Nonlinear Filter Generator Research Articles

An algebraic attack on stream ciphers with application to nonlinear filter generators and WG-PRNG

An algebraic attack on stream ciphers with application to nonlinear filter generators and WG-PRNG

Period and Some Distribution Properties of a Nonlinear Filter Generator with Dynamic Mapping

Period and Some Distribution Properties of a Nonlinear Filter Generator with Dynamic Mapping

Linear complexity of second order PN_sequences addition with single order PN_sequence in nonlinear filter generator

A method of analyzing the root presence test for Nonlinear Filter Generator is presented. We have proved that the Key’s upper bound on linear complexity hold for 2nd order product sequence with addition of single order sequence and also for a non-zero linear combination of such sequences under some conditions. Some of these sequences are balanced sequences and satisfy statistical randomness property than the Key's and Groth's sequences. The analysis can also be extended to Word-Oriented Nonlinearly Filtered Primitive Transformation Shift Registers.

Cryptographic Properties of Equivalent Ciphers

In this work the use of nonlinear filtering functions applied to Linear Feedback Shift Registers (LFSRs) to generate cryptographic sequences has been studied. Emphasis is on the class of equivalent nonlinear filter generators whose elements produce exactly the same sequence. Given a pair (filtering function, LFSR), the work develops a method of computing equivalent filtering functions applied to different LFSRs, where all these filters generate exactly the same cryptographic sequence. The security of a cipher is that of its weakest equivalent. Thus this article allows one to compute weaker equivalents of apparently secure generators.

Linearization of nonlinear filter generators and its application to cryptanalysis of stream ciphers

Nonlinear filter generators are commonly used as keystream generators in stream ciphers. A nonlinear filter generator utilizes a nonlinear filtering function to combine the outputs of a linear feedback shift register (LFSR) to improve the linear complexity of keystream sequences. However, the LFSR-based stream ciphers are still potentially vulnerable to algebraic attacks that recover the key from some keystream bits. Although the known algebraic attacks only require polynomial time complexity of computations, all have their own constraints. This paper uses the linearization of nonlinear filter generators to cryptanalyze LFSR-based stream ciphers. Such a method works for any nonlinear filter generators. Viewing a nonlinear filter generator as a Boolean network that evolves as an automaton through Boolean functions, we first give its linearization representation. Compared to the linearization representation in Limniotis et al. (2008), this representation requires lower spatial complexity of computations in most cases. Based on the representation, the key recoverability is analyzed via the observability of Boolean networks. An algorithm for key recovery is given as well. Compared to the exhaustive search to recover the key, using this linearization representation requires lower time complexity of computations, though it leads to exponential time complexity.

A novel low‐complexity scheme for improving security of NLFG‐based symmetric key cryptosystem using secure concatenated RS–QCLDPC code

AbstractThe major requirements of a secure high‐speed communication system are low delay, good error performance, low redundancy, and good security. A simple nonlinear filter generator (NLFG)‐based cryptosystem is proposed in this paper to provide low delay with high security. Enhanced security is attained by embedding security in the channel encoder. An efficient concatenation of Reed–Solomon code and a secure quasi‐cyclic low density parity check code is used as channel encoder in the proposed cryptosystem to provide good error performance with low redundancy and to enhance security of NLFG with low structural complexity. The proposed efficient design of key‐based dense scrambling matrix and permutation matrix greatly simplifies the hardware structure. The novel method for generation of intentional error vector with modification of NLFG helps to reduce both the delay and power consumption. The integrated system is designed in such a way that both NLFG‐based stream cipher and secure channel coder complement each other to overcome the cryptographic weakness with a low hardware cost. The analytical and simulation results show that the proposed system attains significant security advantage against typical attacks and offers very good error performance. Copyright © 2015 John Wiley & Sons, Ltd.

Guess and Determine Attacks on Filter Generators—Revisited

Although there are many different approaches used in cryptanalysis of nonlinear filter generators, the selection of tap positions has not received enough attention yet. In this paper we examine the security of nonlinear filter generators that output several bits at the time against a variant of a guess and determine attack that takes into account the tap positions of the generator. In difference to the filter state guessing attack (FSGA) introduced by Pasalic (2009), our approach further reduces the input preimage space by using a given placement of the tap positions. The new attack, though a simple generalization of the FSGA, in many cases outperforms both classical algebraic attacks and the FSGA. In particular, the new attack is much more efficiently applied against filter generators that use a vectorial Maiorana-McFarland than classical algebraic attacks or the FSGA. As a proof of the concept we apply our attack to the stream cipher SOBER-t32 without stuttering and show that our attack performs slightly better than a guess and determine attack proposed by Babbage et al.

Vectorial Boolean functions and induced algebraic equations

A general mathematical framework behind algebraic cryptanalytic attacks is developed. The framework relates to finding algebraic equations induced by vectorial Boolean functions and, in particular, equations of low algebraic degree. The equations may involve only a subset of input variables and may or may not be conditioned on the values of output variables. In addition, the equations may have a constrained form interesting for the so-called fast algebraic attacks. A possible divide-and-conquer effect is pointed out and the notion of algebraic immunity order, naturally extending the notion of correlation immunity order, is defined. An application of general results to stream ciphers known as combiners with or without memory, with possibly multiple outputs, is studied in particular detail and the concept of divide-and-conquer algebraic attacks is introduced. Special properties of combiners with finite input memory, such as nonlinear filter generators, are also established. It is also pointed out that Groumlbner basis algorithms may be used for finding low-degree induced algebraic equations

Remarks on improved inversion attacks on nonlinear filter generators

Remarks on improved inversion attacks on nonlinear filter generators

Improved inversion attacks on nonlinear filter generators

Improved inversion attacks on nonlinear filter generators are proposed with computational complexity equal to O(2r−m), where r denotes the length of the shift register, and m denotes the largest gap between cells with taps to the filter function or connection polynomial. It is shown that the previously proposed set of design criteria does not prevent the improved inversion attack and an additional criterion is proposed based on the relationship between the positions of taps to the filter function and positions of taps to the connection polynomial.

Vulnerability of multibit clock-controlled cascadesto inversion attack

The inversion attack on nonlinear filter generators is adapted to deal with cascades of clock-controlled shift registers with multibit outputs. It is shown that under certain conditions such cascades may be vulnerable to these attacks.

Generalized inversion attack on nonlinear filter generators

A nonlinear filter generator is a basic keystream generator for stream cipher applications consisting of a single linear feedback shift register whose output is filtered by a nonlinear combining function. A binary nonlinear filter generator is viewed as a finite input memory automaton with one binary input and one binary output. The generalized inversion attack on a binary nonlinear filter generator is developed and analyzed by the theory of critical branching processes. Its objective is to recover the unknown input sequence from a given segment of the output sequence, provided that the filter function is known. Unlike the inversion attack, which requires that the filter function be linear in the first or the last input variable, this attack can be applied for any filter function. Both theory and systematic experiments show that its time complexity remains dose to 2/sup M/, which is the time complexity of the inversion attack, where M denotes the input memory size in bits.

Configurable nonlinear filter generator

A configurable nonlinear filter generator is proposed. The nonlinear function employed is key controllable. By changing the key, a different sequence will be obtained. Simulated results show that an optimal linear complexity profile of the sequence can be generated.

Fast correlation attacks on nonlinear filter generators

The fast correlation attack based on iterative probabilistic decoding is applied to nonlinear filter generators in order to investigate the effect of multiple linear transforms of the same linear recurring sequence being correlated to the keystream sequence. Systematic experimental results on random balanced as well as on some special filter functions show that the attack is successful if the number of parity-checks used is sufficiently large given the correlation coefficient of the best affine approximation to the filter function. In addition, the attack is shown to be more successful when applied to independent correlation noise present in memoryless combiners with distinct input shift registers.