Introduktion til kryptografi. (Introduction to cryptography).
Book: N. Koblitz: A course in number theory and cryptography. Second edition.
Graduate Texts in Mathematics 114, Springer 1994.
Course plan: Chapters III.1, I, III.2, II.1-2,
IV.1-4, V.1-5, VI.1-3.
Detailed plan:
19.12: VI.2,3.
16.12: VI.2,3.
12.12: VI.1.
09.12: End V.5: Quadratic sieve + number field sieve.
05.12: V.5: Quadratic sieve.
02.12: Review session.
28.11: End V.4.
25.11: V.4: Continued fractions.
Recommended exercises: Homework no. 3.
21.11: V.4: Continued fractions.
18.11: Background from analytic number theory + Begin V.4.
Recommended exercises: V.4: 1(a),(b), 2(a) (p. 159); + browse some of the notes.
14.11: Background from analytic number theory. Notes
11.11: End V.3 + Background from analytic number theory.
Recommended exercises: V.3: 3, 8(a) (pp. 153-154); V.2: 7 (p. 143).
07.11: V.3.
04.11: V.2, begin V.3.
Recommended exercises: V.2: 5, 6 (pp. 142-143); V.3: 1(b),(c), 2 (p. 153).
31.10: End V.1, begin V.2.
28.10: V.1.
24.10: Begin V.1.
21.10: IV.4.
Recommended exercises: II.2: 17 (p. 51); V.1: 3, 5(a),(b), 10, 14 (pp. 135-136).
10.10: End IV.3 + Paper by Pohlig and Hellman:
IEEE Trans. Inform. Theory 24 (1978), 106--110.
07.10: Begin IV.3.
Recommended exercises: I.2: 3 (p. 15); IV.2: 4 (p. 96); IV.3: 7 (p. 109).
03.10: IV.1, IV.2.
30.09: End II.2.
Recommended exercises: II.2: 21 (p. 52); IV.2: 6 (p. 97).
26.09: End II.1, begin II.2.
23.09: II.1.
Recommended exercises: II.1: 13, 16, 17 (pp. 41-42); II.2: 1, 2, 3 (p. 50).
Correction to II.1.13: Part (b) should read: `Under what conditions is every element $\neq 0, 1, -1$ either a generator or the square of a generator?'
19.09: Begin II.1.
16.09: III.2.
Recommended exercises: III.2: 7 (p. 78); I.3: 23 (pp. 26-27); II.1: 1, 2 (p. 40).
12.09: End I.3, I.4.
09.09: Division algorithm + I.3: Eulers \phi function. Extraction of square roots.
Recommended exercises: I.2: 11, 12 (p. 17); I.3: 7, 11(a) (p. 25); I.4: 3, 4, 5 (p. 29).
05.09: I.2, begin I.3.
02.09: III.1 and I.1.