Abstract

Pseudorandom generators, which produce keystreams for stream ciphers by the exclusive-or sum of output bits from alternately clocked linear feedback shift registers, are vulnerable to cryptanalysis. In order to increase their resistance to attacks, we introduce a nonlinear scrambler at the output of these generators. The role of the scrambler plays the nonlinear feedback shift register. In addition, we propose the Modified Alternating Step Generator (MASG1S) built with the nonlinear scrambler and regularly or irregularly clocked linear feedback shift registers with nonlinear filtering functions.

Highlights

  • Pseudorandom generators of a keystream composed of linear feedback shift registers (LFSR) are basic components of classical stream ciphers

  • M method of improving the alternating step generator (ASG), proposed in [10], was to exchange some LFSRs for feedback with carry shift registers (FCSR) and the XOR sum to be added to the (ADD) as an output function

  • S 2.2 The MASG Family C In 18 and [19] we proposed a family of modified alternating step generators (MASG)

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Summary

Introduction

Pseudorandom generators of a keystream composed of linear feedback shift registers (LFSR) are basic components of classical stream ciphers. Stop and go or alternating clocking of shift registers are two of the methods to increase linear complexity of the keystream. Other techniques introduce non-linearity to the feedback or to the output of the shift register All these methods increase resistance of keystream generators to reconstruction of the internal state as well as the member functions from the output sequence. In [19] we proposed the three modifications: MASG, MASG0 and MASG1 These modified alternating step generators give sequences with maximal period, good statistical properties and higher linear complexity than the ASG. From the analysis of the attacks we conclude that at the output of the alternating step generator a linear function (XOR) should be replaced with a non-linear one. C filtering functions and initialization method is particular realization of this idea

Alternating Step Generators
Modified Alternating k-Generators
Attacks on the Alternating Step Generators
Edit Probability Correlation Attack
Johansson’s Attack
New Reduced Complexity Attack
Algebraic Attack
Non-linear Feedback Shift Register as a Scrambler
MASG1 with the Scrambler
Initializing the M ASG1S
Randomness Properties
Resistance of Alternating Step Generators with Scrambler to Attacks
Full Text
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