Multiple impossible differential cryptanalysis of reduced-round NBC

Abstract

NBC is a class of Type-II generalized Feistel structure algorithms with excellent software and hardware implementation performance. In this paper, we evaluate the security of NBC from the view point of multiple impossible differential. More precisely, using the idea of combining the matrix method and “meet-in-the-middle,” we first obtain 4 types of 11-round impossible differentials for NBC-128 and 32 types of 14-round impossible differentials for NBC-256, respectively. Then, according to the characteristics of Feistel structure and the distinguisher, we perform 17-round, 19-round, and 22-round multiple impossible differential cryptanalysis on NBC-128-128, NBC-128-256, and NBC-256-256, respectively. Results indicate that NBC has sufficient security to resist an impossible differential attack, and the data and time complexity of our attack has been significantly reduced compared to previous ones.

Keywords:

• block cipher
• generalized Feistel structure
• impossible differential cryptanalysis
• matrix method
• NBC

Acknowledgments

We thank the anonymous reviewers for their useful comments that helped to improve the paper.

Disclosure statement

The authors have no competing interests or other interests that might be perceived to influence the results and/or discussion reported in this paper.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Database availability statement

No new data were generated or analyzed in support of this research.

Additional information

Funding

This work was partially supported by the Key Project of Gansu Natural Science Foundation (Grant No. 23JRRA685), the National Natural Science Foundation of China (Grant No. 62172337), and the Funds for Innovative Fundamental Research Group Project of Gansu Province (Grant No. 23JRRA684).

Notes on contributors

Lifang Liang

Lifang Liang received an M.S. from Northwest Normal University, China, in 2023. Since 2023, she has been a PhD student at Northwest Normal University, China. Her research interests include block ciphers and information security.

Xiaoni Du

Xiaoni Du is a professor of the College of Mathematics and Statistics, Northwest Normal University, China. She received her PhD in Cryptography from Xidian University. Her current research interests include information security, cryptography, and coding.