A Solution of the Inverse Problem to Doubling of Twisted Edwards Curve Point
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 c...
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| Видавець: | Кам'янець-Подільський національний університет імені Івана Огієнка |
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| Дата: | 2019 |
| Автор: | |
| Формат: | Стаття |
| Мова: | rus |
| Опубліковано: |
Кам'янець-Подільський національний університет імені Івана Огієнка
2019
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| Онлайн доступ: | http://mcm-math.kpnu.edu.ua/article/view/174210 |
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Репозиторії
Mathematical and computer modelling. Series: Physical and mathematical sciences| Резюме: | 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 |
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