**Translations of Mathematical Monographs**

2007;
243 pp;
Hardcover

MSC: Primary 11;
Secondary 94

**Print ISBN: 978-0-8218-4090-0
Product Code: MMONO/232**

List Price: $97.00

AMS Member Price: $77.60

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#### Supplemental Materials

# Number-Theoretic Algorithms in Cryptography

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*O. N. Vasilenko*

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.

#### Readership

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