Fully paramaterisable Galois Field arithmetic processor over GF(3/sup m/) suitable for elliptic curve cryptography

2004 ◽  
Author(s):  
T. Kerins ◽  
E.M. Popovici ◽  
W.P. Marnane
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Galois Field ◽  
Arithmetic Processor

scholarly journals Elliptic Curve Cryptosystem for Email Encryption

2010 ◽  
pp. 230-235
Author(s):  
Abhijit Mitra ◽  
Saikat Chakrabarty ◽  
Poojarini Mitra
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Galois Field ◽  
Elliptic Curve Cryptosystem ◽  
Public Network ◽  
Plain Text ◽  
The Core ◽  
Encryption And Decryption ◽  
Cryptographic Algorithms ◽  
Secure Transmission

The idea of information security lead to the evolution of cryptography. In other words, cryptography is the science of keeping information secure. It involves encryption and decryption of messages. The core of cryptography lies in the keys involved in encryption and decryption and maintaining the secrecy of the keys. Another important factor is the key strength, i.e. the difficulty in breaking the key and retrieving the plain text. There are various cryptographic algorithms. In this project we use Elliptic Curve Cryptography (ECC) over Galois field. This system has been proven to be stronger than known algorithms like RSA, DSA, etc. Our aim is to build an efficient elliptic curve cryptosystem for secure transmission or exchange of confidential emails over a public network.

User Confidentiality Protection in Cloud Computing Using Enhanced Elliptic Curve Cryptography (ECC) Algorithm

2017 ◽  
Vol 7 (11) ◽  
pp. 132 ◽  
Author(s):  
Abdu Osman
Keyword(s):  
Cloud Computing ◽  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Service Providers ◽  
Discrete Logarithm ◽  
Cloud Service ◽  
Galois Field ◽  
Business Partners ◽  
Prime Modulus ◽  
Confidentiality Protection

Abstract— a lot of customers are concerned about their weakness to attack if their critical IT resources are beyond the firewall. The tremendously scalable nature of cloud computing allows users to access vast amounts of data and use computing resources distributed across different interfaces. Cloud entities, such as cloud service providers, users and business partners, share the resources available at different levels of technological operations. This paper focuses on user confidentiality protection in cloud computing using enhanced elliptic curve cryptography (ECC) algorithm over Galois Field GF(2m). The Strength of the proposed ECC algorithm depends on the complexity of computing discrete logarithm in a large prime modulus, and the Galois Field allows mathematical operations to mix up data easily and effectively. The methodology used involves encrypting and decrypting data to ensure user confidentiality protection and security in the cloud. Results show that the performance of ECC over Galois Field, in two area of evaluation, was better than the ECC algorithm which is used for comparison purpose.

scholarly journals Model Proyeksi (X/Z2, Y/Z2) pada Kurva Hesian Secara Paralel Menggunakan Mekanisme Kriptografi Kurva Eliptik

2012 ◽  
Vol 12 (1) ◽  
pp. 65
Author(s):  
Winsy Weku
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Elliptic Curve Cryptography ◽  
Galois Field ◽  
Public Key ◽  
Public Key Cryptosystem ◽  
Projection Model ◽  
Galois Fields ◽  
Time Operation ◽  
Modular Inversion

MODEL PROYEKSI (X/Z2, Y/Z2) PADA KURVA HESIAN SECARA PARALEL MENGGUNAKAN MEKANISME KRIPTOGRAFI KURVA ELIPTIKABSTRAK Suatu kunci publik, Elliptic Curve Cryptography (ECC) dikenal sebagai algoritma yang paling aman yang digunakan untuk memproteksi informasi sepanjang melakukan transmisi.  ECC dalam komputasi aritemetika didapatkan berdasarkan operasi inversi modular. Inversi modular adalah operasi aritmetika dan operasi yang sangat panjang yang didapatkan berdasar ECC crypto-processor. Penggunaan koordinat proyeksi untuk menentukan Kurva Eliptik/ Elliptic Curves pada kenyataannya untuk memastikan koordinat proyeksi yang sebelumnya telah ditentukan oleh kurva eliptik E: y2 = x3 + ax + b yang didefinisikan melalui Galois field GF(p)untuk melakukan operasi aritemtika dimana dapat diketemukan bahwa terdapat beberapa multiplikasi yang dapat diimplementasikan secara paralel untuk mendapatkan performa yang tinggi. Pada penelitian ini, akan dibahas tentang sistem koordinat proyeksi Hessian (X/Z2, Y,Z2) untuk meningkatkan operasi penggandaan ECC dengan menggunakan pengali paralel untuk mendapatkan paralel yang maksimum untuk mendapatkan hasil maksimal. Kata kunci: Elliptic Curve Cryptography, Public-Key Cryptosystem, Galois Fields of Primes GF(p PROJECTION MODEL (X/Z2, Y/Z2) ON PARALLEL HESIAN CURVE USING CRYPTOGRAPHY ELIPTIC CURVE MECHANISM ABSTRACT As a public key cryptography, Elliptic Curve Cryptography (ECC) is well known to be the most secure algorithms that can be used to protect information during the transmission. ECC in its arithmetic computations suffers from modular inversion operation. Modular Inversion is a main arithmetic and very long-time operation that performed by the ECC crypto-processor. The use of projective coordinates to define the Elliptic Curves (EC) instead of affine coordinates replaced the inversion operations by several multiplication operations. Many types of projective coordinates have been proposed for the elliptic curve E: y2 = x3 + ax + b which is defined over a Galois field GF(p) to do EC arithmetic operations where it was found that these several multiplications can be implemented in some parallel fashion to obtain higher performance. In this work, we will study Hessian projective coordinates systems (X/Z2, Y,Z2) over GF (p) to perform ECC doubling operation by using parallel multipliers to obtain maximum parallelism to achieve maximum gain. Keywords: Elliptic Curve Cryptography , Public-Key Cryptosystem , Galois Fields of  Primes GF(p)

Study of Safe Elliptic Curve Cryptography over Gaussian Integer

2020 ◽  
Vol E103.A (12) ◽  
pp. 1624-1628
Author(s):  
Kazuki NAGANUMA ◽  
Takashi SUZUKI ◽  
Hiroyuki TSUJI ◽  
Tomoaki KIMURA
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Gaussian Integer

Enhanced Security Authentication of WiMAX using EC3A

2017 ◽  
Vol 7 (8) ◽  
pp. 219
Author(s):  
Mohd Javed ◽  
Khaleel Ahmad ◽  
Ahmad Talha Siddiqui
Keyword(s):  
Cellular Automata ◽  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Information Rate ◽  
Security Authentication ◽  
Encryption And Decryption ◽  
High Information

WiMAX is the innovation and upgradation of 802.16 benchmarks given by IEEE. It has numerous remarkable qualities, for example, high information rate, the nature of the service, versatility, security and portability putting it heads and shoulder over the current advancements like broadband link, DSL and remote systems. Though like its competitors the concern for security remains mandatory. Since the remote medium is accessible to call, the assailants can undoubtedly get into the system, making the powerless against the client. Many modern confirmations and encryption methods have been installed into WiMAX; however, regardless it opens with up different dangers. In this paper, we proposed Elliptic curve Cryptography based on Cellular Automata (EC3A) for encryption and decryption the message for improving the WiMAX security

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