Abstract.A family of pseudorandom generators based on the decisional Diffie-Hellman assumption is proposed. The new construction is a modified and generalized version of the Dual Elliptic Curve generator proposed by Barker and Kelsey. Although the original Dual Elliptic Curve generator is shown to be insecure, the modified version is provably secure and very efficient in comparison with the other pseudorandom generators based on discrete log assumptions.Our generator can be based on any group of prime order provided that an additional requirement is met (i.e., there exists an efficiently computable function that in some sense enumerates the elements of the group). Two specific instances are presented. The techniques used to design the instances, for example, the new probabilistic randomness extractor are of independent interest for other applications.
The reasons for the lag of the indicators of the leading Russian coal mines engaged in the longwall mining of the flat-lying coal seams from similar foreign mines are considered. The analysis of the efficiency of the longwall face move operations at the JSC SUEK-Kuzbass mines was carried out. A significant excess of the planned deadlines for the longwall face move during the thick flat-lying seams mining, the reasons for the low efficiency of disassembling operations and the main directions for improving the technology of disassembling operations are revealed. The directions of ensuring the operational condition of the recovery room formed by the longwall face are considered. The recommended scheme of converged coal seams mining and a three-dimensional model of a rock mass to justify its parameters are presented. Numerical studies using the finite element method are performed. The results of modeling the stress-strain state of a rock mass in the vicinity of a recovery room formed under conditions of increased stresses from the boundary part of a previously mined overlying seam are shown. The main factors determining the possibility of ensuring the operational condition of the recovery rooms are established. It is shown that it is necessary to take into account the influence of the increased stresses zone when choosing timbering standards and organizing disassembling operations at a interbed thickness of 60 m or less. A sufficient distance from the gob of above- or undermined seams was determined to ensure the operational condition of the recovery room of 50 m, for the set-up room – 30 m. Recommendations are given for improving technology and organization of the longwall face move operations at the mines applied longwall mining of flat-lying coal seams with the formation of a recovery room by the longwall face.
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