General Diffusion Analysis: How to Find Optimal Permutations for Generalized Type-II Feistel Schemes

Cauchois, Victor; Gomez, Clément; Thomas, Gaël

doi:10.13154/tosc.v2019.i1.264-301

Cited by 2 publications

(7 citation statements)

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“…To ease the problem of finding optimal permutations, the focus has been made on even-odd permutations as they seem to achieve better diffusion [3,5]. The belief that evenodd permutations are better has only been formally established by exhausting all the optimal permutations up to 2k = 20 [3]. In this paper, relying on a novel algorithm based on iterative path building, we will show that this is true up to 2k = 32.…”

Section: Diffusion Roundmentioning

confidence: 96%

“…As recalled in introduction, finding permutations minimizing the diffusion round has deserved a lot of attention during the past few years. To ease the problem of finding optimal permutations, the focus has been made on even-odd permutations as they seem to achieve better diffusion [3,5]. The belief that evenodd permutations are better has only been formally established by exhausting all the optimal permutations up to 2k = 20 [3].…”

Section: Diffusion Roundmentioning

confidence: 99%

“…Definition 3. Given a permutation π over 2k elements, the Feistel permutation graph associated to π is the graph G π = (V, E) where: (3,2), (5,4), . .…”

Section: Graph Representation Of a Feistel Permutationmentioning

confidence: 99%

“…As explained in [3], in the even-odd case, the permutation can be split in two parts, the odd to even edges and the even to odd edges. This makes the search easier (k!)…”

Section: Skeletonsmentioning

confidence: 99%

“…It is worthy to note that such an optimal permutation was then used to design block ciphers such as TWINE [11]. At FSE'19 Cauchois et al identified new equivalence classes regarding the diffusion rounds and, together with new algorithms, were able to give optimal permutations up to 2k = 20 [3]. Furthermore, restricting the search to even-odd permutations (i.e.…”

Section: Introductionmentioning

confidence: 99%

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New Algorithm for Exhausting Optimal Permutations for Generalized Feistel Networks

Delaune

Derbez

Gontier

et al. 2022

Lecture Notes in Computer Science

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The Feistel construction is one of the most studied ways of building block ciphers. Several generalizations were proposed in the literature, leading to the Generalized Feistel Network (GFN) construction, in which the round function operates on each pair of blocks in parallel until all branches are permuted. At FSE'10, Suzaki and Minematsu studied the diffusion of such construction, raising the question of how many rounds are required so that each block of the ciphertext depends on all blocks of the plaintext. Exhausting all possible permutations up to 16 blocks, they observed that there were always optimal permutations mapping even-number input blocks to odd-number output blocks and vice versa. Recently, both Cauchois et al. and Derbez et al. proposed new algorithms to build optimal even-odd permutations for up to 36 blocks. In this paper, we present a new algorithm based on iterative path building to search for optimal Feistel permutation. This algorithm is much faster in exhausting optimal non-even-odd permutations than all the previous approaches. Our first result is a computational proof that no non-even-odd permutation reaches a better diffusion round than optimal even-odd permutations up to 32 blocks. Furthermore, it is well known that permutations with an optimal diffusion round do not always lead to optimal permutations against differential cryptanalysis. We investigate several new criteria to build permutations leading to more secure GFN.

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Section: Diffusion Roundmentioning

confidence: 96%

Section: Diffusion Roundmentioning

confidence: 99%

“…Definition 3. Given a permutation π over 2k elements, the Feistel permutation graph associated to π is the graph G π = (V, E) where: (3,2), (5,4), . .…”

Section: Graph Representation Of a Feistel Permutationmentioning

confidence: 99%

“…As explained in [3], in the even-odd case, the permutation can be split in two parts, the odd to even edges and the even to odd edges. This makes the search easier (k!)…”

Section: Skeletonsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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