Abstract
A solution for the inverse doubling problem is obtained for elliptic curves represented in the twisted Edwards form. Estimates of the complexity of the division operation into two are obtained in comparison with the doubling of the point. One of the applications of the divisibility properties of a curve point into two is considered to determine the order of a point in a cryptosystem based on discrete logarithm problem.The necessary and sufficient conditions for the divisibility of a point of a curve by 2 are found. The possibility of using these curves to generate a crypto-resistant sequence of a large period is investigated.All possible numbers of the result of the division of a point into two and the dependence of these quantities on the dividend point are studied. The necessary and sufficient conditions for the existence of 4 different preimages of a point when dividing it into two are investigated. Pairing-friendly curves of prime or near-prime order are absolutely essential in certain pairing-based schemes like short signatures with longer useful life
Highlights
The article summarizes the development of computational mathematics during 50 years’ period (1969–2019) in the field of accuracy and efficiency of computational algorithms. It is emphasized on the global error of the computational algorithm (с. a.), estimates of its quality, the formulation of computations optimization problems, computational algorithms that are optimal in accuracy and processing speed, reserves of calculations optimization, testing the quality of applied software, computer technologies solving the problems of applied and computational mathematics with the given values of quality characteristics in accuracy and processing speed
До останнього зауваження можна лише додати, що інтерпретація відображає, крім усього іншого, рівень інтелекту, освіти, наукового досвіду і т.д
Summary
The article summarizes the development of computational mathematics during 50 years’ period (1969–2019) in the field of accuracy and efficiency of computational algorithms. РЕШЕНИЕ ОБРАТНОЙ ЗАДАЧИ К УДВОЕНИЮ ТОЧКИ СКРУЧЕННОЙ КРИВОЙ ЭДВАРДСА НАД КОНЕЧНЫМ ПОЛЕМ. Получено решение задачи обратной к удвоению точки для кривой представленной в скрученной форме Эдвардса. Найдены необходимые и достаточные условия делимости точки G X ,Y кривой Ea,d на 2. Важность операции делимости точки на 2 при криптоанализе уже частично замечена криптографами. Исследованы необходимые и достаточные условия существования 4 разных прообразов точки G X ,Y при делении ее на два. Цель роботы — получение новых [2, 3] и уточнение старых критериев делимости точки кривой не только напополам, но и на 4 над полем Fpn. Важность операции делимости точки на 2 при криптоанализе уже частично описана в работе А. Наша цель найти эти условия и исследовать возможности их применения для скрученной кривой Эдвардса.
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