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Number-Theoretic Algorithms in Cryptography

O. N. Vasilenko Moscow State University, Moscow, Russia
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Hardcover ISBN: 978-0-8218-4090-0
Product Code: MMONO/232
List Price: $103.00 MAA Member Price:$92.70
AMS Member Price: $82.40 Electronic ISBN: 978-1-4704-1814-4 Product Code: MMONO/232.E List Price:$97.00
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AMS Member Price: $123.60 Click above image for expanded view Number-Theoretic Algorithms in Cryptography O. N. Vasilenko Moscow State University, Moscow, Russia Available Formats:  Hardcover ISBN: 978-0-8218-4090-0 Product Code: MMONO/232  List Price:$103.00 MAA Member Price: $92.70 AMS Member Price:$82.40
 Electronic ISBN: 978-1-4704-1814-4 Product Code: MMONO/232.E
 List Price: $97.00 MAA Member Price:$87.30 AMS Member Price: $77.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$154.50 MAA Member Price: $139.05 AMS Member Price:$123.60
• Book Details

Translations of Mathematical Monographs
Volume: 2322007; 243 pp
MSC: Primary 11; Secondary 94;

Algorithmic number theory is a rapidly developing branch of number theory, which, in addition to its mathematical importance, has substantial applications in computer science and cryptography. Among the algorithms used in cryptography, the following are especially important:

• algorithms for primality testing;
• factorization algorithms for integers and for polynomials in one variable;
• applications of the theory of elliptic curves;
• algorithms for computation of discrete logarithms;
• algorithms for solving linear equations over finite fields;
• algorithms for performing arithmetic operations on large integers.

The book describes the current state of these and some other algorithms. It also contains extensive bibliography. For this English translation, additional references were prepared and commented on by the author.

Graduate students and research mathematicians interested in algorithmic number theory and its applications.

• Chapters
• Primality testing and construction of large primes
• Factorization of integers with exponential complexity
• Factorization of integers with subexponential complexity
• Application of elliptic curves to primality testing and factorization of integers
• Algorithms for computing discrete logarithm
• Factorization of polynomials over finite fields
• Reduced lattice bases and their applications
• Factorization of polynomials over the field of rational numbers with polynomial complexity
• Discrete Fourier transform and its applications
• High-precision integer arithmetic
• Solving systems of linear equations over finite fields
• Facts from number theory

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 2322007; 243 pp
MSC: Primary 11; Secondary 94;

Algorithmic number theory is a rapidly developing branch of number theory, which, in addition to its mathematical importance, has substantial applications in computer science and cryptography. Among the algorithms used in cryptography, the following are especially important:

• algorithms for primality testing;
• factorization algorithms for integers and for polynomials in one variable;
• applications of the theory of elliptic curves;
• algorithms for computation of discrete logarithms;
• algorithms for solving linear equations over finite fields;
• algorithms for performing arithmetic operations on large integers.

The book describes the current state of these and some other algorithms. It also contains extensive bibliography. For this English translation, additional references were prepared and commented on by the author.

Graduate students and research mathematicians interested in algorithmic number theory and its applications.

• Chapters
• Primality testing and construction of large primes
• Factorization of integers with exponential complexity
• Factorization of integers with subexponential complexity
• Application of elliptic curves to primality testing and factorization of integers
• Algorithms for computing discrete logarithm
• Factorization of polynomials over finite fields
• Reduced lattice bases and their applications
• Factorization of polynomials over the field of rational numbers with polynomial complexity
• Discrete Fourier transform and its applications
• High-precision integer arithmetic
• Solving systems of linear equations over finite fields
• Facts from number theory
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.