Résumé : In this talk, we will sum up our recent research results concerning the introduction of a new representation for FCSRs based upon a known LFSRs representation. This matrix based representation allows to construct FCSRs with a more compact hardware representation and a quicker diffusion while preserving the usual and proven good properties (good periods, ℓ-sequences, good statistical behaviors, etc.). Moreover, this new approach circumvents the weaknesses of the Fibonacci and Galois representations. We also show how to extend the LFSRs representation to a particular LFSR case called the windmill case. LFSRs are well-known primitives used in cryptography especially for stream cipher design. However they have some drawbacks when looking at their resistance against algebraic attacks because of their linearity. In the contrary, FCSRs are inherently resistant to algebraic attacks due to the non-linearity of the update function. Using the new representation, we propose two new stream ciphers based on the so-called “ring” FCSR representation. The first proposal called F-FCSR is dedicated to hardware applications whereas the second proposal called X-FCSR is designed for software purposes but is also efficient in hardware.