Practical Computational Number Theory with Python: Mathematical Foundations, Algorithms, and Cryptographic Applications

What if you could turn the mathematics of prime numbers, modular arithmetic, and cryptography into working Python code?Practical Computational Number Theory with Python bridges the gap between mathematical theory and practical programming, showing you not only how number-theoretic algorithms work, but why they work.From divisibility and the Euclidean algorithm to primality testing, integer factorization, modular arithmetic, RSA, discrete logarithms, finite fields, and elliptic-curve cryptography, this book takes you step by step from foundational concepts to practical computational applications.Inside, you'll learn how to: - Build practical number-theory algorithms with Python- Work with primes, factors, GCDs, and modular arithmetic- Implement primality testing and factorization techniques- Explore Euler's theorem, quadratic residues, and continued fractions- Build and analyze RSA cryptography- Understand Diffie-Hellman and discrete logarithms- Work with finite fields and elliptic curves- Conduct computational experiments and practical projectsWho is this book for?This book is ideal for Python programmers, computer science and mathematics students, software developers, cybersecurity enthusiasts, and aspiring cryptography practitioners who want to understand the mathematics behind the algorithms they use.You don't need to be an advanced mathematician. If you're ready to learn, experiment, and write Python, this book provides a practical path from number-theory fundamentals to modern cryptographic applications.Learn the mathematics. Write the algorithms. Run the experiments. Understand what makes modern cryptography work.