On the Fourier Spectra of the Infinite Families of Quadratic APN Functions

It is well known that a quadratic function defined on a finite field of odd degree is almost bent (AB) if and only if it is almost perfect nonlinear (APN). For the even degree case there is no apparent relationship between the values in the Fourier spectrum of a function and the APN property. In this article we compute the Fourier spectrum of the new quadranomial family of APN functions. With this result, all known infinite families of APN functions now have their Fourier spectra and hence their nonlinearities computed.Comment: 12 pages, submitted to Adavances in the Mathematics of communicatio

A Highly Nonlinear Differentially 4 Uniform Power Mapping That Permutes Fields of Even Degree

Functions with low differential uniformity can be used as the s-boxes of symmetric cryptosystems as they have good resistance to differential attacks. The AES (Advanced Encryption Standard) uses a differentially-4 uniform function called the inverse function. Any function used in a symmetric cryptosystem should be a permutation. Also, it is required that the function is highly nonlinear so that it is resistant to Matsui's linear attack. In this article we demonstrate that a highly nonlinear permutation discovered by Hans Dobbertin has differential uniformity of four and hence, with respect to differential and linear cryptanalysis, is just as suitable for use in a symmetric cryptosystem as the inverse function.Comment: 10 pages, submitted to Finite Fields and Their Application

On the Equivalence of Quadratic APN Functions

Establishing the CCZ-equivalence of a pair of APN functions is generally quite difficult. In some cases, when seeking to show that a putative new infinite family of APN functions is CCZ inequivalent to an already known family, we rely on computer calculation for small values of n. In this paper we present a method to prove the inequivalence of quadratic APN functions with the Gold functions. Our main result is that a quadratic function is CCZ-equivalent to an APN Gold function if and only if it is EA-equivalent to that Gold function. As an application of this result, we prove that a trinomial family of APN functions that exist on finite fields of order 2^n where n = 2 mod 4 are CCZ inequivalent to the Gold functions. The proof relies on some knowledge of the automorphism group of a code associated with such a function.Comment: 13 p

A Few More Quadratic APN Functions

We present two infinite families of APN functions on GF(2n) where n is divisible by 3 but not 9. Our families contain two already known families as special cases. We also discuss the inequivalence proof (by computation) which shows that these functions are new

A Few More Quadratic APN Functions

We present two infinite families of APN functions on GF(2n) where n is divisible by 3 but not 9. Our families contain two already known families as special cases. We also discuss the inequivalence proof (by computation) which shows that these functions are new

A novel, highly efficient cavity backshort design for far-infrared TES detectors

In this paper we present a new cavity backshort design for TES (transition edge sensor) detectors which will provide increased coupling of the incoming astronomical signal to the detectors. The increased coupling results from the improved geometry of the cavities, where the geometry is a consequence of the proposed chemical etching manufacturing technique. Using a number of modelling techniques, predicted results of the performance of the cavities for frequencies of 4.3–10 THz are presented and compared to more standard cavity designs. Excellent optical efficiency is demonstrated, with improved response flatness across the band. In order to verify the simulated results, a scaled model cavity was built for testing at the lower W-band frequencies (75–100 GHz) with a VNA system. Further testing of the scale model at THz frequencies was carried out using a globar and bolometer via an FTS measurement set-up. The experimental results are presented, and compared to the simulations. Although there is relatively poor comparison between simulation and measurement at some frequencies, the discrepancies are explained by means of higher-mode excitation in the measured cavity which are not accounted for in the singlemode simulations. To verify this assumption, a better behaved cylindrical cavity is simulated and measured, where excellent agreement is demonstrated in those results. It can be concluded that both the simulations and the supporting measurements give confidence that this novel cavity design will indeed provide much-improved optical coupling for TES detectors in the far-infrared/THz band