The task of a fast correlation attack is to efficiently restore the initial content of a linear feedback shift register in a stream cipher using a detected correlation with the output sequence. We show that by modeling this problem as the problem of learning a binary linear multivariate polynomial, algorithms for polynomial reconstruction with queries can be modified through some general techni...

To date, most applications of algebraic analysis and attacks on stream ciphers are on those based on linear feedback shift registers (LFSRs). In this paper, we extend algebraic analysis to non-LFSR based stream ciphers. Specifically, we perform an algebraic analysis on the RC4 family of stream ciphers, an example of stream ciphers based on dynamic tables, and investigate its implications to pot...

Pseudorandom generators based on linear feedback shift registers (LFSR) are a traditional building block for cryptographic stream ciphers. In this report, we review the general idea for such generators, as well as the most important techniques of cryptanalysis.

This work presents novel multipliers for Montgomery multiplication defined on binary fields GF(2). Different to state of the art Montgomery multipliers, this work uses a Linear Feedback Shift Register (LFSR) as the main building block. We studied different architectures for bit-serial and digit-serial Montgomery multipliers using the LFSR and the Montgomery factors x and x. The proposed multipl...

The filter generator consists of a linear feedback shift register (LFSR) and a Boolean filtering function that combines some bits from the shift register to create a key stream. A new attack on the filter generator has recently been described by Rønjom and Helleseth [6]. This paper gives an alternative and extended attack to reconstruct the initial state of the LFSR using the underlying subspac...

This paper describes some attacks on word-oriented stream ciphers that use a linear feedback shift register (LFSR) and a non-linear lter. These attacks rely on exploiting linear relationships corresponding to multiples of the connection polynomial that de ne the LFSR.

In 2009, Solé and Zinoviev (Eur. J. Combin., vol. 30, no. 2, pp. 458-467, 2009) proposed an open problem of arithmetic interest to study the period of the inversive pseudorandom number generators (IPRNGs) and to give conditions bearing on a, b to achieve maximal period, we focus on resolving this open problem. In this paper, the period distribution of the IPRNGs over the Galois ring (Zpe ,+,×) ...

We consider the adjacency graphs of linear feedback shift registers (LFSRs) with reducible characteristic polynomials. Let l(x) be a characteristic polynomial, and l(x) = l1(x)l2(x) · · · lr(x) be a decomposition of l(x) into co-prime factors. Firstly, we show a connection between the adjacency graph of FSR(l(x)) and the association graphs of FSR(li(x)), 1 ≤ i ≤ r. By this connection, the probl...

We extend the notions of correlation-immune functions and resilient functions to functions over any finite alphabet. A previous result due to Gopalakrishnan and Stinson is generalized as we give an orthogonal array characterization, a Fourier transform and a matrix characterization for correlation-immune and resilient functions over any finite alphabet endowed with the structure of an Abelian g...

Pseudorandom generators, which produce keystreams for stream ciphers by the exclusiveor sum of outputs of alternately clocked linear feedback shift registers, are vulnerable to cryptanalysis. In order to increase their resistance to attacks, we introduce a non-linear scrambler at the output of these generators. Non-linear feedback shift register plays the role of the scrambler. In addition, we ...