ElGamal Research Articles

Analysis of the k-ary Euclid for tuples of integers

In our paper we discuss the k-ary Euclid Algorithm for counting the great common divisor (GCD) of two or more integers and suggest some improvements. This gives us a possibility to parallelize and speed up the calculating of GCD, which has a variety of applications in the Number Theory, Modular Arithmetic and the Cryptography Algorithms such as RSA, ElGamal encryption system and others.

A Novel Authentication Method for Big Data Environment

Security is essential for any networks. As the essential communication mode, the security mechanism for multicast isn't just the measure to guarantee verified communications, yet additionally the precondition for other security services. Attacks are one of the most significant worries for security experts. Attackers more often than not access an enormous number of computers by misusing their vulnerabilities to set up attack armed forces. This paper shows a twofold way validation mechanism which uses the usefulness of Elliptical Curve Cryptography, Kerberos System, and ElGamal algorithm. ECC algorithm used to encrypt the user information, whereas ElGamal used to encrypt the secret key itself to ensure more securit in the networks.

Cryptographic Key Exchange Authentication using Two Servers PAKE

The key trade procedure is well thought-out significant fractions of cryptographic method towards defend protected end-to-end communications. All existing techniques need two servers to be active to authenticate but this technique can authenticate even one server is up and other server is down due to attack as active server authenticate user by taking his parts. In this paper, design an idea Password-authenticated key exchange (PAKE) method to verify clients by utilizing two servers, first client secret phrase will be splitted into two sections and afterward mystery key will be produced for each part and after that by utilizing key and splitted secret phrase will be encoded utilizing Elgamal Encryption. Each encoded part and key will be send to every server. Every server will have its very own key and in the event that aggressor traded off one server, at that point he won't ready to login till he got client information of second server, by utilizing this strategy no assailant can bargain the two servers.

A key exchange protocol using matrices over group ring

The first published solution to key distribution problem is due to Diffie–Hellman, which allows two parties that have never communicated earlier, to jointly establish a shared secret key over an insecure channel. In this paper, we propose a new key exchange protocol in a non-commutative semigroup over group ring whose security relies on the hardness of Factorization with Discrete Logarithm Problem (FDLP). We have also provided its security and complexity analysis. We then propose a ElGamal cryptosystem based on FDLP using the group of invertible matrices over group rings.

ElGamal cryptosystem‐based secure authentication system for cloud‐based IoT applications

Life in modern society becomes easier due to the rapid growth of different technologies like real-time analytic, ubiquitous wireless communication, commodity sensors, machine learning and embedded systems. Nowadays, there seems to be a need to merge these technologies in the form of Internet of Things (IoT) so that smart systems can be achieved. On the other hand, cloud computing is a pillar in IoT by which end users get connected through the cloud servers for getting different services. However, to recognise the legitimacy of communicators during communication sessions through insecure channels like the Internet, serious issues in cloud-based IoT applications need to be addressed. Thus, authentication procedure is highly desirable to remove the unapproved access in IoT applications. This study presents an ElGamal cryptosystem and biometric information along with a user's password-based authentication scheme for cloud-based IoT applications refereed as SAS-Cloud. Security of the proposed scheme has been analysed by well popular random oracle model and it is found that SAS-Cloud has the ability to defend all the possible attacks. Furthermore, the performance of SAS-Cloud has been evaluated and it was found that SAS-Cloud has better efficiency than other existing competing ElGamal cryptosystem-based authentication schemes.

Linear (t,n) Secret Sharing Scheme with Reduced Number of Polynomials

Threshold secret sharing is concerned with the splitting of a secret into n shares and distributing them to some persons without revealing its information. Any t ≤ n persons possessing the shares have the ability to reconstruct the secret, but any persons less than t cannot do the reconstruction. Linear secret sharing scheme is an important branch of secret sharing. The purpose of this paper is to propose a new polynomial based linear (t, n) secret sharing scheme, which is based on Shamir’s secret sharing scheme and ElGamal cryptosystem. Firstly, we withdraw some required properties of secret sharing scheme after reviewing the related schemes and ElGamal cryptosystem. The designed scheme provides the properties of security for the secret, recoverability of the secret, privacy of the secret, and cheating detection of the forged shares. It has half computation overhead than the previous linear scheme.

An efficient approach for secure multi-party computation without authenticated channel

Secure multi-party sum is one of the most important secure multi-party computation protocols. It has been widely applied to solve many privacy-preservation problems such as privacy-preserving data mining, secure auction, secure electronic voting, and privacy-preserving statistical data analysis. To guarantee the correctness of the final output and to enhance the security level, the existing secure multi-party sum protocols have to use authenticated channels, even secure channels for participants to communicate, however such a usage requirement significantly reduces their performance. Furthermore, these secure multi-party sum protocols are impossible to run on public networks. In this paper, we propose a new secure multi-party sum protocol that can ensure the correctness of the output result as well as securely protecting the parties’ privacy against attacks without requiring any authenticated/secure channel. The proposed protocol is based on a multi-party sum function employing a variant of ElGamal encryption and a Schnorr signature-derived authentication method, in which both these cryptographic tools use the same private and public keys. Additionally, our comparative evaluation shows that the proposed protocol is efficient and practical.

A privacy-preserving RFID authentication protocol based on El-Gamal cryptosystem for secure TMIS

The healthcare environment now provides the facility for patients to communicate with doctors from home via the Internet; this facility is very useful for seriously ill patients. Errors in medication are hazardous and can cause significant harm to patients; therefore, patient medication and information safety are essential issues in such a healthcare environment. To protect this sensitive information, an authentication protocol is needed. Moreover, in the context of sharing data including a patient's personal information, privacy leakage has become one of the most challenging issues in a telecare medicine information system (TMIS). In this paper, we propose a privacy-preserving radio frequency identification (RFID) authentication protocol based on the El-Gamal cryptosystem, for enhancing patient medication safety in a TMIS. The proposed protocol can achieve a number of security services and can also resist several types of attacks. We have also shown the results obtained by conducting an "Automated Validation of Internet Security Protocols and Applications" (AVISPA) simulation of our protocol. The simulation results verify that the proposed protocol is safe against active and passive attacks. The results of an informal security analysis also indicate that patient information is highly private, and the system is protected against possible related attacks. Our protocol is not only better in terms of protecting the privacy of patients but it also achieves better performance than similar existing protocols.

Discrete Sliding Mode Control for Chaos Synchronization and Its Application to an Improved El-Gamal Cryptosystem

This paper is concerned with the design of an improved El-Gamal cryptosystem based on chaos synchronization. The El-Gamal cryptosystem is an asymmetric encryption algorithm that must use the public and private keys, respectively, in the encryption and decryption processes. However, in our design, the public key does not have to appear in the public channel. Therefore, this proposed improved El-Gamal cryptosystem becomes a symmetric-like encryption algorithm. First, a discrete sliding mode controller is proposed to ensure the synchronization of master and slave chaotic systems; next, a novel improved El-Gamal cryptosystem is presented. In the traditional El-Gamal cryptosystem, the public key is static and needs to be open which provides an opportunity to attack. However, in this improved design, due to the chaos synchronization, the public key becomes dynamic and does not appear in public channels. As a result, drawbacks of long cipher text and time-consuming calculation in the traditional El-Gamal cryptosystem are all removed. Finally, several performance tests and comparisons have shown the efficiency and security of the proposed algorithm.

Cloud-ElGamal and Fast Cloud-RSA Homomorphic Schemes for Protecting Data Confidentiality in Cloud Computing

Homomorphic encryption (HE) is an encryption form that offers a third-party with the ability to carry out computations on encrypted data. This property can be considered as a great solution to get over some obstacles limiting the wide-spread adoption of cloud computing (CC) services. Since CC environments are threatened by insider/outsider security attacks and since CC consumers often access to CC services using resource-limited devices, the HE schemes need to be promoted at security level and at running time to work effectively. For this reason, at EMENA-TSSL'16 and at WINCOM'16, the authors respectively boosted the RSA and ElGamal cryptosystems at security level, Cloud-RSA and Cloud-ElGamal. At SCAMS'17 and at EUSPN'17, the authors then suggested two fast variants of the Cloud-RSA scheme. All proposed schemes support the multiplicative homomorphism (MH) over the integers. The aim of this article is to compare the Cloud-ElGamal scheme with the Cloud-RSA schemes. This article first briefly presents the HE schemes and analyzes their security. This article then implements the schemes, compare and discuss their efficiency.

On the Security of a Variant of ElGamal Encryption Scheme

Recently, based on the Paillier cryptosystem [1] , Yi et al. outline a distributed ElGamal cryptosystem which allows for both a much simpler distributed key generation procedure and a more efficient distributed decryption of messages from a large plaintext domain [2] . In this paper, we analyze the security of their proposed variant of ElGamal encryption scheme and demonstrate that their proposed variant is not secure as claimed. Thus, whether an additively homomorphic cryptosytem satisfying the desired properties exists remains an open question.

Research and Design of an Improved ElGamal Digital Signature Algorithm

Firstly, the digital signature technology and its basic principle are introduced. Then, an ElGamal digital signature algorithm based on discrete logarithm is described, and two aspects of security and signature efficiency are improved on the basis of this algorithm, and the correctness, security and complexity of the improved scheme are analyzed. The results show that the improved ElGamal algorithm achieves the purpose of improvement.

Data integrity proof and secure computation based on elgamal algorithm and iris extraction in cloud storage

Data integrity proof and secure computation based on elgamal algorithm and iris extraction in cloud storage

An Efficient Anonymous Authentication Scheme with Secure Communication in Intelligent Vehicular Ad-hoc Networks

Vehicular ad-hoc networks (VANETs) have become increasingly significant in intelligent transportation systems, they play a great role in improving traffic safety and efficiency. In the deployment of intelligent VANETs, intelligent vehicles can efficiently exchange important or urgent traffic information and make driving decisions. Meanwhile, secure data communication and vehicle’s identity privacy have been highlighted. To cope with these security issues, in this paper, we construct an efficient anonymous authentication scheme with secure communication in intelligent VANETs. Combing the ElGamal encryption technique with a modified Schnorr signature technique, the proposed scheme provides secure anonymous authentication process for encrypted message in the vehicle-to-infrastructure communication model, and achieves identity privacy, forward security, and reply attack resistance simultaneously. Moreover, except the trusted authority (TA), any outside entity cannot trace the real identity of an intelligent vehicle. The proposed scheme is designed on an identity-based system, which can remove the costs of establishing public key infrastructure (PKI) and certificates management. Compared with existing authentication schemes, the proposed scheme is much more practical in intelligent VANETs.

Improving One-Time Pad Algorithm on Shamir’s Three-Pass Protocol Scheme by Using RSA and ElGamal Algorithms

This study aims to cover the shortcomings of the one-time pad algorithm used in the Shamir’s three-pass protocol scheme. In this study, the technique used to cover the weakness of one-time pad algorithm is by changing each ciphertext generated from the three paths in the three pass protocol scheme. Ciphertext modification is performed by encrypting the cipher-text by using the RSA and Elgamal algorithms to generate super ciphertext. The first line and the third line are encrypted by using the RSA algorithm and the second line is using ElGamal algorithm. Both algorithms are aimed at keeping no secret key exchange which is a major requirement of the three pass protocol scheme. The evaluation results show that the weakness of one-time pad algorithm can be overcome. Although the processing time of three pass protocol increases, but the longer the plaintext character the closer the processing time ratio to one. The research showsThe only way for plaintext to be formed by cryptoanalysis is they must succeed to decrypt the three super ciphertexts back into the three initial ciphertexts first. But it is not easy if RSA and ElGamal algorithms use the big prime number.

Modification of chipertext Elgamal algorithm using split merge

The development of increasingly sophisticated technology with more intensive use of computers facilitates human work activities, so that security problems arise that misuse information that can endanger users. The third parties who commit crimes against users are called cryptanalyst. Cryptanalyst interferes with computer networks in many forms such as data theft. Cryptography is a security solution for cryptanalysts; one of them is by using the El-Gamal algorithm. Researchers have proposed El-Gamal modification with good results, but not all security problems can be solved. The algorithm cannot guarantee protection against the adaptive attack. This article proposes the application of split merge method on the El-Gamal algorithm to improve security. The study describes the system analysis and design. Since the combination uses large prime number calculations, it is expected to be effective to make cryptanalyst more difficult to break the plaintext.

METHODS TOWARD ENHANCING RSA ALGORITHM : A SURVEY

Cryptography defines different methods and technologies used in ensuring communication between two parties over any communication medium is secure, especially in presence of a third part. This is achieved through the use of several methods, such as encryption, decryption, signing, generating of pseudo-random numbers, among many others. Cryptography uses a key, or some sort of a password to either encrypt or decrypt a message that needs to be kept secret. This is made possible using two classes of key-based encryption and decryption algorithms, namely symmetric and asymmetric algorithms. The best known and the most widely used public key system is RSA. This algorithm comprises of three phases, which are the key generation phase, encryption phase, and the decryption phase. Owing to the advancement in computing technology, RSA is prone to some security risks, which makes it less secure. The following paper preview different proposals on different methods used to enhance the RSA algorithm and increase its security. Some of these enhancements include combining the RSA algorithm with Diffie-Hellman or ElGamal algorithm, modification of RSA to include three or four prime numbers, offline storage of generated keys, a secured algorithm for RSA where the message can be encrypted using dual encryption keys, etc.

On desynchronised multivariate algorithms of El Gamal type for stable semigroups of affine Cremona group

Families of stable cyclic groups of nonlinear polynomial transformations of affine spaces Kn over general commutative ring K of increasing with n order can be used in the key exchange protocols and related to them El Gamal multivariate cryptosystems. To use high degree of noncommutativity of affine Cremona group correspondents have to modify multivariate El Gamal algorithm via the usage of conjugations for two polynomials of kind gk and g−1 given by key holder (Alice) or giving them as elements of different transformation groups. The idea of hidden tame homomorphism and comlexity of decomposition of polynomial transwormation into word of elements of Cremona semigroup can be used. We suggest usage of new explicit constructions of infinite families of large stable subsemigroups of affine Cremona group of bounded degree as instruments of multivariate key exchange protocols. Recent results on generation of families of stable transformations of small degree and density via technique of symbolic walks on algebraic graphs are observed. Some of them used for the implementation of schemes as above with feasible computational complexity. We consider an example of a new implemented quadratic multivariate cryptosystem based on the above mentioned ideas.

Research and comparative analysis of algorithms of asymmetric encryption

Using a developed software product, a comparative analysis of asymmetric text data encryption algorithms, their advantages and disadvantages, cryptographic strength, experimental evaluation of their characteristics with respect to the efficiency of their computer memory usage, the duration of key generation, data encryption and decryption ability of algorithms, key dimensions, volumes of encrypted and decrypted files has been made. Based on the results obtained, recommendations were given on the use of the encryption methods considered. The RSA and ElGamal algorithms are chosen as asymmetric encryption algorithms.From the point of view of practical implementation, both in software and hardware, there is no tangible difference between these two methods. However, in their characteristics they are noticeably different. Briefly, the main estimated results obtained are as follows: the cryptographic strength of the ElGamal algorithm is significantly higher than that of the RSA algorithm; the RSA algorithm has a higher speed when encrypting information, and the ElGamal algorithm has the best during decryption; as the key sizes increase, the decryption time by the RSA algorithm grows exponentially, while the duration of the decryption by the ElGamal algorithm has a linear growth order; the RSA algorithm showed 2 times better bandwidth than the ElGamal algorithm in the process of encoding information, but the ElGamal algorithm proved 10 times better throughput compared to the RSA algorithm in the process of decrypting information; the length of the encrypted data by the ElGamal algorithm is 2 times longer than the original data, while the size of the data encrypted by the RSA algorithm is larger than the size of the original data by an average of 1.4; for all key lengths, the ElGamal algorithm creates a pair of public and private keys on average 10 times faster than the RSA algorithm, which is especially noticeable with a significant increase in key sizes; for the ElGamal algorithm, the key generation time increases linearly with increasing key sizes, while for the RSA algorithm it grows exponentially.

ElGamal Broadcasting Multi-Signcryption Protocol with UC Security

ElGamal Broadcasting Multi-Signcryption Protocol with UC Security