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.