@article{Biryukov_Khovratovich_Perrin_2017, title={Multiset-Algebraic Cryptanalysis of Reduced Kuznyechik, Khazad, and secret SPNs}, volume={2016}, url={https://tosc.iacr.org/index.php/ToSC/article/view/572}, DOI={10.13154/tosc.v2016.i2.226-247}, abstractNote={<p>We devise the first closed formula for the number of rounds of a blockcipher with secret components so that these components can be revealed using multiset, algebraic-degree, or division-integral properties, which in this case are equivalent. Using the new result, we attack 7 (out of 9) rounds of Kuznyechik, the recent Russian blockcipher standard, thus halving its security margin. With the same technique we attack 6 (out of 8) rounds of Khazad, the legacy 64-bit blockcipher. Finally, we show how to cryptanalyze and find a decomposition of generic SPN construction for which the inner-components are secret. All the attacks are the best to date.</p>}, number={2}, journal={IACR Transactions on Symmetric Cryptology}, author={Biryukov, Alex and Khovratovich, Dmitry and Perrin, Léo}, year={2017}, month={Feb.}, pages={226–247} }