The cryptanalysis of a public-key implementation of finite group mappings

Minghua Qu and Vanstone [2] have proposed a public-key cryptosystem (FGM) which is based on factorizations of a binary vector space (i.e., transversal logarithmic signatures of an elementary abelian 2-group). In this paper a generalized (basis-independent) decryption algorithm is given, which shows that there are many equivalent private keys, and a method of efficiently obtaining such an equivalent private key is given. The FGM cryptosystem is thus rendered insecure. Although the FGM cryptosystem is defined in terms of linear algebra, the attack given here is essentially group-theoretic in nature. Thus this attack throws doubt on any cryptosystem which relies on the security of transversal logarithmic signatures.This author was supported by S.E.R.C. Research Grant GR/H23719.     

Is the Data Encryption Standard a group? (Results of cycling experiments on DES)

The Data Encryption Standard (DES) defines an indexed set of permutations acting on the message space ={0,1}⁶⁴. If this set of permutations were closed under functional composition, then the two most popular proposals for strengthening DES through multiple encryption would be equivalent to single encryption. Moreover, DES would be vulnerable to a known-plaintext attack that runs in 2²⁸ steps on the average. It is unknown in the open literature whether or not DES has this weakness.Two statistical tests are presented for determining if an indexed set of permutations acting on a finite message space forms a group under functional composition. The first test is a meet-in-the-middle algorithm which uses O(K) time and space, where K is the size of the key space. The second test, a novel cycling algorithm, uses the same amount of time but only a small constant amount of space. Each test yields a known-plaintext attack against any finite, deterministic cryptosystem that generates a small group.The cycling closure test takes a pseudorandom walk in the message space until a cycle is detected. For each step of the pseudorandom walk, the previous ciphertext is encrypted under a key chosen by a pseudorandom function of the previous ciphertext. Results of the test are asymmetrical: long cycles are overwhelming evidence that the set of permutations is not a group; short cycles are strong evidence that the set of permutations has a structure different from that expected from a set of randomly chosen permutations.Using a combination of software and special-purpose hardware, the cycling closure test was applied to DES. Experiments show, with overwhelming confidence, that DES is not a group. Additional tests confirm that DES is free of certain other gross algebraic weaknesses. But one experiment discovered fixed points of the so-called weak-key transformations, thereby revealing a previously unpublished additional weakness of the weak keys.Support for this research was provided in part by the National Science Foundation under contract number MCS-8006938 and by the International Business Machines Corporation.     

Algebraic Model of Linear Triatomic Molecules

1IntroductionThesylnmenyofthemolecularrotationvibrationspectrehavebeeninvestigatedintensivelybylarhelloetal.[l].Theysuggestthatthesymmetryoftherotation-vibrationspectrafordiatomicmoleculesisdescribedbymeansofthegroupU(4).Thetriatomicmoleculeshasbeenc...     

Research on indoor electromagnetic radiation field of multiple antenna system

The complexity of the indoor environment brings great challenges to predict the electromagnetic radiation field of multiple antenna systems. Based on the Finite Difference Time Domain (FDTD) algorithm, using the mobile phone shielding device as the multiple antenna systems example, the mobile phone shielding device??s indoor electromagnetic radiation field is researched by measurment method and simulation method. The effectivity of prediction method is verified by comparing the prediciton results with the measurment results. About 80% of the error can be controlled less than 4 ± dB. The quantitative research has certain guiding significance to the prediction of the multiple antenna systems radio wave propagation.     

基于概率假设密度滤波和动力学方程约束的空间群目标数量和位置分辨

空间目标具有射程远、速度快等特点,为了有效解决密集性高、可分性差的高速空间目标群饱和攻击问题,实现非合作空间群目标数量和位置的尽早分辨,该文基于随机有限集(RFS)理论和动力学方程约束研究了空间“团状”目标数量和位置分辨问题,提出目标监测早期解决大量距离靠近、运动特征差异不明显的高速空间群目标数量和位置估计的相关算法,该算法利用概率假设密度(PHD)滤波器能够解决未知时变环境下目标个数与状态估计的特点,将高斯混合PHD (GM-PHD)滤波和空间目标动力学方程相结合,在解决不可分辨空间群目标数量和位置估计问题的同时,充分利用空间目标动力学方程对群内目标状态进行实时调整,提高空间目标位置状态估计精度,解决不可分辨空间目标群边跟踪边分辨问题,相关算法可为空间群目标数量和群内特殊价值个体目标位置尽快分辨、连续稳定跟踪和可靠动向预报等提供数据基础。     

Optical properties of Ge1-yCy alloys

The Ge_1-yC_y semiconductor alloy system offers promise as a material for use in heterostructure devices based on Si as well as other materials. We have grown Ge_1-y C_y alloys by solid source molecular beam epitaxy on Si substrates. Layer thicknesses ranged from 0.01 to 3 μm, and Auger electron spectroscopy and secondary ion mass spectrometry indicated C fractions up to 3 at. %. Optical absorption in the near-infrared region indicated a shift in the energy bandgap from that of Ge which was attributed to the effects of alloying. The dependence of the bandgap on composition was consistent with linear interpolations of the Ge and C conduction band minimums. We observed a fundamental absorption edge characteristic of an indirect bandgap material. Photoluminescence spectra at 11K of thick, relaxed layers indicated single broad peaks near the expected bandgap energy.     

Electrical properties of Si1−x−yGexCy and Ge1−yCy alloys

The effects of carbon on the structural and electrical properties of Si_1−x−yGe_xC_y and Ge_1−yC_y alloys grown by the molecular beam epitaxy have been examined by Hall effect measurements, current-voltage measurements, x-ray diffraction, and atomic force microscopy. Hall effect measurements showed that the addition of carbon increased the hole mobility in GeC compared to pure Ge, we attributed this increase to improved crystalline quality and reduced surface roughness. Current-voltage characteristics of SiGeC/Si and GeC/Si heterojunction diodes showed that with increasing carbon, the reverse leakage current decreased and the forward turn-on voltage increased, attributed to the increase in bandgap energy and reduction of intrinsic carrier concentration n_i.