## CryptoDB

### Paper: Beyond-Birthday-Bound Security for 4-round Linear Substitution-Permutation Networks

Authors: Yuan Gao , School of Cyber Science and Technology, Shandong University, Qingdao, Shandong, China Chun Guo , School of Cyber Science and Technology, Shandong University, Qingdao, Shandong, China Meiqin Wang , School of Cyber Science and Technology, Shandong University, Qingdao, Shandong, China Weijia Wang , School of Cyber Science and Technology, Shandong University, Qingdao, Shandong, China Jiejing Wen , School of Cyber Science and Technology, Shandong University, Qingdao, Shandong, China DOI: 10.13154/tosc.v2020.i3.305-326 URL: https://tosc.iacr.org/index.php/ToSC/article/view/8704 Search ePrint Search Google Recent works of Cogliati et al. (CRYPTO 2018) have initiated provable treatments of Substitution-Permutation Networks (SPNs), one of the most popular approach to construct modern blockciphers. Such theoretical SPN models may employ non-linear diffusion layers, which enables beyond-birthday-bound provable security. Though, for the model of real world blockciphers, i.e., SPN models with linear diffusion layers, existing provable results are capped at birthday security up to $2^{n/2}$ adversarial queries, where $n$ is the size of the idealized S-boxes. In this paper, we overcome this birthday barrier and prove that a 4-round SPN with linear diffusion layers and independent round keys is secure up to $2^{2n/3}$ queries. For this, we identify conditions on the linear layers that are sufficient for such security, which, unsurprisingly, turns out to be slightly stronger than Cogliati et al.'s conditions for birthday security. These provides additional theoretic supports for real world SPN blockciphers.
##### BibTeX
@article{tosc-2020-30543,
title={Beyond-Birthday-Bound Security for 4-round Linear Substitution-Permutation Networks},
journal={IACR Transactions on Symmetric Cryptology},
publisher={RUB},
volume={2020, Issue 3},
pages={305-326},
url={https://tosc.iacr.org/index.php/ToSC/article/view/8704},
doi={10.13154/tosc.v2020.i3.305-326},
author={Yuan Gao and Chun Guo and Meiqin Wang and Weijia Wang and Jiejing Wen},
year=2020
}