Security analysis of SDDO-based block cipher for wireless sensor network

Switchable data-dependent operations (SDDOs) that were introduced by Moldovyan (MMM-ACNS 2003, LNCS, vol 2776, pp 316–327. Springer, Heidelberg, 2003), have been proposed as a primitive suitable to designing efficient ciphers with simple key scheduling. These solve the problems of the weakness of key change process, and also the SDDO-based ciphers provide a high performance with smaller hardware requirement in implementation. Since Hawk-64, MD-64 (Bac et al. in Int J Comput Sci Netw Secur 10(3):54–60, 2010), KT-64 (Minh et al. in IJCSNS 19(1):10–18, 2010) are being used have block size of 64 bits, the BMD-128 (Bac et al. in Int J Comput Netw Inf Secur 11:1–10, 2012) has extended the size of block to 128 bits, show the improvement with high applicability, flexibility in fast and highly efficient telecommunication system, and high security against most known attack methods, such as slide attack, differential attack. In this paper, however, we indicate that the BMD-128 block cipher is still possible to be exploited with the related-key differential cryptanalysis. By constructing the related-key amplified boomerang differential characteristic with high probability on a 7-round reduced BMD-128, we can propose the related-key amplified boomerang attack on it with complexities of 279\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{79}$$\end{document} in data, 282\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{82}$$\end{document} bytes in memory, and 2129\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{129}$$\end{document} in computational time.