Number Theory with Applications to Cryptography

Number Theory with Applications to Cryptography
PDF
  • eBook:
    Number Theory with Applications to Cryptography
  • Author:
    Stefano Spezia
  • Edition:
    -
  • Categories:
  • Data:
    November 1, 2019
  • ISBN:
    177407351X
  • ISBN-13:
    9781774073513
  • Language:
    English
  • Pages:
    290 pages
  • Format:
    PDF

Book Description
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.

Content

SECTION I: DIOPHANTINE EQUATIONS
Chapter 1. A Disaggregation Approach for Solving Linear Diophantine Equations
Chapter 2. Diophantine Equations. Elementary Methods
Chapter 3. Diophantine Equations. Elementary Methods II
Chapter 4. Almost and Nearly Isosceles Pythagorean Triples
Chapter 5. A Public Key Cryptosystem based on Diophantine Equations of Degree Increasing Type

SECTION II: THE RIEMANN ZETA FUNCTION AND THE FUNDAMENTAL THEOREM OF ARITHMETIC
Chapter 6. Hamiltonian for the Zeros of the Riemann Zeta Function
Chapter 7. Fractional Parts and Their Relations to the Values of the Riemann Zeta Function

SECTION III: CONGRUENCES
Chapter 8. 11-Dissection and Modulo 11 Congruences Properties for Partition Generating Function
Chapter 9. Effective Congruences for Mock Theta Functions
Chapter 10. On Integer Solutions of the Cubic Equations Over Certain Fields
Chapter 11. Iterative Sliding Window Method for Shorter Number of Operations in Modular Exponentiation and Scalar Multiplication

SECTION IV: DISCRETE LOG PROBLEM, ELLIPTIC CURVES, MATRICES AND PUBLIC-KEY CRYPTOGRAPHY
Chapter 12. Implementation of Pollard Rho over binary fields using Brent Cycle Detection Algorithm
Chapter 13. Cryptanalysis of a Proposal Based on the Discrete Logarithm Problem Inside Sn
Chapter 14. Research on Attacking a Special Elliptic Curve Discrete Logarithm Problem
Chapter 15. Are Matrices Useful in Public-Key Cryptography?

SECTION V: CONTINUED FRACTIONS
Chapter 16. An Application of Fibonacci Sequence on Continued Fractions
Chapter 17. On The Quantitative Metric Theory of Continued Fractions in Positive Characteristic
Chapter 18. Some New Continued Fraction Sequence Convergent to the Somos QuadraticRecurrence Constant
Chapter 19. Continued Fractions for Some Transcendental Numbers

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