RC4 is an important encryption algorithm that can be used for information protection on many communication networks, as it is simple and fast in implementation, but it has weaknesses in its keystream bytes such that these bytes are biased to some different values of the private key. The main contribution of this chapter is to design new, efficient, and fast algorithms to analyze the RC4 algorithm based on single-byte bias and double-byte bias. Many stream cipher algorithms are based on the use of linear feedback shift registers (LFSRs) particularly in the hardware, but the design of RC4 algorithm evades the use of LFSRs. This algorithm consists of two main components to generate the key namely: the key scheduling algorithm (KSA) and the pseudo-random generation algorithm (PRGA), implemented sequentially. RC4 and developed algorithms were implemented in C# programming and a new efficient experiment was designed based on proving single bias in the first 32 bytes of the keystream.