Analysis of nonlinear sequences and streamciphers
Teo, SuiGuan (2013) Analysis of nonlinear sequences and streamciphers. PhD thesis, Queensland University of Technology.

SuiGuan Teo Thesis
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Abstract
Streamciphers are common cryptographic algorithms used to protect the confidentiality of framebased communications like mobile phone conversations and Internet traffic. Streamciphers are ideal cryptographic algorithms to encrypt these types of traffic as they have the potential to encrypt them quickly and securely, and have low error propagation.
The main objective of this thesis is to determine whether structural features of keystream generators affect the security provided by stream ciphers.These structural features pertain to the stateupdate and output functions used in keystream generators. Using linear sequences as keystream to encrypt messages is known to be insecure. Modern keystream generators use nonlinear sequences as keystream.The nonlinearity can be introduced through a keystream generator's stateupdate function, output function, or both.
The first contribution of this thesis relates to nonlinear sequences produced by the wellknown Trivium stream cipher. Trivium is one of the stream ciphers selected in a final portfolio resulting from a multiyear project in Europe called the ecrypt project. Trivium's structural simplicity makes it a popular cipher to cryptanalyse, but to date, there are no attacks in the public literature which are faster than exhaustive keysearch. Algebraic analyses are performed on the Trivium stream cipher, which uses a nonlinear stateupdate and linear output function to produce keystream. Two algebraic investigations are performed: an examination of the sliding property in the initialisation process and algebraic analyses of Triviumlike streamciphers using a combination of the algebraic techniques previously applied separately by Berbain et al. and Raddum. For certain iterations of Trivium's stateupdate function, we examine the sets of slid pairs, looking particularly to form chains of slid pairs. No chains exist for a small number of iterations.This has implications for the period of keystreams produced by Trivium.
Secondly, using our combination of the methods of Berbain et al. and Raddum, we analysed Triviumlike ciphers and improved on previous on previous analysis with regards to forming systems of equations on these ciphers. Using these new systems of equations, we were able to successfully recover the initial state of BiviumA.The attack complexity for BiviumB and Trivium were, however, worse than exhaustive keysearch. We also show that the selection of stages which are used as input to the output function and the size of registers which are used in the construction of the system of equations affect the success of the attack.
The second contribution of this thesis is the examination of state convergence. State convergence is an undesirable characteristic in keystream generators for stream ciphers, as it implies that the effective session key size of the stream cipher is smaller than the designers intended. We identify methods which can be used to detect state convergence. As a case study, theMixer streamcipher, which uses nonlinear stateupdate and output functions to produce keystream, is analysed. Mixer is found to suffer from state convergence as the stateupdate function used in its initialisation process is not onetoone. A discussion of several other streamciphers which are known to suffer from state convergence is given. From our analysis of these stream ciphers, three mechanisms which can cause state convergence are identified.The effect state convergence can have on stream cipher cryptanalysis is examined. We show that state convergence can have a positive effect if the goal of the attacker is to recover the initial state of the keystream generator.
The third contribution of this thesis is the examination of the distributions of bit patterns in the sequences produced by nonlinear filter generators (NLFGs) and linearly filtered nonlinear feedback shift registers. We show that the selection of stages used as input to a keystream generator's output function can affect the distribution of bit patterns in sequences produced by these keystreamgenerators, and that the effect differs for nonlinear filter generators and linearly filtered nonlinear feedback shift registers. In the case of NLFGs, the keystream sequences produced when the output functions take inputs from consecutive register stages are less uniform than sequences produced by NLFGs whose output functions take inputs from unevenly spaced register stages. The opposite is true for keystream sequences produced by linearly filtered nonlinear feedback shift registers.
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ID Code:  63358 

Item Type:  QUT Thesis (PhD) 
Supervisor:  Simpson, Leonie, Dawson, Ed , & Wong, Kenneth 
Keywords:  stream ciphers, keystream generators, linear feedback shift register (LFSR), nonlinear, feedback shift register (NLFSR), clockcontrol, boolean functions, stateupdate, functions, output functions, keystream sequence properties, nonlinear filter generator,, linearly filtered NLFSR, slid pairs, A5/1, Trivium, mixer, summation generator, state convergence, cryptanalysis, timememorydata tradeoff attacks, algebraic attacks, F4 algorithm, Gröbner basis 
Divisions:  Past > QUT Faculties & Divisions > Faculty of Science and Technology 
Institution:  Queensland University of Technology 
Deposited On:  14 Oct 2013 06:20 
Last Modified:  22 Jun 2017 14:46 
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