Kindly note that we have put a lot of effort into researching the best books on Number Theory and Cryptography subject and came out with a recommended list of top 10 best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on "Number Theory and Cryptography" as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.
1. “A Course in Number Theory and cryptography” by Neal Koblitz
“A Course in Number Theory and cryptography” Book Review: This book provides the introduction to modern and ancient arithmetic topics. Major chapters included are elementary number theory, finite fields and quadratic residues, cryptography, public key. Other topics mentioned are primality and factoring, elliptic curves. Exercises and problems are provided for student’s practice. mathematics and engineering students can use this book.


2. “Elliptic Curves: Number Theory and Cryptography” by Lawrence C Washington
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“Elliptic Curves: Number Theory and Cryptography” Book Review: This book describes the fundamental principles of elliptic curves in numerical analysis. The chapters included are the basic theory, torsion points, elliptic curves and the discrete logarithm problem. Other topics included are elliptic curves cryptography, elliptic curves over Q and isogenies. Equations and problems are discussed at length. This book is useful for mathematical and engineering students.


3. “Computational Number Theory and Modern Cryptography” by Song Y Yan
“Computational Number Theory and Modern Cryptography” Book Review: This book discusses the core principles of computational number theory and cryptography. Chapters introduced are primality testing, integer factorization, secretkey cryptography, discrete logarithmbased cryptography. Other topics discussed are quantum computational number theory, quantum resistant cryptography and elliptic curve. Bibliographic notes and references are added for further reading. Equations and diagrams are discussed in depth. This book is suitable for computer engineering and mathematics students.
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4. “Number Theory: Structures, Examples, and Problems” by Titu Andreescu and Dorin Andrica
“Number Theory: Structures, Examples, and Problems” Book Review: This book covers the important topics of number theory. Main chapters included are divisibility, power of integers, floor function and fractional part, digits of numbers. Other topics mentioned are arithmetic functions, Diophantine equations, binomial coefficient. Problems and examples are described thoroughly. Additional problems are added to test the knowledge of students. This book is useful for engineering and mathematics students.


5. “Computational Number Theory (Discrete Mathematics and Its Applications)” by Abhijit Das
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“Computational Number Theory (Discrete Mathematics and Its Applications)” Book Review: This book presents the major topics of compactional number theory. Main chapters included are arithmetic of integers and polynomials, elliptic curves, primality testing. Other topics mentioned are cryptography, cryptanalysis, public key cryptography. All the topics are mentioned in a detailed manner with plenty of examples. This book is suitable for graduate students of engineering.


6. “Number Theory Cryptography and Its Applications to GNU/Linux Software” by Giovanni A Orlando  
7. “Number Theory for Computing” by M E Hellmann and Song Y Yan
“Number Theory for Computing” Book Review: This book provides the introduction to classic number theory and its applications. Main chapters involved are elementary number theory, algorithmic number theory, primality testing, integer factorization. Other topics discussed are quantum numbertheoretic algorithms, computer systems design, cryptography and information security. Bibliographic notes are added at the end of every chapter for further reading and review purposes. This book is useful for undergraduate students studying computing and information technology, electrical and electronics engineering.


8. “Elementary Number Theory, Cryptography and Codes” by M Welleda Baldoni and Ciro Ciliberto
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“Elementary Number Theory, Cryptography and Codes” Book Review: This book discusses the basic methods of algebra and number theory. Major chapters included are roundup on numbers, computational complexity, factoring integers, continued fractions. Other topics involved are congruences, unique factorization domains, finite fields, quadratic residues, primality tests. Multiple choice questions and computational exercises are provided for student’s practice. Programming exercises containing program questions are also included to test students’ knowledge. This book can be used by advanced mathematical and computational engineering students.


9. “Number Theory in Science and Communication” by Manfred Schroeder
“Number Theory in Science and Communication” Book Review: This book contains complete knowledge of number theory and its applications. Major chapters introduced are the natural numbers, primes, the prime distribution, fractions: continued, Egyptian and farey. Other topics mentioned are linear congruences, Diophantine equations, the theorems of format, Wilson and Euler. Equations and graphs are discussed in a detailed manner. A total of 30 chapters are discussed thoroughly in this book. This book is suitable for undergraduate computer, IT engineering students.


10. “Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories (Encyclopaedia of Mathematical Sciences)” by Yu I Manin and Alexei A Panchishkin
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“Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories (Encyclopaedia of Mathematical Sciences)” Book Review: This book covers the principles of number theory along with uptodate modern problems. Major chapters included are nonAbelian generalizations of class field theory, recursive computability and Diophantine equations. Other topics mentioned are zeta and Lfunctions, Wiles’ proof of Fermat’s last theorem, and relevant techniques coming from a synthesis of various theories. Extensive problems and solutions are mentioned in this book for better understanding. This book is useful for graduate level students of computational engineering and applied mathematics students.


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