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Comparison of Public Key Cryptography in Different Security International Journal of Recent Development in Engineering and Technology Website: www.ijrdet.com (ISSN 2347-6435(Online) Volume 8, Issue 12, December 2019) Comparison of Public Key Cryptography in Different Security Level Zarni Sann1, Thi Thi Soe2, Khaing Myat Nwe3 1,3Faculty of Computer Systems and Technologies, University of Computer Studies (Mandalay), Myanmar 2Faculty of Computer Science, University of Computer Studies (Mandalay), Myanmar Abstract— Information security is one of the key challenges The El-Gamal algorithm depends on certain parameters in data communication. For secure information which are affecting the performance, speed and security of communication over public network, different cryptographic the algorithm. This paper gives an overview of these three methods are applied. There have many public key cryptosystems and a performance comparison of these cryptography systems and they have difference performance. cryptosystems based on execution time in different key size This system proposes the performance of the three public key cryptography systems: RSA (Rivest Shamir Adelman), and file size [6]. ElGamal and ECC (Elliptic Curve Cryptography) by This paper is organized into five sections including this comparing encryption and decryption messages. This paper section. Section 2 gives Overview of the cryptography presents the implementation and comparison of RSA, Elgamal systems. Section 3 describes the background theory of the and ECC for variable text files sizes. Our goal is to calculate three public key cryptosystems: RSA, ElGamal and ECC. encryption time, decryption time, and key size based on In section 4 gives the results of the comparison of three different file size for each algorithm to identify which cryptosystems with the figure and chats. Section 5 algorithms outperforms others in term of evaluation describes the conclusion and further extension of this parameters. system. Keywords— Key generation, Encryption, Decryption, RSA, ElGamal, ECC II. CRYPTOGRAPHY Cryptography, over the ages, has been an art practiced I. INTRODUCTION by many who have devised ad hoc techniques to meet some A public key cryptosystem is an asymmetric of the information security requirements. The last twenty cryptosystem where the key is constructed of a public key years have been a period of transition as the discipline and a private key. The public key, known to all, can be moved from an art to a science.[8] It can be characterized used to encrypt messages. Only a person that has the by two types of cryptography systems: (1) Symmetric or corresponding private key can decrypt the message [1]. private key cryptography system and (2) Asymmetric or One of the most widely used public key cryptosystem is public key cryptography system. RSA. In RSA a public key is constructed by multiplication A. Public Key Cryptography System of two very large primes. To completely break RSA one needs to find the prime factors. In practice, RSA has Public-key cryptosystems help solve the key distribution proved to be quite slow, especially the key generation problem by using separate keys for encryption and algorithm. RSA also requires longer keys in order to be decryption, and making the encryption key public. Anyone secure compared to some other cryptosystems like elliptic can then encrypt a message, but only parties in possession curve cryptosystems (ECC) [5]. of the private key can decrypt messages. Public key ECC is one public key cryptosystem, which has proven systems are also known as asymmetric key cryptography to be faster than RSA. It is based on a discrete logarithm [1]. problem in elliptic curve groups. ECC has been around for some time and has some existing implementations [7]. III. IMPLEMENTATION METHODS IN THE SYSTEM El-Gamal encryption/decryption is based on the In this section, the three public key cryptography difficulty of the discrete algorithm problem where it is systems: Rivest Shamir Adelman (RSA), ElGamal and straight forward to raise numbers of large powers but it is Elliptic Curve Cryptography (ECC) are presented as much harder to do the inverse computation of the discrete implementation of the system. logarithm. 1 International Journal of Recent Development in Engineering and Technology Website: www.ijrdet.com (ISSN 2347-6435(Online) Volume 8, Issue 12, December 2019) B. RSA Encryption Given m, the receiver A can recover the original RSA is widely used in encrypted connection, digital message m by reversing the padding scheme. certificates core algorithms. Public key algorithm invented C. Elliptic Curve Cryptography (ECC) in 1977 by Ron Rivest, Adi Shamir and Leonard Adelman The idea of using Elliptic curves in cryptography was (RSA). It is the main operation of RSA to compute modular introduced by Victor Miller and N. Koblitz as an exponentiation. Since RSA is based on arithmetic modulo alternative to established public-key systems such as DSA large numbers, it can be slow in constraining environments. and RSA. An elliptic curve E(F p) over a finite field F p is Especially, when RSA decrypts the cipher text and defined by the parameters a, b ∈ Fp. An elliptic curve is generates the signatures, more computation capacity and given by an equation in the form of: time will be required. Reducing modules in modular exponentiation is a technique to speed up the RSA y2 = x3+ ax + b where 4a3 + 27b2 ≠ 0. (6) decryption. The security of RSA comes from integer to find. Generation of random prime numbers gives the The set of points on E (F p) also include point O, which algorithm extra strength and efficiency [2, 5]. is the point at infinity and which is the identity element under addition. This problem is defined as: RSA Key Generation Given points X, Y on the elliptic curve, find z such that: A RSA public and private key pair can be generated X = zY (7) using the algorithm below: 1. Choose two random prime numbers p and q such that The elliptic curve parameters for cryptographic schemes the bit length of p is approximately equal to the bit should be carefully chosen in order to resist all known length of q. attacks of Elliptic Curve Discrete Logarithmic Problem (ECDLP) [2, 3, 7]. Hence, the method of encryption COMPUTE N SUCH THAT N = P * Q. (1) proposed here provides sufficient security against cryptanalysis at relatively low computational overhead. 2. Compute f (n) such that ECC Key Generation Φ (N) = (P – 1)*(Q – 1). (2) To generate a public and private key pair for use in ECC 3. Choose a random integer e such that e <φ (n) and gcd communications, an entity would perform the following (e, φ (n)) = 1, then compute the integer d such that: steps: E*D = 1 MOD Φ(N). (3) 1. Find an elliptic curve E (K), where K is a finite field such as F p or F2 n, and a find point Q on E (K). n is the 4. (n, e) is the public key, and d is the private key. order of Q. Recommended domain parameters for E(K) RSA Encryption are suggested in [6]. Suppose the sender B wishes to send a message (say 'm') 2. Select a pseudo random number x such that 1≤ x≤(n- 1). to the user A. To encrypt the message using the RSA 3. Compute point P = x Q. (8) encryption scheme, the sender B must obtain A's public key 4. ECC key pair is (P, x), where P is public key, and x is pair (e, n). The message to send must now be encrypted private key. using this pair (e, n). However, the message 'm' must be ECC Encryption represented as an integer in the interval [0, n-1]. To encrypt To encrypt and send a message P to B, the receiver A it, the user B simply computes the number 'c' where m chooses a random positive integer x and produces the e c = m mod n (4) cipher text Cm consisting to the pair of points [5]. B sends the cipher text c to A. Cm = { xG, Pm + xPB } (9) RSA Decryption Note that A has used B‘s public key PB. The receiver A can recover m from c by using A‘ private ECC Decryption key exponent d by the following computation: To decrypt the cipher text, the receiver B multiplies the m =cd mod n (5) first point in the pair by B‘s secret key and subtracts the result from the second point: 2 International Journal of Recent Development in Engineering and Technology Website: www.ijrdet.com (ISSN 2347-6435(Online) Volume 8, Issue 12, December 2019) Pm + xPB – nB(xG) = Pm + x(nBG) – nB(xG) = Pm (10) (1) Incoming parameter is (e1, e2, p, P) (2) Select a random integer r A has masked the message P by adding xP to it. m B (3) C1 = e1r mod p Nobody but A knows the value of x, so even though P is a B (4) C2 = (P x e2r) mod p public key, nobody can remove the mask xP . B (5) return (C1, C2) D. ElGamal Cryptosystem (6) (C1 and C2 are ciphertexts) The El-Gamal algorithm is a public-key cryptosystem y based on the discrete logarithm problem. It consists of both Note that one can easily find h if one knows m'. the encryption and signature algorithms. ElGamal Therefore, a new y is generated for every message to algorithm is performed in three parts: improve security. For this reason, y is also called an ephemeral key. Key generation for public keys and private keys Encryption for original plaintext message to receive Elgamal Decryption cipher text, and Decryption is the third stage of Elgamal algorithm. Decryption for cipher text to generate original plaintext ElGamal proves and illustrates the decryption theory in the ElGamal algorithm is illustrated in Figure 2.
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