Biblio

The advantage of cryptographic systems based on elliptical curves over traditional systems is that they provide equivalent protection even when the key length used is small. This reduces the load time of the processors of the receiving and transmitting devices. But the development of computer technology leads to an increase in the stability of the cryptosystem, that is, the length of the keys. This article presents a method for converting elliptic curve equations to hidden parameter elliptic curve equations to increase stability without increasing key length.

Elliptic curve is a major area of research due to its application in elliptic curve cryptography. Due to their small key sizes, they offer the twofold advantage of reduced storage and transmission requirements. This also results in faster execution times. The authors propose an architecture to automatically generate test cases, for verification of elliptic curve operational circuits, based on user-defined prime field and the parameters used in the circuit to be tested. The ECC test case generations are based on the Galois field arithmetic operations which were the subject of previous work by the authors. One of the strengths of elliptic curve mathematics is its simplicity, which involves just three points (P, Q, and R), which pass through a line on the curve. The test cases generate points for a user-defined prime field which sequentially selects the input vector points (P and/or Q), to calculate the resultant output vector (R) easily. The testbench proposed here targets field programmable gate array (FPGAs) platforms and experimental results for ECC test case generation on different prime fields are presented, while ModelSim is used to validate the correctness of the ECC operations.

Digital signatures are increasingly used today. It replaces wet signature with the development of technology. Elliptic curve digital signature algorithm (ECDSA) is used in many applications thanks to its security and efficiency. However, some mathematical operations such as inversion operation in modulation slow down the speed of this algorithm. In this study, we propose a more efficient and secure ECDSA. In the proposed method, the inversion operation in modulation of signature generation and signature verification phases is removed. Thus, the efficiency and speed of the ECDSA have been increased without reducing its security. The proposed method is implemented in Python programming language using P-521 elliptic curve and SHA-512 algorithm.

The advantage of elliptic curve (EC) cryptographic systems is that they provide equivalent security even with small key lengths. However, the development of modern computing technologies leads to an increase in the length of keys. In this case, it is recommended to use a secret parameter to ensure sufficient access without increasing the key length. To achieve this result, the initiation of an additional secret parameter R into the EC equation is used to develop an EC-based key distribution algorithm. The article describes the algebraic structure of an elliptic curve with a secret parameter.

The transmission of various facilities and services via the network is known as cloud computing. They involve data storage, data centers, networks, internet, and software applications, among other systems and features. Cryptography is a technique in which plain text is converted into cipher-text to preserve information security. It basically consists of encryption and decryption. The level of safety is determined by the category of encryption and decryption technique employed. The key plays an important part in the encryption method. If the key is leaked, anyone can intrude into the data and there is no use of this encryption. When the data is lost and the server fails to deliver it to the user, then it is to be recovered from any of the backup server using a recovery technique. The main objective is to develop an advanced method to increase the scope for data protection in cloud. Elliptic Curve Cryptography is a relatively new approach in the area of cryptography. The degree of security provides higher as compared to other Cryptographic techniques. The raw data and it’s accompanying as CII characters are combined and sent into the Elliptic Curve Cryptography as a source. This method eliminates the need for the transmitter and recipient to have a similar search database. Finally, a plain text is converted into cipher-text using Elliptic Curve Cryptography. The results are oat aimed by implementing a C program for Elliptic Curve Cryptography. Encryption, decryption and recovery using suitable algorithms are done.

In recent times, security and privacy concerns associated with IoT devices have caught the attention of research community. The problem of securing IoT devices is immensely aggravating due to advancement in technology. These IoT devices are resource-constraint i.e. in terms of power, memory, computation, etc., so they are less capable to secure themselves. So we need a better approach to secure IoT devices within the limited resources. Several studies state that for these lightweight IoT devices Elliptic Curve Cryptography (ECC) suits perfectly. But there are several elliptic curve domain parameter standards, which may be used for different security levels. When any ECC based product is deployed then the selection of a suitable elliptic curve standard according to usability is become very important. So we have to choose one suitable standard domain parameter for the required security level. In this paper, two different elliptic curve standard domain parameters named secp256k1 and secp192k1 proposed by an industry consortium named Standards for Efficient Cryptography Group (SECG) [1] are implemented and then analyzed their performances metrics. The performance of each domain parameter is measured in computation time.

Binary Edwards curves (BEC) over finite fields can be used as an additive cyclic elliptic curve group to enable elliptic curve cryptography (ECC), where the most time consuming is scalar multiplication. This operation is computed by means of the group operation, either point addition or point doubling. The most notorious property of these curves is that their group operation is complete, which mitigates the need to verify for special cases. Different formulae for the group operation in BECs have been reported in the literature. Of particular interest are those designed to work with the differential properties of the Montgomery ladder, which offer constant time computation of the scalar multiplication as well as reduced field operations count. In this work, we review and compare the complexity of BEC differential addition and doubling in terms of field operations. We also provide software implementations of scalar multiplications which employ these formulae under a fair scenario. Our work provides insights on the advantages of using BECs in ECC. Our study of the different formulae for group addition in BEC also showcases the advantages and limitations of the different design strategies employed in each case.

Cryptography is the science or process used for the encryption and decryption of data that helps the users to store important information or share it across networks where it can be read only by the intended user. In this paper, Elliptic Curve Cryptography (ECC) has been proposed because of its small key size, less memory space and high speed. Elliptic curve scalar multiplication is an important part of elliptic curve systems. Here, the scalar multiplication is performed with the help of hybrid Karatsuba multiplier as the area utilization of Karatsuba multiplier is less. An alternative of digital signature algorithm, that is, Elliptic Curve Digital Signature Algorithm (ECDSA) along with the primary operations of elliptic curves have also been discussed in this paper.

In order to protect user privacy and provide better access control in Internet of Things (IoT) environments, designing an appropriate two-party authentication and key exchange protocol is a prominent challenge. In this paper, we propose a lightweight certificateless non-interactive authentication and key exchange (CNAKE) protocol for mutual authentication between remote users and smart devices. Based on elliptic curves, our lightweight protocol provides high security performance, realizes non-interactive authentication between the two entities, and effectively reduces communication overhead. Under the random oracle model, the proposed protocol is provably secure based on the Computational Diffie-Hellman and Bilinear Diffie-Hellman hardness assumption. Finally, through a series of experiments and comprehensive performance analysis, we demonstrate that our scheme is fast and secure.

To improve efficiency of stegosystem on blockchain and balance the time consumption of Encode and Decode operations, we propose a new blockchain-based steganography scheme, called Keys as Secret Messages (KASM), where a codebook of mappings between bitstrings and public keys can be pre-calculated by both sides with some secret parameters pre-negotiated before covert communication. By applying properties of elliptic curves and pseudorandom number generators, we realize key derivation of codebook item, and we construct the stegosystem with provable security under chosen hiddentext attack. By comparing KASM with Blockchain Covert Channel (BLOCCE) and testing on Bitcoin protocol, we conclude that our proposed stegosystem encodes hiddentexts faster than BLOCCE does and can decode stegotexts in highly acceptable time. The balanced time consumption of Encode and Decode operations of KASM make it applicable in the scene of duplex communication. At the same time, KASM does not leak sender’s private keys, so sender’s digital currencies can be protected.

We study the problem of generation of cycles, chains and graphs of pairing-friendly elliptic curves using in succinct non-interactive arguments for knowledge protocols in blockchain. The task to build a “stick” for existing MNT753 cycle is reduced to the factorization problem for big numbers. Together with graphs of pairing friendly elliptic curves we consider auxiliary graphs of their orders (primes or irreducible polynomials) associated to vertices and embedding degrees to edges. Numerical experiments allow us to conjecture that (except of MNT case): 1) for any fixed embedding degrees there exist only finite number of such cycles and, hence, there are no families of such cycles; 2) chains of prime order are very rare; we suppose that there are no polynomial families of such chains. It is hard to find a family of pairing friendly elliptic curves with the base field order q(x) such that ζk ∈ Q[x]/(q(x)) for k \textbackslashtextgreater 6. From other hand our examples show that we can apply Brezing-Weng construction with k=6 and D=3 iteratively to obtain chains of length 3-4. We build 1) a family of 1-chains with embedding degrees 8 and 7, where all orders are given by cyclotomic polynomials; 2) a combination of MNT cycle and near-MNT curve.

Using the physical characteristics of the encryption device, an attacker can more easily obtain the key, which is called side-channel attack. Common side-channel attacks, such as simple power analysis (SPA) and differential power analysis (DPA), mainly focus on the statistical analysis of the data involved in the encryption algorithm, while there are relatively few studies on the Hamming weight of the addresses. Therefore, a new method of address-based Hamming weight analysis, address collision attack, is proposed in this research. The collision attack method (CA) and support vector machines algorithm (SVM) are used for analysis, meanwhile, the scalar multiplication implemented by protected address-bit DPA (ADPA) can be attack on the ChipWhisperer-Pro CW1200.

As the computer architecture technology evolves, communication protocols have been demanded not only having reliable security but also flexible functionality. Advanced cryptography has been expected as a new generation cryptography which suffices such the requirements. A pairing is one of the key technologies of the cryptography and the pairing has been known as having a substantial amount of construction parameters. Recently, the elliptic curve with embedding degree 14 is evaluated as one of the efficient curves for pairing. In the paper, we implement an optimal ate pairing on the elliptic curve by applying several variants of multiplication algorithms of extension field of degree 7 on multiple devices. The best multiplication algorithm among the candidates is derived. Besides, for efficient calculations, we propose a pseudo 7-sparse algorithm and a fast calculation method of final exponentiation. As a result, we discover the proper multiplication algorithm bases on the rate of addition and multiplications on several different computer platforms. Our proposed pseudo 7-sparse algorithm is approximately 1.54% faster than a regular algorithm on almost all tested platforms. Eventually, for the total execution time of pairing we record 9.33ms on Corei5-9500.

The blockchain's cross-chain atomic exchange uses smart contracts to replace trusted third parties, but atomic exchange cannot guarantee the anonymity of transactions, and it will inevitably increase the risk of privacy leakage. Therefore, this paper proposes an atom based on zero-knowledge proof. Improved methods of exchange to ensure the privacy of both parties in a transaction. The anonymous improvement scheme in this article uses the UTXO unconsumed model to add a new anonymous list in the blockchain. When sending assets to smart contracts, zero-knowledge proof is used to provide self-certification of ownership of the asset, and then the transaction is broken down. Only the hash value of the transaction is sent to the node, and the discarded list is used to verify the validity of the transaction, which achieves the effect of storing assets anonymously in the smart contract. At the same time, a smart contract is added when the two parties in the transaction communicate to exchange the contract address of the newly set smart contract between the two parties in the transaction. This can prevent the smart contract address information from being stolen when the two parties in the transaction communicate directly.

The world is facing a new revolutionary technology transition, Internet of things (IoT). IoT systems requires secure connectivity of distributed entities, including in-field sensors. For such external devices, Side Channel Analysis poses a potential threat as it does not require complete knowledge about the crypto algorithm. In this work, we perform Horizontal Correlation Power Analysis (HCPA) which is a type of Side Channel Analysis (SCA) over the Elliptic Curve Diffie Hellman (ECDH) key exchange protocol. ChipWhisperer (CW) by NewAE Technologies is an open source toolchain which is utilized to perform the HCPA by using CW toolchain. To best of our knowledge, this is the first attempt to implemented ECDH on Artix-7 FPGA for HCPA. We compare our correlation results with the results from AES -128 bits provided by CW. Our point of attack is the Double and Add algorithm which is used to perform Scalar multiplication in ECC. We obtain a maximum correlation of 7% for the key guess using the HCPA. We also discuss about the possible cause for lower correlation and few potentials ways to improve it. In Addition to HCPA we also perform Simple Power Analysis (SPA) (visual) for ECDH, to guess the trailing zeros in the 128-bit secret key for different power traces.

Pseudorandom bit generators (PRBG) can be designed to take the advantage of some hard number theoretic problems such as the discrete logarithm problem (DLP). Such type of generators will have good randomness and unpredictability properties as it is so difficult to find an easy solution to the regarding mathematical dilemma. Hash functions in turn play a remarkable role in many cryptographic tasks to achieve various security strengths. In this paper, a pseudorandom bit generator mechanism that is based mainly on the elliptic curve discrete logarithm problem (ECDLP) and hash derivation function is proposed. The cryptographic hash functions are used in consuming applications that require various security strengths. In a good hash function, finding whatever the input that can be mapped to any pre-specified output is considered computationally infeasible. The obtained pseudorandom bits are tested with NIST statistical tests and it also could fulfill the up-to-date standards. Moreover, a 256 × 256 grayscale images are encrypted with the obtained pseudorandom bits following by necessary analysis of the cipher images for security prove.

In this paper we report on the results of selected horizontal SCA attacks against two open-source designs that implement hardware accelerators for elliptic curve cryptography. Both designs use the complete addition formula to make the point addition and point doubling operations indistinguishable. One of the designs uses in addition means to randomize the operation sequence as a countermeasure. We used the comparison to the mean and an automated SPA to attack both designs. Despite all these countermeasures, we were able to extract the keys processed with a correctness of 100%.

The need for faster and practical cryptography is a research topic for decades. In case of elliptic curve cryptography, which was proposed by Koblitz and Miller in 1985 as a more efficient alternative to RSA, the applications in real life started after 2000s. Today, most of the popular applications and protocols like Whatsapp, Signal, iOS, Android, TLS, SSH, Bitcoin etc. make use of Elliptic curve cryptography. One of the important factor for high performance elliptic curve cryptography is the finite field multiplication. In this paper, we first describe how to choose proper prime fields that makes use of Topelitz-matrices to get faster field multiplication, then we give parameter choice details to select prime fields that supports Toeplitz-matrix vector product operations. Then, we introduce the safe curve selection rationale and discuss about security. We propose new curves, discuss implementation and benchmark results and conclude our work.

The exchange of data has expanded utilizing the web nowadays, but it is not dependable because, during communication on the cloud, any malicious client can alter or steal the information or misuse it. To provide security to the data during transmission is becoming hot research and quite challenging topic. In this work, our proposed algorithm enhances the security of the keys by increasing its complexity, so that it can't be guessed, breached or stolen by the third party and hence by this, the data will be concealed while sending between the users. The proposed algorithm also provides more security and authentication to the users during cloud communication, as compared to the previously existing algorithm.

The use of public key cryptosystems ranges from securely encrypting bitcoin transactions and creating digital signatures for non-repudiation. The cryptographic systems security of public key depends on the complexity in solving mathematical problems. Quantum computers pose a threat to the current day algorithms used. This research presents analysis of two Hash-based Signature Schemes (MSS and W-OTS) and provides a comparative analysis of them. The comparisons are based on their efficiency as regards to their key generation, signature generation and verification time. These algorithms are compared with two classical algorithms (RSA and ECDSA) used in bitcoin transaction security. The results as shown in table II indicates that RSA key generation takes 0.2012s, signature generation takes 0.0778s and signature verification is 0.0040s. ECDSA key generation is 0.1378s, signature generation takes 0.0187s, and verification time for the signature is 0.0164s. The W-OTS key generation is 0.002s. To generate a signature in W-OTS, it takes 0.001s and verification time for the signature is 0.0002s. Lastly MSS Key generation, signature generation and verification has high values which are 16.290s, 17.474s, and 13.494s respectively. Based on the results, W-OTS is recommended for bitcoin transaction security because of its efficiency and ability to resist quantum computer attacks on the bitcoin network.

The article presents a proposal for implementing asymmetric cryptography, specifically the elliptic curves for the protection of high-speed data transmission in a corporate network created on the platform of PLC (Power Line Communications). The solution uses an open-source software library OpenSSL. As part of the design, an experimental workplace was set up, a DHCP and FTP server was established. The possibility of encryption with the selected own elliptic curve from the OpenSSL library was tested so that key pairs (public and private keys) were generated using a software tool. A shared secret was created between communication participants and subsequently, data encryption and decryption were performed.

The JavaCard multi-application platform is now deployed to over twenty billion smartcards, used in various applications ranging from banking payments and authentication tokens to SIM cards and electronic documents. In most of those use cases, access to various cryptographic primitives is required. The standard JavaCard API provides a basic level of access to such functionality (e.g., RSA encryption) but does not expose low-level cryptographic primitives (e.g., elliptic curve operations) and essential data types (e.g., Integers). Developers can access such features only through proprietary, manufacturer-specific APIs. Unfortunately, such APIs significantly reduce the interoperability and certification transparency of the software produced as they require non-disclosure agreements (NDA) that prohibit public sharing of the applet's source code.We introduce JCMathLib, an open library that provides an intermediate layer realizing essential data types and low-level cryptographic primitives from high-level operations. To achieve this, we introduce a series of optimization techniques for resource-constrained platforms that make optimal use of the underlying hardware, while having a small memory footprint. To the best of our knowledge, it is the first generic library for low-level cryptographic operations in JavaCards that does not rely on a proprietary API.Without any disclosure limitations, JCMathLib has the potential to increase transparency by enabling open code sharing, release of research prototypes, and public code audits. Moreover, JCMathLib can help resolve the conflict between strict open-source licenses such as GPL and proprietary APIs available only under an NDA. This is of particular importance due to the introduction of JavaCard API v3.1, which targets specifically IoT devices, where open-source development might be more common than in the relatively closed world of government-issued electronic documents.

In this paper, a novel Dynamic Chaotic Biometric Identity Isomorphic Elliptic Curve (DCBI-IEC) has been introduced for Image Encryption. The biometric digital identity is extracted from the user fingerprint image as fingerprint minutia data incorporated with the chaotic logistic map and hence, a new DCBDI-IEC has been suggested. DCBI-IEC is used to control the key schedule for all encryption and decryption processing. Statistical analysis, differential analysis and key sensitivity test are performed to estimate the security strengths of the proposed DCBI-IEC system. The experimental results show that the proposed algorithm is robust against common signal processing attacks and provides a high security level for image encryption application.

A deniable authentication (DA) protocol plays a vital role to provide security and privacy of the mobile nodes in a mobile ad hoc network (MANET). In recent years, a number of similar works have been proposed, but most of them experience heavy computational and communication overhead. Further, most of these protocols are not secure against different attacks. To address these concerns, we devised an identity-based deniable authentication (IBDA) protocol with adequate security and efficiency. The proposed IBDA protocol is mainly designed for MANETs, where the mobile devices are resource-limited. The proposed IBDA protocol used the elliptic curve cryptography (ECC) and identity-based cryptosystem (IBC). The security of our IBDA protocol depends on the elliptic curve discrete logarithm (ECDL) problem and bilinear Diffie-Hellman (BDH) problem.

With the exponential growth in the usage of electronic medical records (EMR), the amount of data generated by the healthcare industry has too increased exponentially. These large amounts of data, known as “Big Data” is mostly unstructured. Special big data analytics methods are required to process the information and retrieve information which is meaningful. As patient information in hospitals and other healthcare facilities become increasingly electronic, Big Data technologies are needed now more than ever to manage and understand this data. In addition, this information tends to be quite sensitive and needs a highly secure environment. However, current security algorithms are hard to be implemented because it would take a huge amount of time and resources. Security protocols in Big data are also not adequate in protecting sensitive information in the healthcare. As a result, the healthcare data is both heterogeneous and insecure. As a solution we propose the Secure Pattern-Based Data Sensitivity Framework (PBDSF), that uses machine learning mechanisms to identify the common set of attributes of patient data, data frequency, various patterns of codes used to identify specific conditions to secure sensitive information. The framework uses Hadoop and is built on Hadoop Distributed File System (HDFS) as a basis for our clusters of machines to process Big Data, and perform tasks such as identifying sensitive information in a huge amount of data and encrypting data that are identified to be sensitive.