Ensimag Rubrique Formation 2022

Advanced Cryptology - WMM53C1

  • Number of hours

    • Lectures 36.0
    • Tutorials 3.0
    • Laboratory works 21.0


    ECTS 6.0


The student should understand the societal challenges of the security of information systems. At the same time, he should
also be able to understand how RSA or ECDLP work.
We complete previous courses, studying more systems using elliptic or hyperelliptic curves, going deeper in the attacks as well as
using multivariable cryptology. The course also reviews the necessary mathematical notions. We eventually introduce cryptology
based on hyperelliptic curves (HECC) and advanced cryptanalysis on ECC. Practical advantages and inconvenients of HECC with
discussion on Software/hardware implementations.

Contact Vanessa VITSE



Cryptanalysis : Notions on DES , algebraic notions : finite abelian groups, polynomial rings, finite fields
Groups, curves and cryptography Finite fields, linear algebra, polynomials, Euclidean algorithm, ideals, rings
Advanced public key methods : good knowledge of the mathematics of finite fields, groups.
Hyperelliptic cryptosystems : same as previous courses.


The exam is given in english only 

continuous control
Cryptanalysis : 2 sessions, Practical Work : 1 large project, 2 short projects
Groupes, Courbes et Cryptography : 3 sessions
Hyperelliptic cryptosystems : 1 Computer classroom
Final Examination : 1 final session with 4 parts.

S1=20%TP+15%CC+65%E1; S2=20%TP+15%CC+65%E2 (if E2>E1)

Additional Information

This course is given in english only EN

Curriculum->M2 Sec, Crypt. and Coding of Info.->SCCI - Semester 3


  • Algebraic Aspects of the Advanced Encryption Standard (Cid,Murphy, Robshaw)ISBN-10 0-387-24363-1
  • Recent proceedings of congress in cryptology (lecture Notes in Computer Science)
  • A course in Computational Algebraic Number Theory, Henri Cohen, Springer
  • Boolean Methods and Models , Cambridge University Press, Cramar Hammer Ed
  • Neal Koblitz, A.J. Menezes, Y.-H. Wu, R.J. Zuccherato, Algebraic Aspects of Cryptography (Algorithms and Computation in
    Mathematics) (Springer, 2004, 3rd Printing)
  • Oliver Pretzel, Codes and Algebraic Curves (Oxford Lecture Series in Mathematics and Its Applications, 8)
  • Emmanuel Peyre , Corps finis et courbes elliptiques. M2P Cryptologie,
    sécurité et codage d'information, , Grenoble, 2006
  • T. Ebrahimi, F. Leprévost, B. Warusfel (ed) : Cryptographie et sécurité des systèmes et réseaux. Hermes-Lavoisier (2006) ISBN 2-
    ? T. Ebrahimi, F. Leprévost, B. Warusfel (ed) : Enjeux de la sécurité multimédia. Hermes-Lavoisier (2006) ISBN 2-7462-1207-2
    ? Handbook of elliptic and Hyperelliptic curve cryptography H. Cohen G. Frey, Chapman & Hall/CRC (2005)