Academia.edu no longer supports Internet Explorer.
To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser.
In this paper we propose an application of public key distribution based on the security depending on the difficulty of elliptic curve discrete logarithm problem. More precisely, we propose an example of Elgamal encryption cryptosystem on the elliptic curve given by the equation: y 2 = x 3 + 70x + 57[73].
In this paper, discrete log-based public-key cryptography is explored. Specifically, we first examine the Discrete Log Problem over a general cyclic group and algorithms that attempt to solve it. This leads us to an investigation of the security of cryptosystems based over certain specific cyclic groups: Fp, F × p , and the cyclic subgroup generated by a point on an elliptic curve; we ultimately see the highest security comes from using E(Fp) as our group. This necessitates an introduction of elliptic curves, which is provided. Finally, we conclude with cryptographic implementation considerations.
Circuits and Systems, 1998. …, 1999
Concept of public key cryptography was first introduced by Difie and Hellman in 1976 which using discrete logarithm problem as base of dificulty. In 1985, T. ElGamal proposed public key cyptosystem scheme based on discrete logarithm problem. Elliptic curve cryptosystems were first proposed in 1985 independently by Neil Koblitz and Victor Miller. Elliptic curve cryptosystems are unique in using elliptic curve groups for arithmetic. This cryptosystem based on discrete logarithm problem in the group of points of an elliptic curve defined over a finite field. The discrete logarithm problem in an elliptic curve group appears to be much harder than the discrete logarithm problem in other groups. Hence elliptic curwes cyptosystem can match the security of other cryptosystems while wing smaller key. In this paper we will discuss a VLSI implementation of Elliptic Curves Cryptosystem for ElGamal encryption scheme.
Journal of Discrete Mathematical Sciences and Cryptography
The ElGamal cryptosystem is one of the most widely used public-key cryptosystems that depends on the difficulty of computing the discrete logarithms over finite fields. Over the years, the original system has been modified and altered in order to achieve a higher security and efficiency. In this paper, a generalization for the original ElGamal system is proposed which also relies on the discrete logarithm problem. The encryption process of the scheme is improved such that it depends on the prime factorization of the plaintext. Modular exponentiation is taken twice during the encryption; once with the number of distinct prime factors of the plaintext and then with the secret encryption key. If the plaintext consists of only one distinct prime factor, then the new method is similar to that of the basic ElGamal algorithm. The proposed system preserves the immunity against the Chosen Plaintext Attack (CPA).
Technical Report of National Institute of Science and Technology (NIST), India, Summer Research Program, 2013 , 2013
To overcome the problems faced in symmetric key algorithms, people have chosen Asymmetric Key algorithms for communication. Communication with Asymmetric algorithms will give us transmission of information without exchanging the key. Public-key cryptography refers to a cryptographic system requiring two separate keys, one of which is secret and one of which is public. Public-key cryptography is widely used. It is an approach used by many cryptographic algorithms and cryptosystems. It underpins such Internet standards as Transport Layer Security (TLS), PGP, and GPG. RSA and Diffie–Hellman key exchange are the most widely used public key distribution systems, while the Digital Signature Algorithm is the most widely used digital signature system. In this report we are mainly concentrating on some asymmetric algorithms which are mostly used. They are RSA cryptosystem and ElGamal Cryptosystem. It also gives brief mathematical explanations. The RSA algorithm is the most commonly used encryption and authentication algorithm and is included as part of the Web browsers from Microsoft and Netscape.RSA is an algorithm for public-key cryptography that is based on the presumed difficulty of factoring large integers, the factoring problem.. The RSA algorithm involves three steps: key generation, encryption and decryption. In this we mainly concentrate on algorithms for Primality Testing, Extended Euclidian’s algorithm, Modular Exponentiation solving algorithm, etc. ElGamal System is a public-key cryptosystem based on the discrete logarithm problem. It consists of both encryption and Signature algorithms. ElGamal encryption is used in the free GNU Privacy Guard software, recent versions of PGP, and other cryptosystems. ElGamal encryption consists of three components: the key generator, the encryption algorithm, and the decryption algorithm. In this we concentrate on the algorithms Cyclic Groups, Modular Exponentiation solving algorithms etc.
Springer, 2018
The thoughts of data security prompt the advancement of Cryptography. At the end of the day, Cryptography is investigation of keeping data secure. In the advanced mark plot a message can be "marked" utilizing a secretly held decoding key. Anybody can confirm this mark utilizing the comparing freely uncovered encryption key. Marks can't be fashioned, and an endorser can't later prevent the legitimacy from claiming his mark. This has evident applications in "electronic mail" and "electronic assets exchange" frameworks. Cryptography, notwithstanding give secrecy, authenticity, integrity and non-revocation. The core of cryptography lies in the keys included and mystery of the keys used to encode or decode. Another vital issue is the key size that determines the strength of the key and complexity in executing brute force attack on the texts to recover the key. There have been different cryptographic algorithms suggested. And we give brief overview of mathematical back ground of public key cryptography. A novel the public key scheme and cryptographic signature system has been proposed and the security of system relies on difficulty of computing discrete logarithm problem over finite field.
2016
Internet has revolutionized the data communication systems. It provides platform to get the information exchanged quickly amongst the communicating parties at the same time it also provides opportunity to adversary to attack on unsecured information. In order to provide confidentiality, integrity and authentication services to unsecured information while transit or static, cryptographic techniques are used. This paper analyses the security strength of two popular and practical public-key cryptography techniques RSA (Rivest Shamir Adleman) and ECC (Elliptic Curve Cryptography). RSA is considered first generation public-key cryptography, which is very popular since its inception while ECC is gaining popularity recently. The security of the RSA cryptosystem is based on the Integer Factorization Problem (IFP) and the security of ECC is based on elliptic curve discrete logarithm problem (ECDLP). The main attraction of ECC over RSA is that the best known algorithm for solving the ECDLP ta...
2009
In this paper, we propose a novel and efficient way to improve the computational complexity of the Elliptic Curve Cryptography [ECC] algorithm. ECC is a public key cryptography system, where the underlying calculations are performed over elliptic curves. The security of ECC is based on solving the Elliptic Curve Discrete Logarithm Problem [EDCLP]. We propose an algorithm to double the computational complexity of the conventional algorithm. The proposed algorithm generates two ECDLP opposed to one problem that was generated by the conventional algorithm being used till now. With the same key size, the proposed algorithm provides more security when compared to public key cryptography systems like RSA and ECC. It can be implemented efficiently in even less time when compared to ECC. The paper discuses the underlying protocol and proves how the enhancement in security and reduction in implementation time is achieved, thereby making it well suited for wireless communication.
Expert Systems with Applications, 2021
In this paper, an alternative public-key cryptosystems (PKCs) are proposed based on the new algebraic problems namely "Dependent RSA Discrete Logarithm Problems" derived from the RSA and Discrete Logarithm (DLog) assumptions together. These PKCs are provably secure for the notions of security: indistinguishable encryptions under chosen-plaintext attacks (IND-CPA), and adaptive chosen-ciphertext attacks (IND-CCA2). Initially, a new algebraic "Computational-Dependent RSA Discrete Logarithm Problem" is presented. Then, its variant named "Decisional-Dependent RSA Discrete Logarithm Problem" is presented. Thereafter, a specific discussion has been done about their hardness and their relations to each other. Also, some arguments are given to validate the cryptographic purpose of these problems. Next, using this decisional variant an efficient PKC: "Dependent RSA Discrete Logarithm" (DRDL) cryptosystem that has indistinguishable encryptions under chosen-plaintext attacks, in the standard model is presented. Further, a PKC variant: DRDL-1 cryptosystem with improved security properties that has indistinguishable encryptions under adaptive chosen-ciphertext attacks using this decisional variant in the random oracle model, with a low computational cost is presented. These new algebraic problems constructed by using the apparent hardness of RSA and Discrete Logarithm (DLog) problems are helpful in combining both efficiency and security. Hence, it becomes more efficient than all the cryptosystems specially designed for the ElGamal cryptosystem to make it indistinguishable encryptions under adaptive chosen-ciphertext attacks.
International Journal of Scientific Research in Science, Engineering and Technology, 2020
Cryptography is an essential and effective method for securing information’s and data. Several symmetric and asymmetric key cryptographic algorithms are used for securing the data. Symmetric key cryptography uses the same key for both encryption and decryption. Asymmetric Key Cryptography also known as public key cryptography uses two different keys – a public key and a private key. The public key is used for encryption and the private key is used for decryption. In this paper, certain asymmetric key algorithms such as RSA, Rabin, Diffie-Hellman, ElGamal and Elliptical curve cryptosystem, their security aspects and the processes involved in design and implementation of these algorithms are examined.
This paper studies the mathematics of elliptic curves, starting with their derivation and the proof of how points upon them form an additive abelian group. I then worked on the mathematics necessary to use these groups for cryptographic purposes, specifically results for the group formed by an elliptic curve over a finite field, E(Fq). I examine the mathematics behind the group of torsion points, to which every point in E(Fq) belongs, and prove Hasse’s theorem along with a number of other useful results. I finish by describing how to define a discrete logarithmic problem using E(Fq) and showing how this can form public key cryptographic systems for use in both encryption and decryption key exchange.
Asymmetric key encryption is also called public key encryption. It uses two keys known as a public and a private key. Data encrypted with one key can be decrypted only with the other key. This paper discusses some public key algorithms and its advantages and disadvantages such as Rivest Shamir Adleman, Diffi-Hellman, Elliptic Curve Cryptography, Elliptic Curve Diffi-Hellman, ElGamal Encryption Algorithm, Knapsack Algorithm, Digital Signature Algorithm and Short Range Natural Numbers.
GIS SCIENCE
Algebraic curves over binary and finite fields used in the design of public key cryptography. This paper discusses some topics in algebraic curve cryptography namely elliptic curve cryptography with recent developments and different algorithms in Elliptic curve cryptography and also discussed discrete logarithmic problem and security protocol.
1997
The security of many cryptographic protocols depends on the di culty of solving the so-called \discrete logarithm" problem, in the multiplicative group of a nite eld. Although, in the general case, there are no polynomial time algorithms for this problem, constant improvements are being made { with the result that the use of these protocols require much larger key sizes, for a given level of security, than may be convenient.
IEEE Transactions on Information Theory, 1985
A new signature scheme is proposed, together with an implementation of the Diffie-Hellman key distribution scheme that achieves a public key cryptosystem. The security of both systems relies on the difficulty of computing discrete logarithms over finite fields.
Public key cryptography is typically used in the field of mathematical, which consist of factors decomposition problem of huge numbers and discrete logarithm problem in finite field. For huge numbers in public key cryptography, factors decomposition problems RSA cryptography is generally used, but in the field of hardware and high-performance computing technology RSA has encountered some difficulties. To overcome such type of difficulties the elliptic curve discrete logarithm is introduced, which provides advantages, whose public key is short, network bandwidth is small and ability to defend against to attack is strong. This paper presents the design principles of elliptic curve public key cryptography, Authentication, Encryption and Decryption with shorter key of RSA.
Cryptography is the technique of transforming an intelligible message into unintelligible format so that the message can't be read or understood by an unauthorized person during its transmission over the public networks. A number of cryptographic techniques have been developed over the centuries. With technological advancement, new techniques have been evolved significantly. Public key cryptography offers a great security for transmitting data over the public networks such as Internet. The popular public key cryptosystems like RSA and Diffie-Hellman are becoming slowly disappearing because of requirement of large number of bits in the encryption and decryption keys. Elliptic Curve Cryptograph (ECC) is emerging as an alternative to the existing public key cryptosystems. This paper describes the idea of Elliptic Curve Cryptography (ECC) and its implementation through two dimensional (2D) geometry for data encryption and decryption. This paper discusses the implementation of ECC over prime field. Much attention has been given on the mathematics of elliptic curves starting from their derivations.
2018
This paper considers the use of cryptography with elliptic curves. It is presented and defined a new cryptosystem algorithm for encryption and decryption using elliptic curves with more than one secret and public keys. Furthermore, it is described the mathematical concepts related to elliptic curves, particularly the discrete logarithm problem on elliptic curves. A description of the Diffie-Hellman algorithm on elliptic curves and elliptic curve encryption algorithm with the recipients' public keys are represented.
An asymmetric algorithm is an encryption technique that uses different keys on the process of encryption and decryption. This algorithm uses two keys, public key, and private key. The public key is publicly distributed while the private key is kept confidentially by the user and this key is required at the time of the decryption process. RSA and ElGamal are two algorithms that implement a public key cryptosystem. The strength of this algorithm lies in the bit length used. The degree of difficulty in RSA lies in the factorization of large primes while in ElGamal lies in the calculation of discrete logarithms. After testing, it is proven that RSA performs a faster encryption process than ElGamal. However, ElGamal decryption process is faster than RSA. Both of these algorithms are cryptographic public-key algorithms but have functions in different ways. RSA is a deterministic algorithm while ElGamal is a probabilistic algorithm.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.