-
Views
-
Cite
Cite
Hao Guo, Zhiyu Zhang, Qianqian Yang, Lei Hu, Yiyuan Luo, A New Method To Find All The High-Probability Word-Oriented Truncated Differentials: Application To Midori, SKINNY And CRAFT, The Computer Journal, Volume 66, Issue 5, May 2023, Pages 1069–1082, https://doi.org/10.1093/comjnl/bxab213
- Share Icon Share
Abstract
This paper proposes a new method to find high-probability truncated differentials using matrix muliplication. For Markov cipher with similar round function, suppose that the transition probability matrix of round function is |$\mathcal{D}$|, then |$\mathcal{D}^{r}$| contains all the differential probabilities of an |$r$|-round block cipher. To reduce the matrix dimension, we consider the word-oriented truncated differential and the truncated transition probability matrix |$\mathcal{T}$|. Regardless of the effect of the |$S$|-box, we focus on whether there is a non-zero difference on one cell instead of the value of the difference. In this case, the matrix dimension reduces significantly and we can calculate |$\mathcal{T}^{r}$| using a workstation. Then all the |$r$|-round truncated differential probabilities can be found from |$\mathcal{T}^{r}$|. And the probability in |$\mathcal{T}^{r}$| is the probability of the whole truncated differential hull but not a single or several truncated differential characteristics. Besides, we make a more accurate probability estimation of the truncated differential of lightweight block cipher. Combined with the truncated differential hull, we found some longer truncated differential distinguishers. And as |$\mathcal{T}^{r}$| stores all the truncated differential probabilities, we can also find all the impossible truncated differentials.