A public-key cryptosystem utilizing cyclotomic fields

While it is well-known that the RSA public-key cryptosystem can be broken if its modulusN can be factored, it is not known whether there are other ways of breaking RSA. This paper presents a public-key scheme which necessarily requires knowledge of the factorization of its modulus in order to be broken. Rabin introduced the first system whose security is equivalent to the difficulty of factoring the modulus. His scheme is based on squaring (cubing) for encryption and extracting square (cube) roots for decryption. This introduces a 14 (19) ambiguity in the decryption. Various schemes which overcome this problem have been introduced for both the quadratic and cubic case. We generalize the ideas of Williams' cubic system to larger prime exponents. The cases of higher prime order introduce a number of problems not encountered in the quadratic and cubic cases, namely the existence of fundamental units in the underlying cyclotomic field, the evaluation of higher power residue symbols, and the increased difficulty of Euclidean division in the field.     

On quadratic forms of height two and a theorem of Wadsworth

Let and be anisotropic quadratic forms over a field of characteristic not . Their function fields and are said to be equivalent (over ) if and are isotropic. We consider the case where and is divisible by an -fold Pfister form. We determine those forms for which becomes isotropic over if , and provide partial results for . These results imply that if and are equivalent and , then is similar to over . This together with already known results yields that if is of height and degree or , and if , then and are equivalent iff and are isomorphic over .

     

Generation of Molecular Fields, Quantum Similarity Measures and Related Questions

A straightforward discussion on how to generate molecular fields is developed within the postulates of quantum mechanics. The theoretical formalism points towards the generalization and extension of the well-known molecular field forms, associated to density function and electrostatic molecular potential (EMP), including another category of fields associated to quantum molecular similarity measures. The results show that the new formalism can be easily applied to obtain an unlimited number of new information about molecular behavior.     

Microcalorimetry as a possible tool for phylogenetic studies of Tetrahymena

Using isothermal microcalorimetry, the growth power-time curves of three strains of Tetrahymena were determined at 28°C. Their Euclidean distances and cluster analysis diagram were obtained by using two thermokinetic parameters (r and Q_log), which showed that T. thermophila BF₁ and T. thermophila BF₅ had a closer relationship. Compared with the single molecular biomarker (ITS1) method, microcalorimetry wasmaybe a simpler, more sensitive andmore economic technique in the phylogenetic studies of Tetrahymena species.     

On the representation of electrostatic fields around ab initio charge distributions

Summary We compare two methods (Mulliken charges and a distributed multipole analysis, DMA) of representing an ab initio charge distribution for calculating the electrostatic field and potential outside the molecule, using pyrimidine and the RNA base uracil as examples. This is done using a 3-D graphical display of the electrostatic fields, which, when used with real-time rotation, zooming and clipping, has many advantages for qualitatively assessing the electrostatic interactions of a molecule. The errors involved in using Mulliken point charges may be of similar magnitude to the total electrostatic field in regions which are important in recognition processes. The DMA representation automatically includes the anisotropic electrostatic effects of non-spherical features in the charge distribution of each atom, and yet the displayed electrostatic fields around the atoms which have lone-pair density do not show marked anisotropy.     

New computer program to calculate the symmetry of molecules

In this paper we, present some MATLAB and GAP programs and use them to find the automorphism group of the Euclidean graph of the C₈₀ fullerence with connectivity and geometry of I _h symmetry point group. It is proved that this group has order 120 and is isomorphic to I _h ≊Z₂×A₅, where Z₂ is, a cyclic group of order 2 and A₅ is the alternating group on five symbols.     

Chemical mass shifts in resonance ejection experiments in the quadrupole ion trap

Chemical mass shifts were measured in a Paul ion trap operated in the mass-selective instability scan with resonance ejection using a custom-built instrument. These shifts, which can be as much as 2%, decrease with increasing endcap electrode separation owing to changes in the higher order contributions to the electric field. They also decrease with decreasing helium buffer gas pressure. Both of these effects are analogous to those found with boundary ejection. This suggests that the previously proposed chemical mass shift mechanism based on compound-dependent collisional modification of the ejection delay produced by field faults near the endcap electrode apertures holds true also for resonance ejection. The influence of the resonance frequency on chemical mass shifts was also investigated and it is shown that at certain working points (values of the Mathieu parameter q(z) and a(z)) non-linear resonances greatly reduce the ejection delay for all ions, regardless of their chemical structures, and thus reduce the magnitude of the chemical mass shift. Energetic collisions leading to dissociation can take place at an earlier stage during the ejection process in the mass analysis scan when using resonance ejection compared with boundary ejection. This leads to even larger chemical mass shifts of fragile ions in resonance ejection. Increasing the resonance voltage amplitude can enhance this effect. The chemical mass shifts of fragile ions increase with increase in the resonance voltage amplitude, whereas negligible changes occur for structurally stable ions.