Polytechnic University of the Philippines
College of Engineering
Bachelor of Science in Computer Engineering
Digital Signal Processing
KAPLAN YORKE MAP
Dapitan, Roxanne I.
Romero, Dana Angelica N.
Engr. Orland Delfino Tubola
January 19, 2012
Cryptography is the science of writing in secret code and is an ancient art; the first documented use of cryptography in writing dates back to circa 1900 B.C. when an Egyptian scribe used non-standard hieroglyphs in an inscription. Some experts argue that cryptography appeared spontaneously sometime after writing was invented, with applications ranging from diplomatic missives to war-time battle plans. It is no surprise, then, that new forms of cryptography came soon after the widespread development of computer communications. In data and telecommunications, cryptography is necessary when communicating over any untrusted medium, which includes just about any network, particularly the Internet.
Over the past decade, it has been tremendous interest in studying the behavior of chaotic systems. This belongs in what they called cryptography. They are characterized by sensitive dependence on initial conditions, similarity to random behavior, and continuous broad-band power spectrum. Chaos has potential applications in several functional blocks of a digital communication system: compression, encryption and modulation. One of the most famous chaos base encryption is Kaplan Yorke.
Kaplan Chaotic Map
The Kaplan–Yorke map is a discrete-time dynamical system. It is an example of a dynamical system that exhibits chaotic behavior. The Kaplan–Yorke map takes a point (xn, yn ) in the plane and maps it to a new point given by:
Xn+1 = 2Xn (mod 1)
Yn+1 = αYn + cos(4πXn)
Note: Due to round off error, successive applications of the modulo operator will yield zero after some ten or twenty iterations...