Duplex-based authenticated encryption modes with a sufficiently large key length are proven to be secure up the birthday bound $$2^{\frac{c}{2}}$$ , where c is capacity. However this not known tight and complexity of best generic attack, which based on multicollisions, much larger: it reaches $$\frac{2^c}{\alpha }$$ $$\alpha $$ represents small security loss factor. There thus an uncertainty tr...

We give a necessary and sufficient condition for strict convexity of the rate function random vector in Rd. This is always satisfied when has finite Laplace transform. also completely describe effective domain under weaker condition.

The structure function of a random matrix ensemble can be specified as the covariance linear statistics $\sum_{j=1}^N e^{i k_1 \lambda_j}$, e^{-i k_2 \lambda_j}$ for Hermitian matrices, and same with eigenvalues $\lambda_j$ replaced by eigenangles $\theta_j$ unitary matrices. As such it written in terms Fourier transform density-density correlation $\rho_{(2)}$. For circular $\beta$-ensemble $\...