Learning outcomes

 

At the end of the cursus, students should be able  

  • to use arithmetics and elliptic functions theory in a correct manner to ciffer any given message or to determine the content to any ciphered message, 
  • to make proofs by mathematical induction,
  • to model system behavior equations by recurrent equations and to solve them. 

 

Goals

See learning outcomes.

Content

The lecture's content is divided into four chapters

  • recurrence equations
  • arithmetics 
  • introduction to cryptography
  • elliptic functions

 

 

 

Table of contents

1 Recurrence Equations


2 Number Theory


3 Cryptography


4 Elliptic Curves

Teaching methods

Academic lectures (15h), accompanied by exercise sessions (15h)

Assessment method

Written exam made of exercices to solve (demonstrations included), proposed in January and Augustus.

Special care will be put on how  students explain their mathematical reasoning and deductions. Clarity and formalism are thus important. 

 

Sources, references and any support material

Many books in this area exist. To cite but only two, there are - R.P. Grimaldi. Discrete and combinatorial mathematics. An applied introduction. Fifth Edition. Pearson Eduction, 2004, or  J. Hoffstein, J. Phiper et J.H. Silverman. An Introduction to Mathematical Cryptography, Springer, 2008.

 

 

Language of instruction

French
Training Study programme Block Credits Mandatory
Bachelor in Computer Science Standard 0 3
Bachelor in Computer Science Standard 2 3