A New Adaptive Security Architecture with Extensible Computation Complexity for Generic Ciphers

Among recent developments on ciphers, attacks involving polynomial cryptanalysis have gained prominent attention in evaluating encryption algorithms for both stream and block ciphers. Algebraic cryptanalysis is also a tool to measure the strength of a cipher in terms of its resistance against different types of polynomial attacks. A contemporary way of representing such ciphers is in terms of multivariate equations over 𝔾𝔽(2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {GF}(2)$\end{document}, which are highly vulnerable to algebraic cryptanalysis. Algebraic cryptanalysis, in its general form, aims to recover the internal secret state bits of the registers of the cipher by solving non-linear algebraic equations. Recent trends in algebraic cryptanalysis tend to use modular addition 2n over logic XOR as a mixing operator to guard against such malicious attacks. Nonetheless, it has been observed that the complexity of modular addition can be drastically decreased with the appropriate formulation of polynomial equations and probabilistic conditions. This article outlines a new design framework for modular addition with added security enhancements to address these issues. Inspiring from this framework, we show that the new design is characterized by user-specified extendable security for stronger encryption and does not impose changes in existing layout of ciphers including stream ciphers such as SNOW2.0, BIVIUM, and grain family, and block ciphers like IDEA, SAFER, AES, and DES. Our proposed design framework can be rapidly scaled to use-specific requirements which boosts the algebraic degree of the overall structure. This, in turn, thwarts the probabilistic conditions by retaining the original hardware complexity sans critical modifications of modular addition 2n.