Permutation polynomials have been studied for a long time and have important applications in cryptography, coding theory and combinatorial designs. In this paper, by means of the multivariate method and the resultant, we propose four new classes of permutation quadrinomials over 𝔽q3, where q is a prime power. We also show that they are not quasi-multiplicative equivalent to known ones. Moreover, we compare their differential uniformity with that of some known classes of permutation trinomials for some small q.

In the key recovery variant of the interpolation attack, exhaustive search is required to find the last round key Km. Therefore, this attack is almost impractical if the size of Km is too large. In this paper, we show that Km can be very efficiently obtained if F(K,x) can be approximated by a low degree polynomial gx(K) in K for any fixed x, where F is a round function of Feistel type block ciphers.

This paper deals with a method of estimating the parameters and the order of a linear system using differential digital filters and the resultant. From the observed signals of the input and output of an objective system, we extract the differential signals from the zero order to an appropriate high order with the same phase characteristics, using several digital filters. On the assumption that the system order is known, we estimate the parameters of the transfer function and evaluate the estimation error bounds. We propose a criterion function generated by the product of the highest order coefficients and the resultant of the numerator and denominator of the estimated transfer function. Applying this criterion function, we can estimate the order of the objective system. The threshold corresponding to this criterion function is evaluated from the deviation in the frequency characteristics of the used differential filters and the error bound of the estimated parameters. In order to demonstrate the propriety of the proposed method, some numerical simulations are presented.