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
- 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)