New cube distinguishers on NFSR-based stream ciphers

In this paper, we revisit the work of Sarkar et al. (Des Codes Cryptogr 82(1–2):351–375, 2017) and Liu (Advances in cryptology—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 $${\texttt {Zero-Sum}}$$ Zero - Sum distinguisher. We apply our new cube finding algorithm to three different nonlinear feedback shift register (NFSR) based stream ciphers $${\textsf {Trivium}}$$ Trivium , $$\textsf {Kreyvium}$$ Kreyvium and $$\textsf {ACORN}$$ ACORN . From the results, we can see a cube of size 39, which gives $${\texttt {Zero-Sum}}$$ Zero - Sum for maximum 842 rounds and a significant non-randomness up to 850 rounds of $${\textsf {Trivium}}$$ Trivium . We provide some small size good cubes for $${\textsf {Trivium}}$$ Trivium , which outperform existing ones. We further investigate $$\textsf {Kreyvium}$$ Kreyvium and $$\textsf {ACORN}$$ ACORN by a similar technique and obtain cubes of size 56 and 92 which give $${\texttt {Zero-Sum}}$$ Zero - Sum distinguisher till 875 and 738 initialization rounds of $$\textsf {Kreyvium}$$ Kreyvium and $$\textsf {ACORN}$$ ACORN respectively. 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.