## Department of Mathematics

Indian Institute Of Technology Madras , Chennai

### New cube distinguishers on NFSR-based stream ciphers

#### Authors:

Kesarwani, Abhishek and Roy, Dibyendu and Sarkar, Santanu and Meier, Willi

#### Journal:

Designs, Codes and Cryptography

2019

#### Abstract:

In this paper, we revisit the work of Sarkar et al. (Des Codes Cryptogr 82(1â€“2):351â€“375, 2017) and Liu (Advances in cryptologyâ€”Crypto 2017, 2017) and show how both of their ideas can be tuned to find good cubes. Here we propose a new algorithm for cube generation which improves existing results on $}{\$\\backslashtexttt \Zero-Sum\\$}{\$Zero-Sumdistinguisher. We apply our new cube finding algorithm to three different nonlinear feedback shift register (NFSR) based stream ciphers $}{\$\\backslashtextsf \Trivium\\$}{\$Trivium, $}{\$\backslashtextsf \Kreyvium\$}{\$Kreyviumand $}{\$\backslashtextsf \ACORN\$}{\$ACORN. From the results, we can see a cube of size 39, which gives $}{\$\\backslashtexttt \Zero-Sum\\$}{\$Zero-Sumfor maximum 842 rounds and a significant non-randomness up to 850 rounds of $}{\$\\backslashtextsf \Trivium\\$}{\$Trivium. We provide some small size good cubes for $}{\$\\backslashtextsf \Trivium\\$}{\$Trivium, which outperform existing ones. We further investigate $}{\$\backslashtextsf \Kreyvium\$}{\$Kreyviumand $}{\$\backslashtextsf \ACORN\$}{\$ACORNby a similar technique and obtain cubes of size 56 and 92 which give $}{\$\\backslashtexttt \Zero-Sum\\$}{\$Zero-Sumdistinguisher till 875 and 738 initialization rounds of $}{\$\backslashtextsf \Kreyvium\$}{\$Kreyviumand $}{\$\backslashtextsf \ACORN\$}{\$ACORNrespectively. To the best of our knowledge, these results are best results as compared to the existing results on distinguishing attacks of these ciphers. We also provide a table of good cubes of sizes varying from 10 to 40 for these three ciphers.

1573-7586

#### Website:

https://doi.org/10.1007/s10623-019-00674-1