Proven constructions in symmetric cryptography

The “mirror” theory and its applications in cryptography

  • Evaluation of the number of solutions of systems of linear non-equality in the finite field.
  • It has been proven for ten years that this theory plays a fundamental role in the security proofs of most secret key cryptographic schemes in the face of so-called “generic” attacks.


– Results of J. Patarin on Feistel diagrams, then Misty, asymmetrical Feistel …

  • New algorithms whose security is proven by “mirror theory” have the advantages of the one-time pad (they are proven safe by information theory) without having the disadvantages (they are not “malleable”)


Design criteria for block cipher algorithms

  • Linear and differential cryptanalysis

– S-boxes must have high non-linearity and good differential properties, linear permutation must have good diffusion (branch number)


  • Theorems linking the cryptographic properties of primitives to the complete security of the algorithm

– Unrealistic hypotheses (e.g. independence of subkeys)

– Upper security terminals probably far from being reached.

– Oversizing of the algorithm (by adding laps)


  • Objective: improve these reduction theorems

– Block encryption algorithms whose security is better mastered and therefore potentially faster


“Resilient” cryptography

  • The aim is to develop cryptographic algorithms capable of withstanding not only conventional cryptographic attacks but also partial leaks of secret data.
  • Particularly important for the security of smart cards for example (see ANR PRINCE project).
  • Extension of the article “The Random Oracle Model and the Ideal Cipher Model Are Equivalent” (J.S. Coron, J. Patarin, Y. Seurin, Crypto’2008, Best Paper)