Course in Number Theory and Cryptography

Häftad, Engelska, 2012

Av Neal Koblitz, NEAL Koblitz

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In part it is the dramatic increase in computer power and sophistica tion that has influenced some of the questions being studied by number theorists, giving rise to a new branch of the subject, called "computational number theory.

Produktinformation

Utgivningsdatum2012-09-03
Mått155 x 235 x 14 mm
Vikt386 g
FormatHäftad
SpråkEngelska
SerieGraduate Texts in Mathematics
Antal sidor235
Upplaga2
FörlagSpringer-Verlag New York Inc.
ISBN9781461264422

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I. Some Topics in Elementary Number Theory.- 1. Time estimates for doing arithmetic.- 2. Divisibility and the Euclidean algorithm.- 3. Congruences.- 4. Some applications to factoring.- II. Finite Fields and Quadratic Residues.- 1. Finite fields.- 2. Quadratic residues and reciprocity.- III. Cryptography.- 1. Some simple cryptosystems.- 2. Enciphering matrices.- IV. Public Key.- 1. The idea of public key cryptography.- 2. RSA.- 3. Discrete log.- 4. Knapsack.- 5 Zero-knowledge protocols and oblivious transfer.- V. Primality and Factoring.- 1. Pseudoprimes.- 2. The rho method.- 3. Fermat factorization and factor bases.- 4. The continued fraction method.- 5. The quadratic sieve method.- VI. Elliptic Curves.- 1. Basic facts.- 2. Elliptic curve cryptosystems.- 3. Elliptic curve primality test.- 4. Elliptic curve factorization.- Answers to Exercises.