F-FCSR: Design of a New Class of Stream Ciphers

Abstract

Abstract. In this paper we present a new class of stream ciphers based on a very simple mechanism. The heart of our method is a Feedback with Carry Shift Registers (FCSR) automaton. This automaton is very similar to the classical LFSR generators, except the fact that it performs operations with carries. Its properties are well mastered: proved period, non-degenerated states, good statistical properties, high non-linearity.The only problem to use such an automaton directly is the fact that the mathematical structure (2-adic fraction) can be retrieved from few bits of its output using an analog of the Berlekamp-Massey algorithm.To mask this structure, we propose to use a filter on the cells of the FCSR automaton. Due to the high non-linearity of this automaton, the best filter is simply a linear filter, that is a XOR on some internal states. We call such a generator a Filtered FCSR (F-FCSR) generator.We propose four versions of our generator: the first uses a static filter with a single output at each iteration of the generator (F-FCSR-SF1). A second with an 8 bit output (F-FCSR-SF8). The third and the fourth are similar, but use a dynamic filter depending on the key (F-FCSR-DF1 and F-FCSR-DF8). We give limitations on the use of the static filter versions, in scope of the time/memory/data tradeoff attack. These stream ciphers are very fast and efficient, especially for hardware implementations.

An Efficient State Recovery Attack on X-FCSR-256

“…W (t) = round 256 (X(t)) = mix(sr(sl(X(t))), (1) where sl, sr and mix mimic the general structure of the AES round function; sl is an s-box function applied at byte level, sr is a row-shifting function operating on bytes, mix is a column mixing function operating on bytes.…”

“…The class of F-FCSRs, Filtered FCSRs, was proposed by Arnault and Berger in [1]. These constructions were cryptanalyzed in [7], using a weakness in the initialization function.…”

Security Provisions in Stream Ciphers Through Self Shrinking and Alternating Step Generator

“…They have good statistical properties, having proved period, highly nonlinear in nature and have non degenerating states. [2].They are much similar to LFSRs except that instead of using addition modulo 2 FCSR uses carry propagations that bring non linearity in to their structure which is main characteristic of FCSR.…”

A New Approach for FCSRs

“…However, two recent results [4,5] have shown weaknesses in stream ciphers using either the Fibonacci or Galois FCSR. Hell and Johansson [5] have exploited the bias in the carries behaviour of a Galois FCSR to mount a very powerful attack against the F-FCSR stream cipher [6,7]. Fisher et al [4] have considered an equivalent of the F-FCSR stream cipher based upon a Fibonacci FCSR to study the linear behavior of the induced system.…”