Reducing elliptic curve logarithms to logarithms in a finite field

Elliptic curve cryptosystems have the potential to provide relatively small block size, high-security public key schemes that can be efficiently implemented. As with other known public key schemes, such as RSA and discrete exponentiation in a finite field, some care must be exercised when selecting the parameters involved, in this case the elliptic curve and the underlying field. Specific classes of curves that give little or no advantage over previously known schemes are discussed. The main result of the paper is to demonstrate the reduction of the elliptic curve logarithm problem to the logarithm problem in the multiplicative group of an extension of the underlying finite field. For the class of supersingular elliptic curves, the reduction takes probabilistic polynomial time, thus providing a probabilistic subexponential time algorithm for the former problem     

Fast exponentiation in subgroups of finite fields

A new method for fast exponentiation is introduced by adapting the work of Gallant, Lambert and Vanstone (see Advances in Cryptology-Crypto 2001 LNCS 2139, p.190-200 Springer-Verlag, 2001) to finite fields: thus, it is applicable to the multiplicative subgroups of non-prime fields with efficient group homomorphisms such as pth powering maps. When applied to a quartic extension of a 256 bit prime field, the proposed method runs up to 60% faster than ordinary exponentiation in a 1024 bit prime field     

Fast computation of wideband RCS using characteristic basis function method and asymptotic waveform evaluation technique

The Asymptotic Waveform Evaluation (AWE) technique is an extrapolation method that provides a reduced-order model of linear system and has already been successfully used to analyze wideband electromagnetic scattering problems. As the number of unknowns increases, the size of Method Of Moments (MOM) impedance matrix grows very rapidly, so it is a prohibitive task for the computation of wideband Radar Cross Section (RCS) from electrically large object or multi-objects using the traditional AWE technique that needs to solve directly matrix inversion. In this paper, an AWE technique based on the Characteristic Basis Function (CBF) method, which can reduce the matrix size to a manageable size for direct matrix inversion, is proposed to analyze electromagnetic scattering from multi-objects over a given frequency band. Numerical examples are presented to illustrate the computational accuracy and efficiency of the proposed method.     

Fast convenient numerical computation of lognormal characteristic functions

No closed-form expression is known for the lognormal characteristic function. Computation of the characteristic function using numerical integration is time consuming and often converges poorly. Alternative published numerical methods for its evaluation are complex and often valid only for particular values of the dB-spread. A novel definite integral form of the lognormal characteristic function is derived. This form lends itself to rapid and convenient computation of the lognormal characteristic function using simple, common methods of numerical integration.     

Extending Nyberg construction on Galois fields of odd characteristic

As is known, the Nyberg design S-boxes possess the cryptographic properties valuable for practical application. Up to date this construction has been considered only for fields of characteristic 2. This paper presents an extension of the Nyberg construction to the fields of odd characteristic. The notion of nonlinearity distance of p-function is introduced, and the affine ternary code is built. The Nyberg design S-boxes with fields characteristic p = 3 for all lengths N ≤ 243 are built. The nonlinearity distances are calculated, and it is shown that with an increase of S-box length, these distances increase essentially faster as compared to the fields of characteristic p = 2.     

Fast method of correlation measurement of planar particle fields

A new correlation algorithm, which combines filtering with correlation, is proposed to extract displacement fields for particle image velocimetry (PIV) and holographic particle velocimetry (HPV). In addition, an integrated circuit (IC) design is proposed to substitute for dedicated floating point processors used in PIV systems. This breakthrough eliminates dedicated processors from PIV     

Fast method for calculation of characteristic parameters of ionospheric radio circuit

A fast method for the determination of the arrival angles and the group delay associated with a given transmitter/receiver circuit at a fixed frequency is presented. The electronic density profile used (MQP) is given, as well as the method and equations utilised for the determination of the propagation characteristics.<>     

The vulnerability of geometric sequences based on fields of odd characteristic

A new method of cryptologic attack on binary sequences is given, using their linear complexities relative to odd prime numbers. We show that, relative to a particular prime number p, the linear complexity of a binary geometric sequence is low. It is also shown that the prime p can be determined with high probability by a randomized algorithm if a number of bits much smaller than the linear complexity is known. This determination is made by exploiting the imbalance in the number of zeros and ones in the sequences in question, and uses a new statistical measure, the partial imbalance.This project was sponsored by the National Security Agency under Grant No. MDA904-91-H-0012. The United States Government is authorized to reproduce and distribute reprints notwithstanding any copyright notation hereon.     

Fast evaluation of an integral occurring in digital filteringapplications

A fast evaluation procedure for the integral I_m,n,p=1/2πj∯_|z|=1H_m,n(z)H _m,n(z^-1)z^p-1dz for arbitrary nonnegative integer-valued m, n, and p, is presented, where H_m,n (z)=Σ_k=0^mb_m,kz^-k /Σ_l=0ⁿa_n,lz^-1,a _n,0≠0 is the transfer function of an arbitrary digital filter. Evaluation of this integral frequently appears in control, communication, and digital filtering. A notable result is the one-term recursion on p, for arbitrary but fixed nonnegative integers m and n. The computational complexity is analyzed, and two illustrative examples demonstrate some of the advantages of this approach     

Monomial and quadratic bent functions over the finite fields of odd characteristic

Considered are p-ary bent functions having the form f(x)=Tr/sub n/(/spl sigma//sub i=0//sup s/a/sub i/x/sup di/). A new class of ternary monomial regular bent function with the Dillon exponent is discovered. The existence of Dillon bent functions in the general case is an open problem of deciding whether a certain Kloosterman sum can take on the value -1. Also described is the general Gold-like form of a bent function that covers all the previously known monomial quadratic cases. The (weak) regularity of the new as well as of known monomial bent functions is discussed and the first example of a not weakly regular bent function is given. Finally, some criteria for an arbitrary quadratic function to be bent are proven.     

Self-dual codes and modules for finite groups in characteristic two

Using representation theoretical methods we investigate self-dual group codes and their extensions in characteristic 2. We prove that the existence of a self-dual extended group code heavily depends on a particular structure of the group algebra KG which can be checked by an easy-to-handle criteria in elementary number theory. Surprisingly, in the binary case such a code is doubly even if the converse of Gleason's theorem holds true, i.e., the length of the code is divisible by 8. Furthermore, we give a short representation theoretical proof of an earlier result of Sloane and Thompson which states that a binary self-dual group code is never doubly even if the Sylow 2-subgroups of G are cyclic. It turns out that exactly in the case of a cyclic or Klein four group as Sylow 2-subgroup doubly even group codes do not exist.     

Electrostatic fields inside two planar distributions of potential

The potentials and fields inside two parallel planar distributions of potential can be written as Green's function integrals. Each Green's function can be evaluated numerically by decomposing it into two series of terms (one for large and one for small distances) which converge rapidly within their intervals of use. The accuracy of truncation after a few terms is evaluated.     

Absorptive bistability in a three-level system interacting with two fields

We have studied the case of purely absorptive bistability in a three-level system interacting with two coherent fields. The results show that in the limit where the neglect of propagation effects is justified, a tunable optical device (TOD) results. It is shown that varying the secondary field amplitude can alter the hysteresis curve of the two-level system dramatically. Under certain conditions, the secondary applied field can eliminate hysteresis and produce a tunable differential gain region. This type of adaptive behavior offers attractive possibilities for optically based analog-digital systems.     

两台多模激光场强度和相位的混沌同步

对空间耦合的两台多模激光场的强度和相位的动力学行为进行了理论分析.当系统的损失受到调制时,在一定的参数范围内,两台激光输出的总强度之间会出现很好的混沌同步,两台激光的对应模式之间也出现相应的混沌同步,但不同模式之间则是完全的混沌状态,每台激光的各个模式强度之间存在模式竞争现象.每台激光场不同模式的相位和相位差之间出现有趣的关系,与强度的混沌同步存在一定的联系.     

Fast fault-tree evaluation for many sets of input data

It is pointed out that system unavailability and failure frequency can be found for many sets of components data via symbolic formulas with few multiplications. The derivation of such symbolic formulas is possible by binary-tree algorithms (specifically the Shannon expansion) which could run very fast on supercomputers allowing for binary-tree parallelism. The reduction factor of the number of multiplications needed in nested versus polynomial forms is roughly half the height of the decomposition tree, and the height of the tree is roughly the number of system components     

谐波环境下基于时域特性分析的电能质量评估

在谐波环境下,电能质量容易发生畸变,电力系统极其不稳定,该研究采用时域特性分析的方法,构建出改进型的电能质量扰动分析模型.该模型能够提取电能扰动特征量、基波幅值变化特征量和加性扰动特征量等,通过Daubechies小波变换实现信号的放大,并对电能质量进行多角度分析.该研究通过对电能质量特征进行量化分析,及时获取谐波、间...     

Fast reduction of potential fields measured over an uneven surfaceto a plane surface

The present work is aimed at rapid reduction of the gravity and magnetic fields observed over an uneven surface to a horizontal plane. The approach suggested is to estimate the Fourier transform of the potential field over an imaginary horizontal plane lying entirely above the ground surface and impose boundary conditions; namely, the solution must satisfy the observed field over the ground surface and vanish over an infinite hemisphere. The desired Fourier transform is obtained in an iterating manner. A 2D FFT algorithm can considerably reduce the computational burden. The FFT approach cannot be used unless the discrete data is available on a rectangular grid. If the observations are scattered, interpolation to the nearest grid point will have to be carried out. Interpolation introduces marginal increase in the rms error. The iterating approach is about 10 times faster than the least squares approach     

两类压缩态光场的特性比较

本文指出光场压缩态|α,z〉A=S(z)D(α)|0〉和|α,z〉B=D(α)S(z)|0〉不完全等价,它们实质上是本文命名的压缩子(Squeezon)湮灭算符b=SaS~+的两个本征态,具有完全相同的压缩特性,但本征值不同,光子统计分布和光子统计特性有显著差异,所含的能量状况亦很不相同。     

Fast radiation pattern evaluation for lens and reflector antennas

A novel algorithm referred to as the fast physical optics (FPO) for computing the radiation patterns of nonplanar aperture antennas over a range of observation angles is presented. The computation is performed in the framework of the conventional physical optics approximation appropriate for the high frequency regime. The proposed algorithm is directly applicable to reflector and lens antennas as well as to radomes. The method comprises two steps. First, a decomposition of the aperture into subdomains and computation of the pertinent radiation pattern of each subdomain. Second, interpolation, phase-correction and aggregation of the radiation patterns into the final pattern of the whole aperture. A multilevel algorithm is formulated via a recursive application of the domain decomposition and aggregation steps. The computational structure of the multilevel algorithm resembles that of the FFT while avoiding its limitations.     

Fast processing of 4 in silicon wafers using two 150 W halogen lamps

We describe a very simple annealing system in which two 150 W halogen lamps are scanned on a Si wafer. Electrical and structural measurements indicate complete activation of the impurities without any appreciable diffusion and a good recovery of the damaged lattice. Moreover, two key processing requirements are satisfied: highly uniform sheet resistance across the wafer (standard deviation 3.5%) and the absence of induced warping of the wafer.