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Mathematics and Statistics

Number Theory with Applications to Cryptography

Number Theory with Applications to Cryptography

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Number Theory with Applications to Cryptography takes into account the application of number theory in the field of cryptography. It comprises elementary methods of Diophantine equations, the basic theorem of arithmetic and the Riemann Zeta function. This book also discusses about Congruences and their use in mock theta functions, Method of Iterative Sliding Window for Shorter Number of Operations in case of Modular Exponentiation and Scalar Multiplication, Discrete log problem, elliptic curves, matrices and public-key cryptography and Implementation of Pollard Rho over binary fields using Brent Cycle Detection Algorithm. It also provides the reader with the significant insights of number theory to the practice of cryptography in order to understand discrete log problem, matrices, elliptic curves and public-key cryptography and the applications of Fibonacci sequence on continued fractions.

Stefano Spezia is Ph.D. holder in Applied Physics at the University of Palermo since April 2012. His major research experience is in noise-induced effects in nonlinear systems, especially in the fields of modeling of complex biological systems and simulation of semiconductor spintronic devices. Associate member of the Italian Physical Society and European Physical Society.