Generalised Mersenne Numbers Revisited

Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography. Their form is such that modular reduction is extremely efficient, thus making them an attractive choice for modular multiplication implementation. However, the issue of residue multiplication efficiency seems to have been overlooked. Asymptotically, using a cyclic rather than a linear convolution, residue multiplication modulo a Mersenne number is twice as fast as integer multiplication; this property does not hold for prime GMNs, unless they are of Mersenne's form. In this work we exploit an alternative generalisation of Mersenne numbers for which an analogue of the above property --- and hence the same efficiency ratio --- holds, even at bitlengths for which schoolbook multiplication is optimal, while also maintaining very efficient reduction. Moreover, our proposed primes are abundant at any bitlength, whereas GMNs are extremely rare. Our multiplication and reduction algorithms can also be easily parallelised, making our arithmetic particularly suitable for hardware implementation. Furthermore, the field representation we propose also naturally protects against side-channel attacks, including timing attacks, simple power analysis and differential power analysis, which is essential in many cryptographic scenarios, in constrast to GMNs.Comment: 32 pages. Accepted to Mathematics of Computatio

Financing of large corporations 1951-55

Corporations - Finance ; Corporations - Accounting

ENVIRONMENTAL SUSTAINABILITY AND WASTE TREATMENT CAPABILITIES OF SMALL-SCALE ANAEROBIC DIGESTION SYSTEMS

Anaerobic digestion is a common form of waste treatment and energy production throughout the world, and in the United States the number of agricultural digesters is increasing at a rate of approximately 10% annually. As the number of digesters grows, efforts to assess the environmental cost of their installation and the potential utility of their by-products are required. This research investigates the relative environmental sustainability of small-scale digesters treating dairy manure in the U.S. and human waste in Haiti, and explores the biogas potential and nutrient transformations resulting from the anaerobic digestion of dairy manure. Specifically, the objectives of the research are: 1) to conduct an eMergy analysis on the two digestion systems to assess the effect of waste source, climate, and infrastructure on system sustainability; and 2) to provide an overview of waste treatment and energy production options for agricultural digesters treating dairy manure in the United States

Some buffet response characteristics of a twin-vertical-tail configuration

A rigid, 1/6 size, full span model of an F-18 airplane was fitted with flexible vertical tails of two different levels of stiffness that were buffet tested in the Langley Transonic Dynamics Tunnel. Vertical tail buffet response results that were obtained over the range of angles of attack from -10 to 40 degs, and over the range of Mach numbers from 0.30 to 0.95 are presented. These results indicate the following: (1) the response occurs in the first bending mode; (2) the response increases with increasing dynamic pressure, but changes in response are not linearly proportional to the changes in dynamic pressure; (3) the response is larger at M = 0.30 than it is at the higher Mach numbers; (4) the maximum intensity of the buffeting is described as heavy to severe using an assessment criteria proposed by another investigator; and (5) the data at different dynamic pressures and for the different tails correlate reasonably well using the buffet excitation parameter derived from the dynamic analysis of buffeting

How America Permitted the Great Recession

Many people have thrown out many ideas as to how the Great Recession happened. Some blame the banks, some blame the system, and others blame the lawmakers. The truth is much more complicated, and many different events lined up to make it happen. The essential fact is that there would likely have been a recession in the 2000s as a result of the commodities price recession of the 90s. What made the recession bad enough to be called the Great Recession was the gradual de-regulation that occurred after Glass-Steagal. Primarily, this paper will deal with the laws surrounding the banking and finance industry, as these are the controls on how finance is managed in the country and how America permitted the Recession to happen, with a couple of moments to define key elements of the workings of how this is going on

Radioactivities induced in some LDEF samples

Radioactivities induced in several Long Duration Exposure Facilities (LDEF) samples were measured by low-level counting at Los Alamos and elsewhere. These radionuclides have activities similar to those observed in meteorites and lunar samples. Some trends were observed in these measurements in terms of profiles in trunnion layers and as a function of radionuclide half-life. Several existing computer codes were used to model the production by the protons trapped in the Earth's radiation belts and by the galactic cosmic rays of some of these radionuclides, Mn-54 and Co-57 in steel, Sc-46 in titanium, and Na-22 in alloys of titanium and aluminum. Production rates were also calculated for radionuclides possibly implanted in LDEF, Be-7, Be-10, and C-14. Enhanced concentrations of induced isotopes in the surfaces of trunnion sections relative to their concentrations in the center are caused by the lower-energy protons in the trapped radiation. Secondary neutrons made by high-energy trapped protons and by galactic cosmic rays produce much of the observed radioactivities, especially deep in an object. Comparisons of the observed to calculated activities of several radionuclides with different half-lives indicate that the flux of trapped protons at LDEF decreased significantly at the end of the mission