Two Simple Composition Theorems with H-coefficients

Abstract : We will present two new and simple theorems that show that when we compose permutation generators with independent keys, then the "quality" of CCA security increases. These theorems (Theorems 2 and 5 of this paper) are written in terms of H-coefficients (which are nothing else, up to some normalization factors, than transition probabilities). Then we will use these theorems on the classical analysis of Random Feistel Schemes (i.e. Luby-Rackoff constructions) and we will compare the results with the coupling technique. Finally, we will show an interesting difference between 5 and 6 Random Feistel Schemes. With 5 rounds on 2n bits → 2n bits, when the number of q queries satisfies √ 2 n q 2 n , we have some "holes" in the H-coefficient values, i.e. some H values are much smaller than the average value of H. This property for 5 rounds does not exist anymore on 6 rounds.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [20 references]  Display  Hide  Download

https://hal.uvsq.fr/hal-02171943
Contributor : Équipe Hal Uvsq <>
Submitted on : Wednesday, July 3, 2019 - 12:29:35 PM
Last modification on : Tuesday, July 9, 2019 - 12:13:37 PM

File

2016-956.pdf
Files produced by the author(s)

Identifiers

Citation

Jacques Patarin. Two Simple Composition Theorems with H-coefficients. 2019. ⟨hal-02171943⟩

Share

Metrics

Record views

33

Files downloads

48