Spectral distinguishing attacks on Luby – Rackoff schemes based on independent two-block texts

For the Luby-Rackoff scheme the matrix $\mathbb{P}$ of transition probabilities of round differences is considered. We find spectrum and eigenspaces of $\mathbb{P}$, matrices $\mathbb{P}^2$ and $\mathbb{P}^4$. In the model of independent two-block texts observation we calculate characteristics of one-vector and two-vector spectral distinguishing attacks.