International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Correlation of Quadratic Boolean Functions: Cryptanalysis of All Versions of Full $\mathsf {MORUS}$

Danping Shi
Siwei Sun
Yu Sasaki
Chaoyun Li
Lei Hu
DOI: 10.1007/978-3-030-26951-7_7 (login may be required)
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Abstract: We show that the correlation of any quadratic Boolean function can be read out from its so-called disjoint quadratic form. We further propose a polynomial-time algorithm that can transform an arbitrary quadratic Boolean function into its disjoint quadratic form. With this algorithm, the exact correlation of quadratic Boolean functions can be computed efficiently.We apply this method to analyze the linear trails of $$\mathsf {MORUS}$$ (one of the seven finalists of the CAESAR competition), which are found with the help of a generic model for linear trails of $$\mathsf {MORUS}$$-like key-stream generators. In our model, any tool for finding linear trails of block ciphers can be used to search for trails of $$\mathsf {MORUS}$$-like key-stream generators. As a result, a set of trails with correlation $$2^{-38}$$ is identified for all versions of full $$\mathsf {MORUS}$$, while the correlations of previously published best trails for $$\mathsf {MORUS}$$-640 and $$\mathsf {MORUS}$$-1280 are $$2^{-73}$$ and $$2^{-76}$$ respectively (ASIACRYPT 2018). This significantly improves the complexity of the attack on $$\mathsf {MORUS}$$-1280-256 from $$2^{152}$$ to $$2^{76}$$. These new trails also lead to the first distinguishing and message-recovery attacks on $$\mathsf {MORUS}$$-640-128 and $$\mathsf {MORUS}$$-1280-128 with surprisingly low complexities around $$2^{76}$$.Moreover, we observe that the condition for exploiting these trails in an attack can be more relaxed than previously thought, which shows that the new trails are superior to previously published ones in terms of both correlation and the number of ciphertext blocks involved.
Video from CRYPTO 2019
  title={Correlation of Quadratic Boolean Functions: Cryptanalysis of All Versions of Full $$\mathsf {MORUS}$$},
  booktitle={Advances in Cryptology – CRYPTO 2019},
  series={Lecture Notes in Computer Science},
  author={Danping Shi and Siwei Sun and Yu Sasaki and Chaoyun Li and Lei Hu},