Quantum Computational Number Theory

This book provides a comprehensive introduction to advanced topics in the computational and algorithmic aspects of number theory, focusing on applications in cryptography. Readers will learn to develop fast algorithms, including quantum algorithms, to solve various classic and modern number theoretic problems. Key problems include prime number generation, primality testing, integer factorization, discrete logarithms, elliptic curve arithmetic, conjecture and numerical verification.§§The author explores how many of the number theoretic problems are widely used as one-way functions in public-key cryptography and digital signatures. Chapters examine how, despite being computational intractable and having no polynomial-time algorithms, these number problems are used to safe-guard internet and e-commerce transactions. The clear practical applications for number problems explain why design efficient algorithms are extremely important in developing techniques and solutions.§§Quantum Computational Number Theory is suitable as a secondary text for advanced-level students in computer science, electronic and communication engineering, and applied mathematics. It can also be used as a reference for researchers in information security and for practitioners in government intelligence agencies and the information security industries.§§