It is known that a naive implementation of the decryption algorithm in the McEliece cryptosystem allows an attacker to recover the secret matrix P by measuring the power consumption. We demonstrate that a similar threat is present in the QC-LDPC variant of the McEliece cryptosystem. We consider a naive implementation of the decryption algorithm in the QC-LDPC McEliece cryptosystem. We demonstra...

The KdV and modified KdV integrable hierarchies are shown to be different descriptions of the same 2D gravitational system – open-closed string theory. Nonperturbative solutions of the multi-critical unitary matrix models map to nonsingular solutions of the ‘renormalisation group’ equation for the string susceptibility, [P̃ , Q] =Q . We also demonstrate that the large N solutions of unitary matr...

We present a systematic introduction to the geometry of linear braided spaces. These are versions of R n in which the coordinates x i have braid-statistics described by an R-matrix. From this starting point we survey the author's braided-approach to q-deformation: braided differentiation, exponentials, Gaussians, integration and forms, i.e. the basic ingredients for q-deformed physics are cover...

Using the notion of quantum integers associated with a complex number q 6= 0, we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q-Jacobi polynomials when |q| < 1, and for the special value q = (1 − √ 5)/(1 + √ 5) they are closely related to Hankel matrices of reciprocal Fibonacci numbers called Filbert matrices. We find a formu...

Given a pair of distinct eigenvalues (λ1, λ2) of an n×n quadratic matrix polynomial Q(λ) with nonsingular leading coefficient and their corresponding eigenvectors, we show how to transform Q(λ) into a quadratic of the form [ Qd(λ) 0 0 q(λ) ] having the same eigenvalues as Q(λ), with Qd(λ) an (n− 1)× (n− 1) quadratic matrix polynomial and q(λ) a scalar quadratic polynomial with roots λ1 and λ2. ...

This paper considers the robust strict positive real (SPR) problem for a family of plants of the form G(s; q) = N(s; q n)D ?1 (s; q d)?, where N(s; q n) and D(s; q d) are multiaane in uncertain parameters q n and q d , respectively , and > 0. In the discrete-time setting, this problem plays an important role in digital quantiza-tion. Several results are presented. First, we prove that this plan...

The problem at hand is the integration of expert forecasts for plane prices into a fully calibrated basic economy. The economy is simulated through an Economic Scenario Generator (ESG), which includes macroeconomic processes, interest rate term structures, etc.. By defining the available best-case, worst-case, and mid-case forecasts to correspond to the 95%, the 50% and the 5% quantiles of the ...

We discuss the Q dependence of the chiral-odd twist-3 distribution e(x,Q). The anomalous dimension matrix for the corresponding twist-3 operators is calculated in the one-loop level. This study completes the calculation of the anomalous dimension matrices for all the twist-3 distributions together with the known results for the other twist-3 distributions g2(x,Q ) and hL(x,Q ). We also have con...

We present a condition on the matrix of an underdetermined linear system which guarantees that the solution of the system with minimal `q-quasinorm is also the sparsest one. This generalizes, and sightly improves, a similar result for the `1-norm. We then introduce a simple numerical scheme to compute solutions with minimal `q-quasinorm, and we study its convergence. Finally, we display the res...

analysis of time series data can involve the inversion of large covariance matrices. for theclass of arma (p, q) processes there are no exact explicit expressions for these inverses, except for thema (1) process. in practice, the sample covariance matrix can be very large and inversion can becomputationally time consuming and so approximate explicit expressions for the inverse are desirable.thi...