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During the 1980s and early 1990s, the world insurance market grew substantially. World insurance premiums in 1993 accounted for about 8 percent of world gross domestic product (GDP), compared to 4 percent in 1984. This article explains a substantial proportion of the variation in property-liability insurance consumption across countries belonging to the(More)
In this paper, we extend a recent piece of work on low-weight polynomial form integers (LWPFIs). We present a new coefficient reduction algorithm based on the Montgomery reduction algorithm and provide its detailed analysis results. We give a condition for eliminating the final subtractions at the end of our Montgomery reduction algorithm adapted to perform(More)
A security analysis of XTR exponentiation algorithms against simple power analysis attack is presented. Under very reasonable assumptions, we prove that there exists a one-to-one correspondence between power trace and XTR operation sequence. With this result and our observations on the behavior of the simultaneous XTR double exponentiation, we show how(More)
We present efficient squaring formulae based on the Toom-Cook multiplication algorithm. The latter always requires at least one non-trivial constant division in the interpolation step. We show such non-trivial divisions are not needed in the case two operands are equal for three, four and five-way squarings. Our analysis shows that our 3-way squaring(More)
In 1999, Jerome Solinas introduced families of moduli called the generalized Mersenne numbers (GMNs), which are expressed in low-weight polynomial form, p = f (t), where t is limited to a power of 2. GMNs are very useful in elliptic curve cryptosystems over prime fields, since only integer additions and subtractions are required in modular reductions.(More)
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