Enhancement RC4 Algorithm Based on Logistic Maps with Multi-Parameters

This paper aims at overcoming the shortcomings of RC4 (Rivest Cipher 4) algorithm that mainly resides in the "key scheduling algorithm" (KSA) of RC4. This paper is a trial to enhance key generation of RC4 on the basis of logistic maps with multi-parameters named (EKSA), the permutation of array of S improved to base of the generator for the random numbers that depend on three logistic maps with two parameters, three parameters and four parameters, the suggested algorithm result the follow : outcome = T ⊕ generated key ⊕ value that is random from EKSA (Lm4p (w)) The secrecy is tested for the enhancement RC4 with EKSA, in addition to the arbitrariness and variable key size effectiveness and different size of the plaintext regarding to those of the original RC4.The outputs display that original RC4 with KSA is less powerful than the the enhancement RC 4 with EKSA.


. Introduction
The most commonly stream cipher is RC4, and worked in many internet protocols for example wired equivalent privacy (WEP), Skype, Wireless protected access (WPA) and secure socket layer, Transport layer security (SSL/TLS) [Craincu, B.2015].The critical components in RC4 algorithm over such a broad space of applications have been its speed and clarity; efficient implementation in both s/w and h/w were exceptionally simple to create.RC4 is simple and fast compared to other encryption methods.Fluhrerand and others . in [Fluhrer, S. etal 2001] they analyzed the KSA which derives the starting state from a variable measurementfs key and explain two noteworthy shortcomings of this process.The shortcoming is within the presence of a huge number of bits of the initial permutation (KSA output).The 2nd shortcoming is related to key powerlessness, which applies when a portion of the key displayed to the KSA in uncovered to the attacker.T.D.B Weerasinghr in [T.D.B Weerasinghe, 2012] displayed the analysis of an essentially adjusted RC4 algorithm, and attempted out a basic alteration of RC4 PRGA, where we can mention it like this: Out Put=M XOR Generated key XOR j. S. M. Hameed and I. N. Mahmood in [Sarab M. Hameed etal 2016] display a unused form of KSA recommended in an endeavor to extend the security of RC4 and get freed of the shortcoming related to the elementary permutation of the S array and the permutation process of the S array.Naji, Ali and Noora (2018), Present improved RC4 key generation using Multi-Chaotic Maps (IKSA), the results of improved RC4 with IKSA is better than RC4 with KSA.
This paper show a new enhancement of the KSA depend on the randomness of the three logistic maps (With (two parameters, three parameters and four parameters)).The logistic maps have many good features such as allergy on primary condition and system parameter, periodicity and mixing properties.In this paper, we invest these interesting properties of logistic maps to generation random number.The S array permutation is proposed to depend on the generated random key.

Overview 2.1 RC4 Algorithm
In 1987, Ron Rivest [Stallings W., 2011], that consider to be member that create RSA put the RC4.RC4 is a shortened form for" Rivest Cipher 4", it is similarly recognized as "Ron's Code 4".The algorithm is depending on theutilize of a random variation.The RC4 algorithm is straightforward and moderately simple to clarify.[Mao W., 2003][ Abdul M.S. Rahma etal, 2015].Figure 1 shows the "Pseudo random number generation algorithm" (PRGA) and "key scheduling algorithm" (KSA)

Logistic maps with One and Multi-Parameters
In different methods for the encryption of the information , The one-dimensional chaotic maps have been massively used as it recognize for its high-level simplicity and skill.In spite of its features it possess some defects, for instance small key space and security deficiency.Consequently, there is deficiencies in the use of logistic maps with one and multi-parameters.

A. Logistic chaotic Map with one parameter
Logistic chaotic map is the simplest nonlinear model of the chaotic map occurs in real systems.The logistic map chaotic scheme is signified as in the following:

Proposed Algorithm
The aim of this part is to generate the enhancement RC4 algorithm (ERC4) fundamentally through two stages.Step 5:/End/

Secrecy of ciphers
Secrecy of ciphers is calculated in terms of the key prevarication (conditional entropy of key given cipher) L is the key length n is the cipher text length 1-Average secrecy test: A variable plaintext size, Fixed key length.:1 and figure 11 (a), (b), (c), and (d), improvement RC4 algorithm with EKSA has operative average secrecy than the original RC4 algorithm with KSA, using a variable plaintext size (128,256,512 and 1024 bits), and fixed key length for each phase(32,64,128 and 256 bits).

Figure 2 :
Figure 2: The logistic map with one parameter

Figure ( 7 )
Figure(7) The logistic map with three parameters.The four parameters logistic map with is signified as:

Table 1 :
Average Secrecy Value vs. Plaintext size

Table 2 :
Average Secrecy Value vs. Key length

Table 2
The next step , numerous diverse trials are performed to test the statistical properties of the cipher text that created from improved RC4 algorithm with EKSA and it is sensitiveness to elementary conditions.The four different statistical tests (frequency test, serial test, poker test and run test) on a lot of binary sequences of key size (32, 64, 128 and 256 bits) and plaintext size (128 and 1024 bits).These binary sequences succeed in all four tests successfully.Results are shown in Table3.

Table 3 :
Randomness Test for Enhancement RC4 Algorithm