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## Coding and Cryptography

2018-2019
Dit vak wordt in het Engels aangeboden. Omschrijvingen kunnen daardoor mogelijk alleen in het Engels worden weergegeven.

### Doel vak

* The student knows basic coding theory (rate, weight, distance,
distance of a code, bounds, error correcting/detecting, linear codes
including parity generating matrix and check matrix and how to use the
latter to find the distance) and can solve problems about and with those
in explicit situations.
* The student knows cyclic linear codes over the field with 2 elements
(cyclic linear code generated by an element, generator polynomials, how
to find them using idempotents, and the relation with divisors of 1+x^n)
and can solve problems about them in explicit situations.
* The student knows the notion of irreducible polynomial, how to work
modulo a polynomial (including the use of a table), the notion of
minimal polynomial, and can calculate with those in explicit situations.
* The students knows cyclic Hamming codes and 2-error correcting
BCH-codes over the field with 2 elements and can apply the decoding
algorithms for those.
* The students knows Reed-Solomon codes of a given design distance and
can apply two decoding algorithms to those in explicit situations.
* The student knows some basics cryptography (including the Miller-Rabin
probabilistic prime test, RSA and ElGamal) and can apply those in
explicit situations.

### Inhoud vak

This course provides a thorough introduction to the theory of error
correcting codes, and also, as a small part of it, treats the algebraic
background of some protocols in cryptography. It is aimed especially at
students of Computer Science. For error correcting codes we shall
include cyclic codes, BCH codes, Reed-Solomon codes and burst error
correction. These are used in the error correcting codes underlying,
for example, CD-ROM, audio CD, and QR-codes. For the small part
on cryptography we discuss some modern public key cryptography
(e.g., RSA, ElGamal, DSA), which form part of the protocol underlying
https.

### Onderwijsvorm

Lectures (four hours) and exercise classes (two hours), organized in two
blocks of three hours (two hours of lectures, one hour of exercise
class).

### Toetsvorm

Written exam and a compulsory assignment. The written exam will count
for 80% of
the grade, the assignment for 20%. If not
both the written exam and the homework are at least 55% each,
then the maximum score will be 54% (which constitutes a fail). There are
resits for both the exam and the assignment, governed by the same rules.

### Literatuur

We shall be working from "Coding theory and cryptography, the
essentials" by Hankerson, Hoffman, Leonard, Lindner, Phelps, Rodger and
Wall (second edition, revised and expanded).

### Doelgroep

XM_CS 1, XM_PDCS 1, XM_MAT_B 1, XM_MAT_E 1, XM_MAT_T 1, XM_MAT_S 1,

### Aanbevolen voorkennis

Some knowledge on linear algebra (vectors, matrices, nullspaces, linear
(in)dependence, basis,
dimension, inner/dot product, some determinants),
on the integers modulo n, and on polynomials.
Although these will be reviewed, experience shows that the
course is difficult to follow without having seen this material before.
This is particularly true for the background on linear algebra, as it
plays a major role in the set-up and study of linear codes and many of
their properties are interpreted using it.

### Algemene informatie

Vakcode X_405041 6 EC P4 400 Engels Faculteit der Bètawetenschappen prof. dr. R.M.H. de Jeu prof. dr. R.M.H. de Jeu prof. dr. R.M.H. de Jeu

### Praktische informatie

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