Security of Public-key Cryptosystems Based on Chebyshev Polynomials over Prime Finite Fields, Conference: Computer Systems and Applications, 2005. IEEE Transactions on Information Theory 31(4): 469-472, Damage Assessment and Recovery from Malicious Attacks for Defensive Information Warfare, High-Performance and Accurate Mathematical Solvers in Hardware, Applications of Number Theory to Cryptography, Cloud Federation Formation and Request Allocation.
A Comparative Study of Elgamal Based Cryptographic Algorithms. The reducible polynomial cryptosystem is rel, it took considerable time to generate a key and to encrypt a. it is more secure than the other algorithms. Conference on Research Trends in Science and T, [7] El-Kassar, A. N., Rizk M., Mirza N., and Awad,Y, ... We enhanced the Exhaustive search and Baby-step giant-step algorithms to work with the modified algorithms. To test the security of the algorithms we use a famous attack algorithm called baby-step-giant algorithm which works in the domain of natural integers.
The obtained results show better performance when compared to existing software versions. It uses asymmetric key encryption for communicating between two parties and encrypting the message. In addition, they require scanning the entire log file from the point of attack to the end, which is inefficient.
In this paper, we consider another extension employing the group of units of Z2[x]/ , where H(x) = h1(x)h2(x)..Hr(x)is a product of irreducible polynomials whose degrees are pairwise relatively prime. Consequently, efficient damage assessment and recovery techniques are demanded. Both Gaussian integers and Lucas sequences have been applied in cryptography.
We demonstrate that the algorithms based on the Gaussian Integer DLP have advantages over the corresponding algorithms based on real integer DLP or Lucas Sequences DLP. After 25 runs of the various algorithms, we can conclude, proximately negligible compared to the time needed for the, b- For the reducible polynomials the time needed to en-, crypt a message is greater than the time needed to, attack schemes and applied them on the classical and mod-, cal algorithm because we have an unknown po, classical algorithm since its attack algorithm needs double.
The algorithms do not require scanning the log file during the damage assessment stage.
To test the security of the algorithms we use a famous attack algorithm called Baby-Step-Giant algorithm which works in the domain of natural integers.
For a detailed look at the algorithms of the extended El-, Gamal encryption scheme in the domain of quotient rings, In order to attack any protocol that uses ElGamal public-, key encryption scheme we have to solve the discrete loga-, gorithm are the baby-step giant-step algorithm and the Pol-.
The proposed algorithm belongs to the family of public key cryptographic algorithms. will be identical to those of the classical case. F[x], by extending the arithmetic needed for the modifications to these domains.
This paper presents the mathematical relationship between Lucas sequences and Gaussian integers.
For this reason, many attempts for exploiting the inherent parallelism of Multigrid have been made to achieve the desired efficiency and scalability of the method. We enhance the Baby-Step-Giant algorithm to work with the modified ElGamal cryptosystems. A conclusion is drawn in section 5. ... We enhance the baby-step-giant algorithm to work with the modified ElGamal digital signature algorithms.
The Digital Signature Algorithm (DSA) is a variant of the ElGamal signature scheme, which should not be confused with ElGamal encryption. cyclic group of units, Proceedings of the International
We also investigate the existing matrix based algorithms and compare their pros and cons to our proposed algorithms. pp. For simplicity, we describe the algorithm in a cyclic group, with negligible probability. The above equation can then be, In rare cases, Pollard’s rho algorithm terminates with, parameters illustrates Pollard’s rho algorithm in the domain, for the given data, table 5.3 shows the values of, Note that there are many integers in the subgroup. Similar work was done by Haraty and El Kassar, Quotient rings of polynomials over f inite f ields with cyclic group of units.
Two kinds of contemporary developments in cryptography are examined. Two of the suggested algorithms follow the data dependency paradigm whereas the third one follows the transaction dependency paradigm. modified the ElGamal scheme to the domain of Gaussian integers. A Publi—Key Cryptosystem and Signature Scheme Based on Discrete Logarithms. the amount of storage required is negligible . Hence, securing databases is a critical concern. A new signature scheme is proposed, together with an implementation of the Diffie-Hellman key distribution scheme that achieves a public key cryptosystem. It also discusses how the theories of communication and computation are beginning to provide the tools to solve cryptographic problems of long standing. First, a Gaussian prime. Over the past years, Multigrid solvers have showed their robustnes, Distributed mechanism for cloud federation formation based on the own experience. We enhance the Pollard's rho algorithm to work with the modified ElGamal cryptosystems. It was described by Taher Elgamal in 1985.
The group is the largest multiplicative sub-group of the integers modulo p, with p prime. This scheme is known as ElGamal cryptosystem, it modi es the Di e-Hellman protocol with the goal so that it can be used as an encryption and decryption proto … The results show that the execution time of the suggested approach is less than any existing approach.
mains, namely the domain of Gaussian integers, the domain of the rings of polynomials over, tions to these domains.
The security of both systems relies on the difficulty of computing discrete logarithms over finite fields. El-Kassar, A. N., Chihadi H., and Zentout D. the time needed to attack the classical one.
469-472, With the evolution of high speed internet technologies, massive data is exchanged everyday between various information systems without any centralized control. Particularly, we show that recovering the corresponding plaintext from a given ciphertext involves the discrete logarithm, Join ResearchGate to discover and stay up-to-date with the latest research from leading experts in, Access scientific knowledge from anywhere. Our approach uses a finite field trigonometry and reveals some aspects concerning the security of a recently proposed public-key encryption algorithm based on those polynomials. ElGamal encryption is an public-key cryptosystem.
In contrary to traditional algorithms, we store the dependencies in data structures to be used to discover the damaged part of the database. 2.4 GHZ CPU, 40 GByte hard-disk, and 512 MB DDRAM. 1) Security of the RSA depends on the (presumed) difficulty of factoring large integers.
ning time as the baby-step giant-step algorithm. it is complex and needs considerable computing time to, the modulus of a given polynomial with respect to a certain, irreducible or reducible polynomial and with respect to a, In this work, we presented the classic ElGamal cryp-, showed that all the algorithms applied the ElGamal cryp-, tosystem correctly and generated public and private k, encrypted using the encryption scheme and were sent in en-, crypted form to a decryption procedure which returned the.
ElGamal encryption is used in the free GNU Privacy Guard software, recent versions of PGP, and other cryptosystems. 2) Security of the ElGamal algorithm depends on the (presumed) difficulty of computing discrete logs in a large prime modulus.
A Comparative Study of Elgamal Based Digital Signature Algorithms, ELGAMAL DWYNCURE SIGNATURE ALGORITHM AN IMPLEMENTATION OF DOUBLE SECURITY IN ELGAMAL DIGITAL SIGNATURE, Relationship between Lucas Sequences and Gaussian Integers in Cryptosystems, El-Gamal public key cryptosystem in the domain of Gaussian integers, The Euler phi-function in the Gaussian integers, Handbook of Applied Cryptography Boca Raton. Advantages of the new method are pointed out and comparisons with the classical case of F2m are made. Numerical examples are provided. El-Kassar et al.
All content in this area was uploaded by Ramzi A. Haraty on Dec 17, 2014, In 1985 a powerful and practical public-key scheme was, produced by ElGamal; his work was applied using large. We analyze the implementation performance using the FPGA vendor's tools.
A Public Key CTyptosystem and a signatuTe scheme based on discTete 10gaTithms. are provided. El-Kassar, A. N. and Haraty Ramzi, ElGamal P ublic − key Cryptosystem U sing Reducible P olynomials over a F inite F ield, Proceedings of the 13th International Conference on Intelligent & Adaptive Systems and Software Engineering (IASSE-2004).
ed.). Examples, algorithms and proofs are given. Idea of ElGamal cryptosystem
In this work we implement the clas-, security of the algorithms we use a famous attack algorithm, Cryptography is the art or science of keeping messages, cryptography.
Nice, France. In this project, we present a hardware implementation of the V-cycle Multigrid method for finding the solution of a 2D-Poisson equation.
We implement the classical and modified ElGamal digital signature scheme to compare and to test their functionality, reliability and security. Modified RSA in the Domains of Gaussian Integers and Polynomials Over Finite Fields. Widening applications of teleprocessing have given rise to a need for new types of cryptographic systems, which minimize the need for secure key distribution channels and supply the equivalent of a written signature.
Databases are exposed to interception, The problem of finding the solution of partial differential equations (PDEs) plays a central role in modeling real world problems. ElGamal Public-Key Cryptosystem Using Reducible Polynomials Over a Finite Field. However, the history of system break-ins guarantees that there is always a chance for a successful attack on the data. We demonstrate the robustness of Multigrid over other similar iterative solvers, such as Jacobi and successive over relaxation (SOR), in both hardware and software. Traditional recovery methods do not take into consideration the existing dependencies between different data items and transactions. ElGamal public-key and digital signature scheme were modified from the domain of natural integers, Z, to the domains of Gaussian integers, Z[i], and polynomials over finite fields, F[x].
the extended ElGamal cryptosystem is enlarged, its order is, larger than the square of that used in the classical ElGamal, cryptosystem, with no additional efforts required for, The three algorithms of the classical method can be mod-, The ElGamal public-key cryptosystem is also extended, in the setting of the cyclic group of the, ElGamal public-key cryptosystem scheme we are only in-. Download full-text PDF Download full-text PDF Read full-text. In 1985 a powerful and practical public-key scheme was produced by ElGamal; his work was applied using large prime integers. Elgamal’s Algorithm in Cryptography Rashmi Singh, Shiv Kumar (M.Tech.) It also explores the complexity of Discrete Logarithm Problem (DLP) for Gaussian integers modulo prime by reducing it to Lucas Sequences DLP and real integer DLP. Elementary number theory and its applications (3.
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