# Number Theory with Applications to Cryptography

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- 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**

**Content**

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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