Root Finding Interpolation Attack

How to Improve Interpolation Attack

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 ci...

An Efficient Interpolation Attack

We introduce an efficient interpolation attack which gives the tighter upper bound of the complexity and the number of pairs of plaintexts and ciphertexts required for the attack. In the previously known interpolation attack there is a problem in that the required complexity for the attack can be overestimated. We solve this problem by first, finding the actual number of coefficients in the pol...

Lag Based Hermite Interpolation Method for Solving a Root of Nonlinear Equations

In this paper we propose a learning based iterative numerical method for computing a rootξ of a non-linear equation of the form f(x) = 0 in the interval [a,b]. Lag based method through Hermite interpolation modeled root discovery approach is developed and demonstrated in this paper. The new method has been tested for a series of functions considered by several researchers. The numerical experim...

Optimal derivative-free root finding methods based on the Hermite interpolation

We develop n-point optimal derivative-free root finding methods of order 2n, based on the Hermite interpolation, by applying a first-order derivative transformation. Analysis of convergence confirms that the optimal order of convergence of the transformed methods is preserved, according to the conjecture of Kung and Traub. To check the effectiveness and reliability of the newly presented method...

Polynomial Hermite Interpolation for Root Finding and Event Location