A Course in Number Theory and Cryptography [electronic resource] /
by Neal Koblitz.
- 1st ed. 1987.
- VIII, 208 p. online resource.
- Graduate Texts in Mathematics, 114 2197-5612 ; .
- Graduate Texts in Mathematics, 114 .
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 -- V. Primality and Factoring -- §1. Pseudoprimes -- §2. The rho method -- §3. Fermat factorization and factor bases -- §4. The continued fraction method -- VI. Elliptic Curves -- §1. Basic facts -- §2. Elliptic curve cryptosystems -- §3. Elliptic curve factorization -- Answers to Exercises.