Recursive Diffusion Layers for Block Ciphers and Hash Functions

Pouyan Sepehrdad
Springer, 2012
Article de conférence

Résumé

Many modern block ciphers use maximum distance separable (MDS) matrices as the main part of their diffusion layers. In this paper, we propose a new class of diffusion layers constructed from several rounds of Feistel-like structures whose round functions are linear. We investigate the requirements of the underlying linear functions to achieve the maximal branch number for the proposed 44 words diffusion layer. The proposed diffusion layers only require word-level XORs, rotations, and they have simple inverses. They can be replaced in the diffusion layer of the block ciphers MMB and Hierocrypt to increase their security and performance, respectively. Finally, we try to extend our results for up to 88 words diffusion layers.

Official source

https://infoscience.epfl.ch/record/176365?ln=fr

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Efficient Recursive Diffusion Layers for Block Ciphers, and Hash Functions

Pouyan Sepehrdad

Many modern block ciphers use maximum distance separable (MDS) matrices as the main part of their diffusion layers. In this paper, we propose a very efficient new class of diffusion layers constructed from several rounds of Feistel-like structures whose round functions are linear. We investigate the requirements of the underlying linear functions to achieve the maximal branch number for the proposed 4x4 words diffusion layer, which is an indication of the highest level of security with respect to linear and differential attacks. We try to extend our results for up to 8x8 words diffusion layers. The proposed diffusion layers only require simple operations such as word-level XORs, rotations, and they have simple inverses. They can replace the diffusion layer of several block ciphers and hash functions in the literature to increase their security, and performance. Furthermore, it can be deployed in the design of new efficient lightweight block ciphers and hash functions in future.

Springer2015

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Tweakable block cipher as a cryptographic primitive has found wide applications in disk encryption, authenticated encryption mode and message authentication code, etc. One popular approach of designing tweakable block ciphers is to tweak the generic constructions of classic block ciphers. This paper focuses on how to build a secure tweakable block cipher from the Key-Alternating Feistel (KAF) structure, a dedicated Feistel structure with round functions of the form 𝐹𝑖(𝑘𝑖⊕𝑥𝑖) , where 𝑘𝑖 is the secret round key and 𝐹𝑖 is a public random function in the i-th round. We start from the simplest KAF structures that have been published so far, and then incorporate the tweaks to the round key XOR operations by (almost) universal hash functions. Moreover, we limit the number of rounds with the tweak injections for the efficiency concerns of changing the tweak value. Our results are two-fold, depending on the provable security bound: For the birthday-bound security, we present a 4-round minimal construction with two independent round keys, a single round function and two universal hash functions; For the beyond-birthday-bound security, we present a 10-round construction secure up to 𝑂(min{22𝑛/3,22𝑛𝜖−1‾‾‾‾‾‾√4}) adversarial queries, where n is the output size of the round function and 𝜖 is the upper bound of the collision probability of the universal hash functions. Our security proofs exploit the hybrid argument combined with the H-coefficient technique.

Springer, Cham2020

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