© 2015

Quantum Computational Number Theory


Table of contents

  1. Front Matter
    Pages i-ix
  2. Song Y. Yan
    Pages 1-31
  3. Song Y. Yan
    Pages 33-58
  4. Song Y. Yan
    Pages 121-172
  5. Song Y. Yan
    Pages 229-245
  6. Back Matter
    Pages 247-252

About this book


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 discusses quantum algorithms for solving the Integer Factorization Problem (IFP), the Discrete Logarithm Problem (DLP), and the Elliptic Curve Discrete Logarithm Problem (ECDLP) and for attacking IFP, DLP and ECDLP based cryptographic systems. Chapters also cover various other quantum algorithms for Pell's equation, principal ideal, unit group, class group, Gauss sums, prime counting function, Riemann's hypothesis and the BSD conjecture.

Quantum Computational Number Theory is self-contained and intended to be used either as a graduate text in computing, communications and mathematics, or as a basic reference in the related fields. Number theorists, cryptographers and professionals working in quantum computing, cryptography and network security will find this book a valuable asset.


Quantum computational number theory Computational number theory Quantum computing Cryptography Computer algorithms Computational complexity theory Number-theoretic algorithms Integer factorization Discrete logarithm Elliptic curve arithmetic Public-key cryptography Design and analysis of algorithms Fast computation Digital signatures

Authors and affiliations

  1. 1.Wuhan UniversityWuhanChina

Bibliographic information

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“Over the last two decades, the field of quantum computational number theory (QCNT) has grown, and this book summarizes the major developments in the area. … I strongly recommend the book to all young computer science students and to mathematicians who love number theory so they can enjoy this new field.” (Manish Gupta, Computing Reviews, April, 2017)