## Implementation of Elgamal Elliptic Curve Cryptography Using Malab

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The idea of using elliptic curve in cryptography was introduced by Victor Miller [10] and Neal Koblitz as an alternative to established public key systems such as DSA and RSA. In 1985, they proposed a public key cryptosystems analogue of the ElGamal encryption schemes which used Elliptic Curve Discrete Logarithm Problem (ECDLP) [5,6,11]. According to Purbo and Wahyudi [11], Elliptic Curve Cryptography (ECC) can be used in some necessities such as encryption scheme (ElGamal ECC/EC ElGamal), digital signature (ECDSA) and key exchange protocol (Diffie Hellman
ECC/EC Diffie Hellman).

The most time consuming part of the computation is elliptic scalar multiplication. So we need to represent the multiplication algorithm ( see [5] and [6] ) to make the computation more efficient, such as binary algorithm, addition-subtraction algorithm and repeated-dobling algorithm. We use the addition-subtraction algorithm in our implementation and Non Adjacent Form (NAF) to represent the scalar. For computing the elliptic scalar multiplication k.P, k is represented by NAF form.

There are 3 main programmes which will be described in our implementation, they are:
1. Key Generation Programme.
2. Encryption Programme
3. Decryption Programme.
There are many functions must be made
to build the main programmes which
are classified into 3 categories, they are
1) Functon of Modular Arithmetics
2) Function of Elliptic Curve
Arithmatics
3) Function of ElGamal ECC.

International Conference (ICICI 2005)
Implementation of ElGamal Elliptic Curve Cryptography Using Matlab “.
Download: Abstract | Full Papers | Source Code for Matlab Ver 7.

My Project (Essay, papers, Source Code, etc): https://wan.khudri.com

## Abstract – Implementation of Elgamal Elliptic Curve Cryptography Using Malab

Author: Wan Khudri and Sutanto

ABSTRACT

ElGamal Elliptic Curve Cryptography(ECC) is a public key cryptography analogue of the ElGamal encryption schemes which is used Elliptic Curve Discrete Logarithm Problem (ECDLP). The software which is used to implement ElGamal ECC is MATLAB. This implementation consist of 3 main programmes, they are Key Generation, Encryption and Decryption ElGamal ECC. To reach the goal of the implementation, some functions which are able to construct the 3 main programmes are needed. Some functions are available in MATLAB and 31 functions are made by the writer himself. Those functions are classified into 3 categories, they are modular arithmetic function (7 functions), elliptic curve arithmetic function (5 functions) and ElGamal ECC function (19 functions).

The modular artihmetic function is used in addition operation, representation of NAF (Non Adjacent Form), multiplication operation, invers, division, power, and square root in modular arithmetic operation.

The elliptic curve arithmetic function is used in addition operation, elliptic curve equation, invers under addition, subtraction, and elliptic curve scalar multiplication.

The ElGamal function is used in biner-decimal conversion, decimal-biner conversion in ānā bit format, to find lower and upper bound of key length, to generate prime number, to generate coefficient of elliptic curve equation, to find the order of the elliptic group, to generate one elliptic curve point, to calculate the order of point, to generate base point and its order, elliptic curve domain pa rameters, to generate private key and public key, to represent plaintext into number, number into point, point into number, number into plaintext, encryption of ElGamal ECC for one point, and decryption of ElGamal ECC for one chipertext of point.

Key Words: ElGamal, elliptic curve, cryptography, field, public key

International Conference (ICICI 2005)
Implementation of ElGamal Elliptic Curve Cryptography Using Matlab “.
Download: Abstract | Full Papers | Source Code for Matlab Ver 7

My Project (Essay, papers, Source Code, etc): https://wan.khudri.com