CHAOS AND PUBLIC KEY INFRASTRUCTURE (PKI)

The emergence of chaos theory promised a new era in the field of cryptography as
the properties of a chaotic system are exploited. Many studies have been done in this
area, in which various schemes employing chaotic systems have been proposed.
Schemes ranging from different aspects of chaotic systems to the both symmetric and
asymmetric encryption are published. However, according to [1], the author
suggested a more comprehensive insight into both chaotic systems and cryptography
algorithms is needed before doing any design to avoid having a "bothweak and slow
ciphers". The author of [1] has a published work entitled "Public-key Encryption
Based on Chebyshev Maps" [2] and this is utilized as the core of a new public key
encryption scheme. Thenew scheme proposed here is "Public-Key Encryption based
on Logistic Map" which employs many similar concepts as [2].
Athorough study on various polynomials has beenconducted and implementation on
MATLAB has been done which includes conventional public key encryption scheme
such as RSA algorithm. It is continued with the implementation of [2] to test for its
workability in MATLAB p latform. A major problem faced in this implementation
has been solved while implementing the new logistic map scheme. Consequently, the
new scheme is able to provide higher precision, thus higher security level, although
at the price of the performance. Most importantly, however, is the proof of the
workability of the whole new scheme. Theproject thus concludes with comparison of
the new public key scheme based on logistic map with RSA algorithm on MATLAB
platform.