The problem of nite eld basis conversion is to convert from the representation of a eld element in one basis to the representation of the element in another basis. This paper presents new algorithms for the problem that require much less storage than previous solutions. For the nite eld GF(2 m), for example, the storage requirement of the new algorithms is only O(m) bits, compared to O(m 2) for...

Software implementation of finite field operations is becoming more and more widely used in communication, cryptography and multimedia applications. It is more flexible and easier to deploy, compared to dedicated hardware component. However, finite field operations often become the bottle-neck for high throughput applications and are impacting the life time of power constrained devices. It is t...

A new method for the reconstruction of the projected mass distribution of clusters of galaxies from the image distortion of background galaxies is discussed. This method is essentially equivalent to the one we developed previously, i.e., the noise-filtering method, but has several practical advantages: (1) It is much easier to implement; (2) it can be easily applied to widefield images, since t...

We present a scheme to reconstruct the quantum state of a field prepared inside a lossy cavity at finite temperature. Quantum coherences are normally destroyed by the interaction with an environment, but we show that it is possible to recover complete information about the initial state (before interaction with its environment), making possible to reconstruct any s-parametrized quasiprobability...

There are numerous directions from which one can approach the subject of the fast Fourier Transform (FFT). It can be explained via numerous connections to convolution, signal processing, and various other properties and applications of the algorithm. We (along with Geddes/Czapor/Labahn) take a rather simple view from the algebraic manipulation standpoint. As will be apparent shortly, we relate ...

In general, quantum field theories (QFT) require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like QED are not convergent series, but are asymptotic series. We apply neutrix calculus, developed in connection with asymptotic series and divergent integrals, to QFT, obtaining finite renormaliza...

lard and Schnorr algorithm. Farther factorization of prime quadratic integer π = ρρ in the ring 4 [ 2] ±  can be done similarly. Finite field r is represented as quotient ring 4 [ 2] /( ) ± ρ  . Integer exponent k is reduced in corresponding quotient ring by minimization of absolute value of its norm. Algorithms can be used for fast exponentiation in arbitrary cyclic group if its order can b...