Elliptic Curve Diffie-Hellman Key Exchange Research Articles

An image encryption method based on modified elliptic curve Diffie-Hellman key exchange protocol and Hill Cipher

Abstract Digital image protection is crucial since images often contain private and sensitive information in business, medical, and military. One of the best techniques for securing the content of these images is encryption. This article introduces a cryptosystem known as the elliptic curve Diffie-Hellman Hill Cipher (ECDHHC) that uses the modified eliptic curve Diffie-Hellman (ECDH) key exchange protocol to generate the shared secret key integrated with the Hill Cipher. An elliptic curve point-based secret shared key matrix using the ECDHHC, which will be used for encryption and decryption, is generated. Thereafter, the input image is split into a set of 8 × 8 submatrices and then changes the values of these matrices by multiplying each block with the secret shared key matrix. The encrypted image is constructed by merging all encrypted blocks. With this combination, the correlation between adjacent pixels in the ciphered image is effectively removed, and the level of unpredictability and uncertainty for the ciphered image is also enhanced. The suggested approach used the key space, entropy, histogram, antinoise attack, differential attack, and correlation coefficient to evaluate the performance of the encryption method. According to simulation findings, the proposed method offers a high level of security and efficiency, and resists attackers.

Authenticated Public Key Elliptic Curve Based on Deep Convolutional Neural Network for Cybersecurity Image Encryption Application.

The demand for cybersecurity is growing to safeguard information flow and enhance data privacy. This essay suggests a novel authenticated public key elliptic curve based on a deep convolutional neural network (APK-EC-DCNN) for cybersecurity image encryption application. The public key elliptic curve discrete logarithmic problem (EC-DLP) is used for elliptic curve Diffie-Hellman key exchange (EC-DHKE) in order to generate a shared session key, which is used as the chaotic system's beginning conditions and control parameters. In addition, the authenticity and confidentiality can be archived based on ECC to share the EC parameters between two parties by using the EC-DHKE algorithm. Moreover, the 3D Quantum Chaotic Logistic Map (3D QCLM) has an extremely chaotic behavior of the bifurcation diagram and high Lyapunov exponent, which can be used in high-level security. In addition, in order to achieve the authentication property, the secure hash function uses the output sequence of the DCNN and the output sequence of the 3D QCLM in the proposed authenticated expansion diffusion matrix (AEDM). Finally, partial frequency domain encryption (PFDE) technique is achieved by using the discrete wavelet transform in order to satisfy the robustness and fast encryption process. Simulation results and security analysis demonstrate that the proposed encryption algorithm achieved the performance of the state-of-the-art techniques in terms of quality, security, and robustness against noise- and signal-processing attacks.

Design of an Integrated Cryptographic SoC Architecture for Resource-Constrained Devices

One of the active research areas in recent years that has seen researchers from numerous related fields converging and sharing ideas and developing feasible solutions is the area of hardware security. The hardware security discipline deals with the protection from vulnerabilities by way of physical devices such as hardware firewalls or hardware security modules rather than installed software programs. These hardware security modules use physical security measures, logical security controls, and strong encryption to protect sensitive data that is in transit, in use, or stored from unauthorized interferences. Without mechanisms to circumvent the ever-evolving attacking strategies on hardware devices and the data that they process or store, billions of dollars will always be lost to attackers who ply their trade by targeting such vulnerable devices. This paper, therefore, proposes an integrated cryptographic SoC architecture solution to this menace. The proposed architecture provides security by way of key exchange, management, and encryption. The proposed architecture is based on a True Random Number generator core that generates secret keys that are used in Elliptic Curve Diffie-Hellman Key Exchange to perform elliptic curve scalar multiplication to obtain public and shared keys after the exchange of the public keys. The proposed architecture further relies on a Key Derivation Function based on the CubeHash algorithm to obtain Derived Keys that provide the needed security using the ChaCha20_Poly1305 Authenticated Encryption with Associated (AEAD) Data Core. The proposed Integrated SoC architecture is interconnected by AMBA AHB-APB on-chip bus and the system is scheduled and controlled using the PicoRV32 opensource RISC-V processor. The proposed architecture is tested and verified on the Virtex-4 FPGA board using a custom-designed GUI desktop application.

Towards Blockchain-Based Secure Storage and Trusted Data Sharing Scheme for IoT Environment

Nowadays, cloud-based storage systems play a vital role in IoT data storage, processing, and sharing. Despite its contribution, the current cloud-based architecture may cause severe data leakage or jeopardize user privacy. Meanwhile, the cloud-based architecture heavily relies on a trusted third-party auditor (TPA) and runs in a centralized control manner. However, the TPA may not be a completely trustworthy entity, and a single point of failure might cause the centralized system to collapse. Fortunately, with the advent of blockchain technology, the decentralized storage model has gained popularity. A decentralized storage system successfully eradicates the rule of TPA, solves the problem of a single point of failure, and has many advantages over a centralized control architecture, such as low storage prices and high throughput. This study offers a blockchain-based decentralized distributed storage and sharing scheme that provides end-to-end encryption and fine-grained access control. In our proposed IoTChain model, fine-grained permission is based on attribute-based access control (A-BAC) policy by employing the Ethereum blockchain as an auditable access control layer. Smart contracts are tailored for the IoTChain model, which combines the Ethereum blockchain and the interplanetary file system (IPFS). We used an advanced encryption standard (AES) for encryption and the elliptic curve Diffie-Hellman key exchange protocol for secret key sharing between data owners and users. Also, the proof-of-work (PoW) consensus mechanism is replaced with a proof-of-authority (PoA) to minimize system transaction cost and boost system throughput. Additionally, our solution has been tested on the Ethereum official test network Rinkeby, and the results demonstrate that our approach is realistic and economical on the IoT data.

Group Security Authentication and Key Agreement Protocol Built by Elliptic Curve Diffie Hellman Key Exchange for LTE Military Grade Communication

4G mobile communication is a global technology. Therefore, it is essential to enforce confidentiality between mobile users and their networks. This paper presents a Group Security Authentication and Key Agreement Protocol Built by Elliptic Curve Diffie Hellman Key Exchange (GSAKA-ECDHKE) to overcome and address the LTE networks Evolved Packet System Authentication and Key Agreement Protocol (EPS-AKA) protocol flaws and vulnerabilities. GSAKA-ECDHKE is presented for 4G mobile military group communications to provide security, confidentiality, and privacy while the users and networks authenticate. By embedding the Group Commander (GC) role in the EPS-AKA protocol to control the member authentication in the group. GSAKA-ECDHKE protocol is based on Elliptic Curve Diffie Hellman Key Exchange (ECDHKE) and hash function to generate and share secret Elliptic Curve (EC) key to encrypt and protect the routing authentication parameters. The Automated Validation of Internet Security Protocols and Applications (AVISPA) tool is used for security analysis and formal verification. AVISPA demonstrated that GSAKA-ECDHKE had overcome various known security attacks such as Man In The Middle (MITM), replay attacks, and Denial of Services (DoS) attacks, satisfying the evaluated security requirements. Additionally, the suggested protocol provides the lowest communication overheads compared to the existing group-based AKA protocols.

Efficient Hardware Implementation Of Elliptic Curve Diffie-Hellman Key Exchange Protocol

The aim of the present work is the hardware implementation of the elliptic curve Diffie-Hellman (ECDH) key exchange protocol on a reconfigurable circuit of type FPGA at the register-transfer level (RTL). Compared to the standard Diffie- Hellman (DH), based on exponentiation in a finite field, ECDH is known to provide equivalent level of security with lower number of bits used. Reduced bit usage implies less power and logic area are required to implement this cryptographic scheme. This is particularly important in secure embedded system, where a high level of security is required, but with low power consumption. The results show that ECDH can be implemented on FPGA with convincing performances in comparison with other published works

Image Encryption and Authentication With Elliptic Curve Cryptography and Multidimensional Chaotic Maps

Many researchers have used the properties of the popular Elliptic Curve Cryptography(ECC) to devise a stronger and faster image encryption algorithm to assure the secrecy of images during online transmission. In this paper, a robust Elliptic curve based image encryption and authentication model for both grayscale and color images has been proposed. The model uses the secure Elliptic Curve Diffie-Hellman(ECDH) key exchange to compute a shared session key along with the improved ElGamal encoding scheme. 3D and 4D Arnold Cat maps are used to effectively scramble and transform the values of plain image pixels. A well-structured digital signature is used to verify the authenticity of the encrypted image prior to decryption. The model produces good-quality cipher images with an average entropy of 7.9993 for grayscale and 7.99925 for the individual components of color images. The model has high average NPCR of 99.6%, average UACI of 33.3% and low correlation for both grayscale and color images. The model has low computational costs with minimized point multiplication operations. The proposed model is robust with high resilience against statistical, differential, chosen-plaintext(CPA), known-plaintext(KPA) and occlusion attacks.

An Unbalanced Security Protocol for IoT devices

Authenticated key exchange (AKE) protocol is a crucial process in Internet of Things. This paper aims to customize the Elliptic Curve Diffie-Hellman (ECDH)-based AKE according to the computational capability of devices. We propose a method to unbalance the computations in the ECDH key exchange scheme by configuring the more powerful device undertake one scalar multiplication on behalf of the computationally limited one. The analysis results show that the computationally unbalanced protocols are more friendly to computationally limited devices than the original one.

Kleptographic Attack on Elliptic Curve Based Cryptographic Protocols

Kleptography is the study of pilfering secure data secretly and subliminally. The concept of inserting backdoors was introduced two decades ago by Young and Yung. However, still it is a serious threat for modern cryptography. Different studies have proved that exploiting implementation errors of cryptographic algorithms needs less effort as compared to attacking its mathematical structure. Inserting the backdoor modifies the standard method of generating public and private key pairs in such away that the public information is meaningful for the attacker. This paper presents the kleptographic attack on cryptographic algorithm based on Elliptic curves. We show the technique of implementing backdoor against Edwards-curve Digital Signature Algorithm, Elliptic curve Diffie-Hellman key exchange scheme, Elliptic curve Digital Signature Algorithm, Elliptic curve Integrated Encryption Scheme, Elliptic curve ElGamal Encryption and Elliptic curve Qu-Vanstone implicit certificate scheme. In practical approach, backdoors are inserted in such a way that their identification is impossible by analyzing the output of an algorithm. Detection of kleptographic implementation is a complex task and very few studies can be found in this direction. We have explored the possibility of detection of malicious code inside the Elliptic curve based algorithms by using the idea of running time analysis. We have shown that by implementing strong Secretly Embedded Trapdoor with Universal Protection (SETUP) attack against Elliptic curve based algorithms, one can detect the presence of backdoor by analyzing the time difference in execution of an honest vs malicious version of code. We also modified the backdoor insertion mechanism in Edwards-curve Digital Signature Algorithm that results in negligible time difference making it impossible for the user to detect backdoor presence.

Cryptanalysis of elliptic curve hidden number problem from PKC 2017

In PKC 2017, the elliptic curve hidden number problem (EC-HNP) was revisited in order to rigorously assess the bit security of the elliptic curve Diffie–Hellman key exchange protocol. In this paper, we solve EC-HNP by using the Coppersmith technique which combines the idea behind the second lattice method of Boneh, Halevi and Howgrave-Graham for solving the modular inversion hidden number problem. We show that the hidden point in EC-HNP can be recovered asymptotically if about half of the most significant bits of the x-coordinates of the corresponding points are given. A similar result is also obtained for the least significant bits. We provide better bounds than the one in the work of PKC 2017, which needs about 5/6 of the bits as a result of a rigorous algorithm. However, our solution is based on a heuristic assumption. We verify the validity of our heuristic algorithm by computer experiments.

Design of Secure Chatting Application with End to End Encryption for Android Platform

In this paper, a secure chatting application with end to end encryption for smart phones that used the android OS has beenproposed. This is achieved by the use of public key cryptography techniques. The proposed application used the Elliptic Curve DiffieHellman Key Exchange (ECDH) algorithm to generate the key pair and exchange to produce the shared key that will be used for theencryption of data by symmetric algorithms. The proposed Application allows the users to communicate via text messages, voicemessages and photos. For the text message security the standard AES algorithm with a 128 bit key are used. The generated key (160 bit)minimized to 128 bit length by selecting the first 128 bit of the generated key in order to be used by the AES algorithm. For the voice andimage security processes the proposed application used the symmetric algorithm RC4 for this purpose.

FourQ on embedded devices with strong countermeasures against side-channel attacks

This work deals with the energy-efficient, high-speed and high-security implementation of elliptic curve scalar multiplication, elliptic curve Diffie-Hellman (ECDH) key exchange and elliptic curve digital signatures on embedded devices using Four $\mathbb {Q}$ Q and incorporating strong countermeasures to thwart a wide variety of side-channel attacks. First, we set new speed records for constant-time curve-based scalar multiplication, DH key exchange and digital signatures at the 128-bit security level with implementations targeting 8, 16 and 32-bit microcontrollers. For example, our software computes a static ECDH shared secret in $\sim$ ∼ 6.9 million cycles (or 0.86 seconds @8 MHz) on a low-power 8-bit AVR microcontroller which, compared to the fastest Curve25519 and genus-2 Kummer implementations on the same platform, offers 2x and 1.4x speedups, respectively. Similarly, it computes the same operation in $\sim$ ∼ 495 thousand cycles on a 32-bit ARM Cortex-M4 microcontroller, achieving a factor-1.9 speedup when compared to the fastest Curve25519 implementation targeting another Cortex-M4 platform. A similar speed performance is observed in the case of digital signatures. Second, we engineer a set of side-channel countermeasures taking advantage of Four $\mathbb {Q}$ Q 's rich arithmetic and propose a secure implementation that offers protection against a wide range of sophisticated side-channel attacks, including differential power analysis (DPA). Despite the use of strong countermeasures, the experimental results show that our Four $\mathbb {Q}$ Q software is still efficient enough to outperform implementations of Curve25519 that only protect against timing attacks. Finally, we perform a differential power analysis evaluation of our software running on an ARM Cortex-M4, and report that no leakage was detected with up to 10 million traces. These results demonstrate the potential of deploying Four $\mathbb {Q}$ Q on low-power applications such as protocols for the Internet of Things.

Compact ECDSA engine for IoT applications

Security problems introduced with rapid increase in deployment of Internet-of-Things devices can be overcome only with lightweight cryptographic schemes and modules. A compact prime field (GF(p)) elliptic curve digital signature algorithm (ECDSA) engine suitable for use in such applications is presented. Generic architecture of the engine makes it suitable for other elliptic curve (EC) based schemes (EC Diffie–Hellman key exchange, EC integrated encryption, EC factoring etc.) with slight modifications. The presented engine is composed of a simple microcoded controller and application-specific processing units. It can work with ECs of up to 256 bits, while 160-bit ECDSA signature generation takes 490 K cycles. The engine is implemented as an intellectual property (IP) in a 180 nm process. However, its architecture allows it to be implemented on any application specific integrated circuit (ASIC) or FPGA platform with dual-port memory support. In view of its gate count of 11,366 gate equivalents, the presented work is the most compact ECDSA engine with capability for a wide range of curves and different applications.

Efficient Implementation of NIST-Compliant Elliptic Curve Cryptography for 8-bit AVR-Based Sensor Nodes

In this paper, we introduce a highly optimized software implementation of standards-compliant elliptic curve cryptography (ECC) for wireless sensor nodes equipped with an 8-bit AVR microcontroller. We exploit the state-of-the-art optimizations and propose novel techniques to further push the performance envelope of a scalar multiplication on the NIST P-192 curve. To illustrate the performance of our ECC software, we develope the prototype implementations of different cryptographic schemes for securing communication in a wireless sensor network, including elliptic curve Diffie–Hellman (ECDH) key exchange, the elliptic curve digital signature algorithm (ECDSA), and the elliptic curve Menezes–Qu–Vanstone (ECMQV) protocol. We obtain record-setting execution times for fixed-base, point variable-base, and double-base scalar multiplication. Compared with the related work, our ECDH key exchange achieves a performance gain of roughly 27% over the best previously published result using the NIST P-192 curve on the same platform, while our ECDSA performs twice as fast as the ECDSA implementation of the well-known TinyECC library. We also evaluate the impact of Karatsuba’s multiplication technique on the overall execution time of a scalar multiplication. In addition to offering high performance, our implementation of scalar multiplication has a highly regular execution profile, which helps to protect against certain side-channel attacks. Our results show that NIST-compliant ECC can be implemented efficiently enough to be suitable for resource-constrained sensor nodes.

Security Analysis and Improvements of Session Key Establishment for Clustered Sensor Networks

WSN (wireless sensor network) is one of the main technologies in IoT (Internet of Things) applications or services. To date, several schemes have been proposed to establish a pair-wise key between two nodes in WSN, and most of them are designed to establish long-term keys used throughout the network lifetime. However, in the near future, if WSN will be used for information infrastructures in various fields such as manufacturing, distribution, or public facilities management and its life cycle can be as long as that of other common networks, it will definitely be advantageous in terms of security to encrypt messages using session keys instead of long-term keys. In this paper, we propose a session key establishment scheme for clustered sensor networks that is based on elliptic curve Diffie-Hellman (ECDH) key exchange and hash chain. The proposed scheme eliminates vulnerabilities of existing schemes for WSN and has improved security. The proposed scheme is efficient in terms of energy costs compared to related schemes.

A key management technique based on elliptic curves for static wireless sensor networks

AbstractThis paper presents a key distribution scheme based on elliptic curve Diffie–Hellman (ECDH) key exchange for static wireless sensor networks with node addition. The proposed scheme relies on the transitory master key approach for secret key establishment and addresses the man‐in‐the‐middle attack in ECDH key exchange. The major advantage of the proposed method compared with the state‐of‐the‐art schemes is the high resilience offered by this scheme even if nodes are compromised in the initialisation phase. The communication overhead, computational cost and storage requirement of the proposed method is very less compared with the elliptic curve‐based approaches available in the literature. The proposed scheme can also support large networks without affecting the security and efficiency. Copyright © 2015 John Wiley & Sons, Ltd.

구글 보이스 취약점을 통한 안드로이드 서드 파티 어플리케이션의 사용자 인증 개선방안 연구

In the Android market, a large portion of the market share consists of third party applications, but not much research has been performed in this respect. Of these applications, mobile Voice Over IP (VoIP) applications are one of the types of applications that are used the most. In this paper, we focus on user authentication methods for three representative applications of the Google Voice service, which is a famous mobile VoIP application. Then, with respect to the Android file system, we developed a method to store and to send user information for authentication. Finally, we demonstrate a vulnerability in the mechanism and propose an improved mechanism for user authentication by using hash chaining and an elliptic curve Diffie-Hellman key exchange.

Seladg: Secure Energy Efficient Location Aware Data Gathering Approach for Wireless Sensor Networks

Abstract Recent trends in wireless sensor networks leads to the development of new protocols for data gathering. In this paper, a secure energy efficient location aware data gathering approach is introduced to secure data gathering. An Elliptic Curve Diffie Hellman Key Exchange (ECDHKE) algorithm is utilized for key generation and key exchange between the sensor nodes to maintain security and prevent the data from malicious nodes. The performance of the proposed scheme is validated in terms of packet drop, throughput, energy consumption, residual energy and network lifetime. The proposed scheme achieves better performance than the existing EEHA and SMART schemes.

ECC Based IKE Protocol Design for Internet Applications

The Internet Key Exchange (IKE) protocol is most widely used as a secure key exchange protocol to exchange key materials and negotiate security associations between two security gateways for any secure communications over Internet. However, the original IKE is too flexible, complex and weak to denial-of-service (DoS) attack; several enhanced IKE version have been proposed to replace the original one. In this paper, an elliptic curve cryptography (ECC) based and certificate less IKE protocol is proposed. It eliminates the use of certificates for authentication, replaces the RSA based Diffie-Hellman (DH) key exchange by Elliptic Curve Diffie-Hellman (ECDH) key exchange, and instead of cookies, hash value of initiator's public key, identity and IP address is used to prevent DoS attack. One advantage of the proposed scheme is that it provides same level of security as RSA with less key size, as well as it generates an ECC based common secret key, used for symmetric encryption, which requires less processing time, less computation cost and less storage space than the time required in the public key encryption-based techniques.

Algorithm for Elliptic Curve Diffie-Hellman Key Exchange Based on DNA Tile Self-Assembly

Algorithm for Elliptic Curve Diffie-Hellman Key Exchange Based on DNA Tile Self-Assembly