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…
Daftar isi: 1. EPIMENIDES,GODEL,RUSSEL,DAN CANTOR 1.1 Epimenides 1.2 Godel 1.3 Russel 1.4 Cantor 2. TEORI INFORMAL PADA PUNGSI KOMPUTABEL 2.1 Fungsi fungsi 2.2 String 2.3 Fungsi komputabel,himpunan listabel dan himpunan decidabel 2.4 Fungsi universal dan himpinan tak decidabel 2.5 Teorema rice 3. FUNGSI FUNGSI REKURSIF PRIMITIF 3.1 Rekursi primitif 3.2 Minimasi dan kuantifay…
PART 1: AUTOMATA AND LANGUAGES. 1. Regular Languages. 2. Context-Free Languages. PART 2: COMPUTABILITY THEORY. 3. The Church-Turing Thesis. 4. Decidability. 5. Reducibility. 6. Advanced Topics in Computability Theory. PART 3: COMPLEXITY THEORY. 7. Time Complexity. 8. Space Complexity. 9. Intractability. 10. Advanced Topics in Complexity Theory.
CONTENTS: 1.Integers 1.1.Natural Numbers 1.2.The Euclidean Algorithm 1.3.Fermat's Little Theorem and Its Generalisations 1.4.The Ring of Integers Modulo n. The Field Zp 1.5.Representation of Numbers 2.Cryptology 2.1.Classical Secret-Key Cryptology 2.2.Modern Public-Key Cryptology 2.3.Computational Complexity 2.4.The RSA Public-Key Cryptosystem 2.5.Applications of Cryptology 3…