University of GuilanComputational Sciences and Engineering2783-2503Articles in Press20240219Accelerated brute force attack on stream cipher systems on LFSR115128758810.22124/cse.2024.25975.1065ENAlirezaBabaeiFaculty of Basic Sciences, Shahed University, Tehran, Iran0009000975159634HamidHaj Seyyed JavadiFaculty of Computer Engineering, Shahed University, Tehran, Iran0000-0003-0082-036XNaderJafari RadFaculty of Basic Sciences, Shahed University, Tehran, IranJournal Article20231107Algebraic attack is an emergent decryption method. The main objective in this decryption is to form and solve a set of multivariate polynomial equations on finite fields. The present findings show that algebraic attacks have been significantly successful and effective on a specific type of stream ciphers system and linear-feedback shift register systems (LFSRs). One of the reasons for this is that linear functions are used for updating LFSRs, although the nonlinear types can also be approximated by an appropriate linear function, and this increases the necessity of paying attention to it. In the present article, an attempt is made to present the main idea of algebraic attacks on stream ciphers systems, to explain these ideas by certain concrete examples. Particularly, a synchronous stream cipher system based on LFSRs, entitled the LILI stream ciphers, and algebraic attacks on them, will be discussed. In algebraic attacks, solving a set of multivariate polynomial equations is needed. In the present research, the extended linearization algorithm (XL) will be used to deal with an attained set of equations. Additionally, some of the accelerated extended algorithms (XL) for dealing with the set of equations algebraic resulted from the attacks on stream cipher systems, will be analyzed and their efficiency will be examined in the frame of certain examples.