الفهرس 
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Abstract
Public-key cryptography algorithms are the most important data encryption methods, as they are used extensively in many applications to protect important data and files. There are two important types of public key cryptographic algorithms (Discrete Logarithm and Exponential). Both types have RSA and El-Gamal The Public-key algorithms are characterized by good randomness and long code break time, but with the development of computers and the acceleration of CPUs, the necessity to develop these algorithms is appeared in order to increase randomization and complexity. Chaotic maps theory [4,5], is an important method used for this purpose.Chaos maps theory is concerned with the study of complex disciplined mathematical systems [6]. It is beginnings were formulated in 1961, which is less indiscriminate than the term ”chaotic system” [7,8]. It can be defined as a dynamic system because each outcome depends on one or more of its previous results.