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Lightweight stream ciphers are highly demanded in IoT applications. In orderto optimize the hardware performance, a new class of stream cipher has beenproposed. The basic idea is to employ a single Galois NLFSR with maximum periodto construct the cipher. As a representative design of this kind of streamciphers, Espresso is based on a 256-bit Galois NLFSR initialized by a 128-bitkey. The $2^{256}-1$ maximum period is assured because the Galois NLFSR istransformed from a maximum length LFSR. However, we propose aGalois-to-Fibonacci transformation algorithm and successfully transform theGalois NLFSR into a Fibonacci LFSR with a nonlinear output function. Thetransformed cipher is broken by the standard algebraic attack and the R\onjom-Helleseth attack with complexity $\mathcal{O}(2^{68.44})$ and$\mathcal{O}(2^{66.86})$ respectively. The transformation algorithm is derivedfrom a new Fibonacci-to-Galois transformation algorithm we propose in thispaper. Compare to existing algorithms, proposed algorithms are more efficientand cover more general use cases. Moreover, the transformation result showsthat the Galois NLFSR used in any Espresso-like stream ciphers can be easilytransformed back into the original Fibonacci LFSR. Therefore, this kind ofdesign should be avoided in the future.

Generalized NLFSR Transformation Algorithms and Cryptanalysis of the Class of Espresso-like Stream Ciphers