent leakage caused by underlying long integer multiplications, so-called global shuffling countermeasure which breaks such collision correlation by independently randomizing the execution order of unit operations such as single precision multiplication and carry propagation, is considered as promising countermeasure if theoretical randomness of shuffling order is guaranteed. In this paper, we firstly analyze the practical security of the global shuffling long integer multiplications by exhibiting a combined single trace attack on software implementations on an ARM Cortex-M4 microcontroller. Our combined attack consists of a simple power analysis for revealing random permutation vectors which enables later collision-based single trace attack. First we demonstrate how to reveal random permutation vectors for carry propagation process of whole global shuffling long integer multiplications within a single power trace by simple power analysis accompanied with straightforward substitution of power consumption samples. Then we perform collision-based single trace attacks after rearranging the order of subtraces for unit carry propagations based on revealed permutation vectors. Since the vulnerability to simple power analysis is originated from the if-statement for selection of proper entries of the permutation vectors, we propose a novel countermeasure which eliminates such selection with simple addition and modulus operation and also demonstrate practical result achieving regularity in power trace patterns.

An hyper elliptic curve based efficient signcryption scheme for user authentication

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.

Formal Verification of Forward-Secure Authenticated Key Exchange Scheme for Location-based Service Application

A Location-based service (LBS) is a popularinformation service which uses the geographical position of theuser to provide service. Major challenges for wide deploymentof such services is security and privacy, in our paper we propose a generic model of authenticated key exchange (AKE)protocol termed as forward-secure authenticated key exchangeprotocol (FSAKE) which uses elliptic curve cryptosystem. TheFSAKE protocol supports concurrent sessions and is used fortheexchange of secure seed values which are used in forward-securepseudo-random number generators to generate secret keys formessage authentication and symmetric encryption. The FSAKEprotocol is a key evolving scheme which updates the long-termkeys (LTKs) at regular intervals and guarantees the security ofthe past keys and mitigates the damage caused by exposure ofthe current key. We make use of Scyther model checking tool toprove the correctness of FSAKE protocol security.

EMBEDDING FINITE FIELDS INTO ELLIPTIC CURVES

Many elliptic curve cryptosystems require an encoding function from a finite field Fq into Fq-rational points of an elliptic curve. We propose a uniform encoding to general elliptic curves over Fq. We also discuss about an injective case of SWU encoing for hyperelliptic curves of genus 2. Moreover we discuss about an injective encoding for elliptic curves with a point of order two over a finite field and present a description for these elliptic curves.

A Secure Anonymous Authentication Protocol for Roaming Service in Resource-Constrained Mobility Environments

Mobile user authentication is very crucial to ensure the authenticity and privacy of roaming users in mobility environments. The existing communication technologies are highly vulnerable to security threats and pose a great challenge for the wireless networks being used today. Because the mode of a wireless channel is open, these networks do not carry any inherent security and hence are more prone to threats. Consequently, designing a robust scheme for roaming service in the mobile environment is always challenging. Recently, Kuo et al. proposed an efficient authentication protocol for roaming and they claimed that the protocol can resist several security threats in mobile networks. In this paper, we analyze the security of Kuo et al.’s. authentication protocol and show that the protocol is exposed to an insider attack, replay attack, denial-of-service attack and cannot provide fair key agreement, user untraceability, and local password verification. To combat these security flaws, we propose a secure authentication scenario for roaming service using elliptic curve cryptosystem. The proposed authentication protocol is implemented in HLPSL language using automated validation of internet security protocols and applications as a formal verification tool to prove that the novel protocol is free from known attacks. Further, we applied Burrows–Abadi–Needham logic to validate the correctness of the authentication system. The proposed protocol not only improves security but also retains a low communicational and computational overhead.

A novel DNA based password authentication system for global roaming in resource-limited mobile environments

Mobile environments are highly vulnerable to security threats and pose a great challenge for the wireless and mobile networks being used today. Because the mode of a wireless channel is open, these networks do not carry any inherent security and hence are more prone to attacks. Therefore, designing a secure and robust protocol for authentication in a global mobile network is always a challenging. In these networks, it is crucial to provide authentication to establish a secure communication between the Mobile User (MU), Foreign Agent (FA) and Home Agent (HA). In order to secure communication among these entities, a number of authentication protocols have been proposed. The main security flaw of the existing authentication protocols is that attackers have the ability to impersonate a legal user at any time. Moreover, the existing authentication protocols in the literature are exposed to various kind of cryptographic attacks. Besides, the authentication protocols require larger key length and more computation overhead. To remedy these weaknesses in mobility networks, DNA (Deoxyribo Nucleic Acid) based authentication scheme using Hyper Elliptic Curve Cryptosystem (HECC) is introduced. It offers greater security and allows an MU, FA and HA to establish a secure communication channel, in order to exchange the sensitive information over the radio link. The proposed system derive benefit from HECC, which is smaller in terms of key size, more computational efficiency. In addition, the security strength of this authentication system is validated through widely accepted security verification tool called ProVerif. Further, the performance analysis shows that the DNA based authentication system using HECC is secure and practically implementable in the resource-constrained mobility nodes.

A Lightweight and Provable Secured Certificateless Signcryption Approach for Crowdsourced IIoT Applications

Industrial Internet of Things (IIoT) is a new type of Internet of Things (IoT), which enables sensors to merge with several smart devices to monitor machine status, environment, and collect data from industrial devices. On the other hand, cloud computing provides a good platform for storing crowdsourced data of IIoT. Due to the semi-trusted nature of cloud computing and communication through open channels, the IIoT environment needs security services such as confidentiality and authenticity. One such solution is provided by the identity-based signcryption. Unfortunately, the identity-based signcryption approach suffers from the key escrow problem. Certificateless signcryption is the alternative of identity-based signcryption that can resolve the key escrow problem. Here, we propose a lightweight certificateless signcryption approach for crowdsourced IIoT applications with the intention of enhancing security and decreasing the computational cost and communication overhead. The security and efficiency of the proposed approach are based on the hyper elliptic curve cryptosystem. The hyper elliptic curve is the advance version of the elliptic curve having small parameters and key size of 80 bits as compared to the elliptic curve which has 160-bits key size. Further, we validate the security requirements of our approach through automated validation of Internet security protocols and applications (AVISPA) tool with the help of high level protocol specification language (HLPSL). Moreover, our lightweight and secured scheme will attract low resource devices and will become a perk in the environment of IIoT.

Efficient Implementation on Low-Cost SoC-FPGAs of TLSv1.2 Protocol with ECC_AES Support for Secure IoT Coordinators

Security management for IoT applications is a critical research field, especially when taking into account the performance variation over the very different IoT devices. In this paper, we present high-performance client/server coordinators on low-cost SoC-FPGA devices for secure IoT data collection. Security is ensured by using the Transport Layer Security (TLS) protocol based on the TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA256 cipher suite. The hardware architecture of the proposed coordinators is based on SW/HW co-design, implementing within the hardware accelerator core Elliptic Curve Scalar Multiplication (ECSM), which is the core operation of Elliptic Curve Cryptosystems (ECC). Meanwhile, the control of the overall TLS scheme is performed in software by an ARM Cortex-A9 microprocessor. In fact, the implementation of the ECC accelerator core around an ARM microprocessor allows not only the improvement of ECSM execution but also the performance enhancement of the overall cryptosystem. The integration of the ARM processor enables to exploit the possibility of embedded Linux features for high system flexibility. As a result, the proposed ECC accelerator requires limited area, with only 3395 LUTs on the Zynq device used to perform high-speed, 233-bit ECSMs in 413 µs, with a 50 MHz clock. Moreover, the generation of a 384-bit TLS handshake secret key between client and server coordinators requires 67.5 ms on a low cost Zynq 7Z007S device.

Enhanced Framework for Ensuring Privacy Preserving Image Retrieval in Cloud

Large scale of images data sets are being produced every day by various digital devices. Due to huge computational jobs make people seizure to cloud platforms for their efficient & economical reckoning resources. These computing platforms in which assets are provided as services of the internet. Sensitive information stored in cloud makes more challenging in data security and access control. Once data is uploaded to cloud-platform, the privacy and security of image-data fully depend and believe upon cloud service provider honesty. Our proposed work deals with securing image where high protections are applied on multimedia contents. This paper deals with studies security challenges algorithms lies in image at the time of constructing cloud platform. In this a new enhanced security technique investigated, includes secure by using computation and encryption, act as a security information guard for high secrecy in cloud platform data storage areas. In our research work, cipher-text image is created and performing encryption-decryption at User level. Data hiding and ECC (Elliptic curve cryptosystem) based watermarking technique at cloud computing platform.

M-folding method–based elliptic curve cryptosystem for industrial cyber-physical system

Recently, cyber-physical system is widely used for smart system control in various fields. Various functions of the cyber-physical system must overcome the limited hardware resources constraint of an embedded system. In addition, the data required from the industrial cyber-physical system are critical; therefore, a highly secure encryption technique is required. However, security and computational throughput are incompatible with each other in the cryptographic technique; therefore, the industrial cyber-physical system needs to adopt a highly efficient and secure encryption technique considering the limited available resources. This study applies the m-folding method to the highly secure elliptic curve algorithm to improve efficiency and proposes the cryptosystem optimized for the resource-constrained industrial cyber-physical system. The proposed m-folding method–based elliptic curve encryption showed 50% faster encryption than the existing methods.

Secured and Efficient Data Transmission in Manets Against Malicious Attack using DSR Routing and BCS Clustering with Hybrid AES-ECC Cryptanalysis

Mobile Ad-Hoc Network (MANET) is a self-configuring network of movable nodes linked by wireless creating a random topology. The nodes are free to move randomly. Thus, the networks wireless topology may be haphazard and may alter rapidly. The efficient route is established using Dynamic source routing (DSR) Routing Protocol. The Binary crow search (BCS) algorithm is used for clustering of sensor nodes and maintaining load balancing in an efficient way. Efficient black hole detection using Malicious Node Detection Mechanism-TX/RX (MNS-TX/RX) with optimized routing algorithm is implemented in a secure environment by using Advanced Hybrid Advanced Encryption Standard (AES) cryptanalysis and Elliptic Curve Cryptosystems. Thus “DSR-BCS-HAES-EEC-MANETs” algorithm has precisely detected the black hole node and finds the proper solution for transmitting data for maintaining lifetime and Load- balancing by analyzing performance such as Through-put, routing overhead, packet delivery ratio(PDR), drop, delay and energy consumption in a secure environment.

Energy Efficient Lightweight Mutual Authentication Protocol (REAP) for MBAN Based on Genus-2 Hyper-Elliptic Curve

In the modern era, medical body area network (MBAN) emerges with the development of information and communication technology to improve the quality of healthcare services. As MBAN contains patient’s sensitive information and usually be transmitted via wireless channel, it is vulnerable to security threats and privacy attacks. To preserve privacy, it is important to provide authentication to prevent unauthorized access by intruders. Since MBAN consists of resource constraint devices to monitor physiological conditions, light-weight authentication protocol are in demand to reduce computational time and communication cost. Hence the paper proposes an eneRgy efficient, lightweight mutual authentication protocol for MBAN based on genus 2 hyper-elliptic curve cryptosystem, since it provides high security with smaller key size than Rivest–Shamir–Adleman and elliptic curve cryptosystem. The proposed authentication protocol is validated using the widely accepted AVISPA tool for its secure. In addition, BAN logic is used to analyse the formal security features and resistance to possible attacks are discussed informally.

A Secure and Efficient ECC-Based Anonymous Authentication Protocol

Nowadays, remote user authentication protocol plays a great role in ensuring the security of data transmission and protecting the privacy of users for various network services. In this study, we discover two recently introduced anonymous authentication schemes are not as secure as they claimed, by demonstrating they suffer from offline password guessing attack, desynchronization attack, session key disclosure attack, failure to achieve user anonymity, or forward secrecy. Besides, we reveal two environment-specific authentication schemes have weaknesses like impersonation attack. To eliminate the security vulnerabilities of existing schemes, we propose an improved authentication scheme based on elliptic curve cryptosystem. We use BAN logic and heuristic analysis to prove our scheme provides perfect security attributes and is resistant to known attacks. In addition, the security and performance comparison show that our scheme is superior with better security and low computation and communication cost.

Automatic generation of HCCA-resistant scalar multiplication algorithm by proper sequencing of field multiplier operands

Horizontal collision correlation analysis, in short HCCA, imposes a serious threat to simple power analysis-resistant elliptic curve cryptosystems involving unified algorithms, e.g., Edwards curve unified formula. This attack can be mounted even in the presence of differential power analysis-resistant randomization schemes. In this paper, we have designed an effective countermeasure for HCCA protection, where the dependency of side-channel leakage from a school–book multiplication with the underlying multiplier operands is investigated. We have shown how changing the sequence in which the operands are passed to the multiplication algorithm introduces dissimilarity in the information leakage. This disparity has been utilized in constructing a minimal cost countermeasure against HCCA. This countermeasure integrated with an effective randomization method has been shown to successfully thwart HCCA. Additionally we provide experimental validation for our proposed countermeasure technique on a SASEBO platform. To the best of our knowledge, this is the first time that asymmetry in information leakage has been utilized in designing a side-channel countermeasure.

RSMA: Reputation System-Based Lightweight Message Authentication Framework and Protocol for 5G-Enabled Vehicular Networks

Traditional public key infrastructure-based authentication schemes provide vehicular networks with identity authentication and conditional privacy protection, which are not sufficient for assessing the credibility of messages. Additionally, although the new generation of cellular networks (5G) can dramatically improve the transmission efficiency of the messages, many existing authentication schemes are based on complex bilinear pairing operations, and the calculation time is too long to be suitable for delay-sensitive 5G-enabled vehicular networks. To address these issues, we propose a reputation system-based lightweight message authentication framework and protocol for 5G-enabled vehicular networks. The trusted authority (TA) is in charge of reputation management. A vehicle with a reputation score below the given threshold cannot obtain a credit reference from the TA for participating in the communication; therefore, the number of untrusted messages in vehicular networks is reduced from the source. Security analysis shows that our scheme is secure against an adaptively chosen-message attack, and also satisfies a series of requirements of vehicular networks. The scheme is based on the elliptic curve cryptosystem and supports batch authentication; therefore, it shows better performance in terms of time consumption when compared with related schemes.

Efficient Lightweight Hardware Structures of Point Multiplication on Binary Edwards Curves for Elliptic Curve Cryptosystems

This paper presents efficient lightweight hardware implementations of the complete point multiplication on binary Edwards curves (BECs). The implementations are based on general and special cases of binary Edwards curves. The complete differential addition formulas have the cost of [Formula: see text] and [Formula: see text] for general and special cases of BECs, respectively, where [Formula: see text] and [Formula: see text] denote the costs of a field multiplication, a field squaring and a field multiplication by a constant, respectively. In the general case of BECs, the structure is implemented based on 3 concurrent multipliers. Also in the special case of BECs, two structures by employing 3 and 2 field multipliers are proposed for achieving the highest degree of parallelization and utilization of resources, respectively. The field multipliers are implemented based on the proposed efficient digit–digit polynomial basis multiplier. Two input operands of the multiplier proceed in digit level. This property leads to reduce hardware consumption and critical path delay. Also, in the structure, based on the change of input digit size from low digit size to high digit size the number of clock cycles and input words are different. Therefore, the multiplier can be flexible for different cryptographic considerations such as low-area and high-speed implementations. The point multiplication computation requires field inversion, therefore, we use a low-cost Extended Euclidean Algorithm (EEA) based inversion for implementation of this field operation. Implementation results of the proposed architectures based on Virtex-5 XC5VLX110 FPGA for two fields [Formula: see text] and [Formula: see text] are achieved. The results show improvements in terms of area and efficiency for the proposed structures compared to previous works.

High-performance Implementation of Elliptic Curve Cryptography Using Vector Instructions

Elliptic curve cryptosystems are considered an efficient alternative to conventional systems such as DSA and RSA. Recently, Montgomery and Edwards elliptic curves have been used to implement cryptosystems. In particular, the elliptic curves Curve25519 and Curve448 were used for instantiating Diffie-Hellman protocols named X25519 and X448. Mapping these curves to twisted Edwards curves allowed deriving two new signature instances, called Ed25519 and Ed448, of the Edwards Digital Signature Algorithm. In this work, we focus on the secure and efficient software implementation of these algorithms using SIMD parallel processing. We present software techniques that target the Intel AVX2 vector instruction set for accelerating prime field arithmetic and elliptic curve operations. Our contributions result in a high-performance software library for AVX2-ready processors. For example, our library computes digital signatures 19% (for Ed25519) and 29% (for Ed448) faster than previous optimized implementations. Also, our library improves by 10% and 20% the execution time of X25519 and X448, respectively.