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**A course in number theory and cryptography.
2nd ed.**
*(English)*
Zbl 0819.11001

Graduate Texts in Mathematics. 114. New York, NY: Springer-Verlag. x, 235 p. (1994).

Since the appearance of the first edition of the book in 1987 (see Zbl 0648.10001), it has established itself as one of the best introductions to the field of modern cryptography, covering the diverse mathematical background required in an efficient and readable manner. While the book requires little in the way of algebraic or number theoretic background, it covers the mathematical material introduced at an appropriate depth.

This second edition of the book, apart from making corrections and clarifications and adding references, has added several new sections suggested by the continuing evolution of the field. A new section on zero-knowledge proofs and the concept of oblivious transfer is included. The quadratic sieve factoring method is discussed and analyzed, a useful addition to the volume. A discussion of number field sieve factorization is, however, beyond the scope of the book. The use of elliptic curves for primality testing is also introduced. In addition to these mathematical techniques, their application to the cryptographic methods of \(k\)- threshold schemes, probabilistic encryption, hash functions, the Chor- Rivest knapsack cryptosystem, and the new digital signature standard of the US government are discussed.

This second edition of the book, apart from making corrections and clarifications and adding references, has added several new sections suggested by the continuing evolution of the field. A new section on zero-knowledge proofs and the concept of oblivious transfer is included. The quadratic sieve factoring method is discussed and analyzed, a useful addition to the volume. A discussion of number field sieve factorization is, however, beyond the scope of the book. The use of elliptic curves for primality testing is also introduced. In addition to these mathematical techniques, their application to the cryptographic methods of \(k\)- threshold schemes, probabilistic encryption, hash functions, the Chor- Rivest knapsack cryptosystem, and the new digital signature standard of the US government are discussed.

Reviewer: I.F.Blake (Waterloo / Ontario)

### MSC:

11-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory |

11T71 | Algebraic coding theory; cryptography (number-theoretic aspects) |

94A60 | Cryptography |

94-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory |

11A51 | Factorization; primality |