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 factorizatio…
Contents: Part I Quantum communication 1 Quatum information theory for quantum communication 2 Quantum communication for the ultimate capacity and security 3 Quantum communication for the experiments over optical fiber 4 Spin-photo entanglement in semiconductor quantum dots: towards solid-state-based quantum repeaters Part II Quatum metrology and sensing 5 Optical lattice c…
This book is concerned with the theory of computability and complexity over the real numbers. This theory was initiated by Turing, Grzegorczyk, Lacombe, Banach and Mazur and has seen rapid growth in recent years. br Computability and complexity theory are two central areas of research in theoretical computer science. Until recently, most work in these areas concentrated on problems over discret…
The interplay between randomness and computation is one of the most fas cinating scientific phenomena uncovered in the last couple of decades. This interplay is at the heart of modern cryptography and plays a fundamental role in complexity theory at large. Specifically, the interplay of randomness and computation is pivotal to several intriguing notions of probabilistic proof systems and is the…