Improved RC4 Algorithm Based on Multi-Chaotic Maps

The aim of this study is to overcome on the weakness points in RC4 (Rivest Cipher 4) algorithm, there are some blemishes in the Key Scheduling Algorithm (KSA) of RC4. This study presented improved RC4 key generation based on multi-chaotic maps. The new version of KSA coined as improved KSA (IKSA), the permutation of the S array modified to depend on the random numbers generator based on three chaotic maps and the proposed algorithm outputs as follows: Output = M XOR Generated key XOR Random value from IKSA (R3w) The improved RC4 with IKSA is tested for its secrecy, randomness and performance over the variable key length and different plaintext size with respect to those of the original RC4.The results show that the improved RS4 with IKSA is better than the original RC4 with KSA.


INTRODUCTION
RC4 is the vastly stream cipher and used in many internet protocols such as wired equivalent privacy (WEP), Skype, Wireless Protected Access (WPA) and Secure Socket Layer, Transport layer security (SSL/TLS) (Crainicu, 2015). The important factors in RC4 algorithm over such an extensive domain of applications have been its speed and simplicity; efficient implementation in both software and hardware were very easy to develop. RC4 is very simple and fast compared to other encryption algorithms. Weerasinghe (2012) presented the analysis of a simply modified RC4 algorithm and tried out a simple modification of RC4 PRGA, where we can mention it like this: Out Put = M XOR Generated key XOR j. Hameed and Mahmood (2016) present a new version of KSA is suggested in an attempt to increase the security of RC4 and get rid of the weakness related to the initial permutation of the S array and the permutation process of the S array.
In Fluhrer et al. (2001) we analyzed the KSA which derives the initial state from a variable size key and describe two significant weaknesses of this process. The first weakness is in the existence of a large number of bits of the initial permutation (KSA output). The second weakness is related to key vulnerability, which applies when part of the key presented to the KSA in exposed to the attacker.
In this study we present a new improvement of the KSA depend on the randomness of the three chaotic maps (Logistic, tent and Chebyschev). The chaotic maps have many good features such as allergy on primary condition and system parameter, periodicity and mixing properties. In this study, we invest these interesting properties of chaotic maps to generation random number. The S array permutation is suggested to depend on the generated random key.

MATERIALS AND METHODS
RC4 Algorithm: Ron Rivest (Stallings, 2011), one of the inventors of RSA inserted the RC4 algorithm in 1987. RC4 is an acronym for" Rivest Cipher 4", it is also known as "Ron's Code 4". The algorithm is based on the use of a random permutation. The RC4 algorithm is simple and relatively easy to explain (Mao, 2003;Rahma and Hussein, 2015 Step 3 Step 4 Step 4 Step 4 Step 5  • Improved key scheduling algorithm, a new version of KSA called IKSA is proposed. In this proposal as shown in Fig. 4, we choose three chaotic maps (Logistic, Chebysehev and tent) and their Eq. are (1), (2) and (3), respectively. The secret key is SEED, which is the initial condition of each map. The algorithm generated by each iteration (w = 0 to 255: the number of iterations) sequences of 24 bits (8-bit blocks for each chaotic maps). R1w, R2w and R3w are extracted from chaotic maps as follows: Logistic map generate R1w Tent map generate R2w Chebysehev map generate R3w In the following way:  Step 4: /The process/ Encryption C = (M K R 3 w) mod 256 Decryption M C Generation key R Step 5: /End/

RESULTS AND DISCUSSION
Algorithm: Secrecy of ciphers: Secrecy of ciphers is calculated in terms of the key equivocation (conditional entropy of key given cipher): where, q i = Pr (C = ci) P ij = Pr (K= ki/C = ci) L = The key length n = The cipher text length • Average secrecy: A variable plaintext size, Fixed key length: As shown by the Table 1 and Fig. 5a to 5d, improvement RC4 algorithm with IKSA has better 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). • Average secrecy: A variable key length, Fixed plaintext size: As shown by the Table 2 and Fig. 6 (a to d), improved RC4 algorithm with IKSA has better average secrecy than the original RC4 algorithm with KSA, using a variable key length (32.64, 128 and 256 bits) and fixed plaintext for each phase (128, 256, 512 and 1024 bits).

CONCLUSION
In this study, the improved RC4 algorithm with IKSA based on chaotic maps is proposed (IRC4 algorithm). This algorithm overcome the weakness of the original RC4 with KSA. The average secrecy for the proposed algorithm is best than the original algorithm. The IRC4 algorithm is characterized by secrecy, performance and efficiency because of the permutation of the S array are modified to depend on the key random generation based on three chaotic maps (logistic, Chebysehev and tent).

CONFLICT OF INTEREST
This study is to provide a solution for bypass the RS4 weakness pointes by introducing improved RC4 key generation that based on multi-chaotic maps. The performance criteria secrecy and randomness were used to compare between the introduced improved algorithm with the original variant.