A New Approach for FCSRs

Abstract

Abstract. The Feedback with Carry Shift Registers (FCSRs) have been proposed as an alternative to Linear Feedback Shift Registers (LFSRs) for the design of stream ciphers. FCSRs have good statistical properties and they provide a built-in non-linearity. However, two attacks have shown that the current representations of FCSRs can introduce weaknesses in the cipher. We propose a new "ring" representation of FCSRs based upon matrix definition which generalizes the Galois and Fibonacci representations. Our approach preserves the statistical properties and circumvents the weaknesses of the Fibonacci and Galois representations. Moreover, the ring representation leads to automata with a quicker diffusion characteristic and better implementation results. As an application, we describe a new version of F-FCSR stream ciphers.

An Efficient State Recovery Attack on the X-FCSR Family of Stream Ciphers

“…The LFSRization process shows that it is relatively cheap to linearize FCSRs, the cost being roughly logarithmic in the size of active carry registers. The attack presented here is not directly applicable to the newer ringFCSRs presented in [3]. The desired LFSRization effect is much less likely…”

“…After the publication of [14], new ring-FCSR versions of the F-FCSR family and X-FCSR-128 were presented in [3] and [5], respectively. All of these new proposals are unbroken at the time of writing.…”

Alternating Step Generator Using FCSR and LFSRs: A New Stream Cipher

“…Cryptanalysis of stream ciphers using F-FCSR were discussed in [14,15]. Design principles of stream ciphers using FCSR presented in [16][17][18][19].…”

Revisiting LFSRs for Cryptographic Applications

“…The implementation is based upon the multiplication by α ∈ F 2 32 satisfying α·(c 3 α 3 +c 2 α 2 +c 1 α 1 +c 0 ) = (c 2 α 3 +c 1 α 2 + c 0 α) + c 3 · V with V an element in F 2 32 . We denote M α the matrix of this linear application seen over F 32 2 :…”