Showing papers by "Moscow Institute of Physics and Technology published in 1991"

Ideals over a non-commutative ring and their application in cryptology

Abstract: A new modification of the McEliece public-key cryptosystem is proposed that employs the so-called maximum-rank-distance (MRD) codes in place of Goppa codes and that hides the generator matrix of the MRD code by addition of a randomly-chosen matrix. A short review of the mathematical background required for the construction of MRD codes is given. The cryptanalytic work function for the modified McEliece system is shown to be much greater than that of the original system. Extensions of the rank metric are also considered.

A Fast Matrix Decoding Algorithm for Rank-Error-Correcting Codes

Abstract: The so-called term-rank and rank metrics and appropriate codes were introduced and investigated in [1 –7]. These metrics and codes can be used for correcting array errors in a set of parallel channels, for scrambling in channels with burst errors, as basic codes in McEliece public key cryptosystem [8], etc. For codes with maximal rank distance (MRD codes) there exists a fast decoding algorithm based on Euclid's Division Algorithm in some non-commutative ring [6]. In this paper a new construction of MRD codes is given and a new fast matrix decoding algorithm is proposed which generalizes Peterson's algorithm [9] for BCH codes.

Magnetoelastic Mode Effect on Spin-Wave Instability Threshold

Abstract: A new attraction has been given to nonlinear effects and ferromagnetic resonance (FMR) phenomena in single crystal ferrites in recent years, motivated by the availability of high-quality epitaxial thin films of yttrium iron garnet (YIG) and its possible use for microwave signal processing. This work presents experimental investigation of the influence of magnetoelastic interaction on nonlinear FMR behavior in normally magnetized YIG films. It is well known that dipole magnetostatic modes (MSM) representing natural oscillations of magnetization vector in bounded ferrite medium become unstable at high microwave power level [1]. Magnetoelastic interaction was previously shown to exert its influence on the first order spin wave instability threshold in bulk ferrite crystals [2]. Planar YIG film — gadolinium gallium garnet (GGG) substrate structures are high quality resonators and the magnetoelastic excitation of elastic modes must be especially strong in the structures and therefore is expected to influence significantly nonlinear behavior in YIG films. In normally magnetized ferrite films MSM instability is caused by the second order parametric processes. Parametric spin-wave (SW) generation is known to occur above the critical level of exciting microwave power Ps. In this work the second order SW instability of dipole MSM is investigated for resonance interaction of secondary SW with elastic system. Strong magnetoelastic interaction of secondary SW with elastic system takes place provided frequencies and wave-numbers of the secondary SW correspond to dispersion curve crossover region of elastic wave (EW) and spin wave.