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...
Gespeichert in:
| Datum: | 2019 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
Кам'янець-Подільський національний університет імені Івана Огієнка
2019
|
| Online Zugang: | http://mcm-math.kpnu.edu.ua/article/view/174210 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Mathematical and computer modelling. Series: Physical and mathematical sciences |
Institution
Mathematical and computer modelling. Series: Physical and mathematical sciences| _version_ | 1856543238611009536 |
|---|---|
| author | Скуратовский, Руслан Вячеславович |
| author_facet | Скуратовский, Руслан Вячеславович |
| author_sort | Скуратовский, Руслан Вячеславович |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2020-01-20T08:43:23Z |
| description | 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 |
| first_indexed | 2025-07-17T10:43:21Z |
| format | Article |
| id | mcm-mathkpnueduua-article-174210 |
| institution | Mathematical and computer modelling. Series: Physical and mathematical sciences |
| language | Russian |
| last_indexed | 2025-07-17T10:43:21Z |
| publishDate | 2019 |
| publisher | Кам'янець-Подільський національний університет імені Івана Огієнка |
| record_format | ojs |
| spelling | mcm-mathkpnueduua-article-1742102020-01-20T08:43:23Z A Solution of the Inverse Problem to Doubling of Twisted Edwards Curve Point Решение обратной задачи к удвоению точки скрученной кривой Эдвардса над конечным полем Скуратовский, Руслан Вячеславович 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 Получено решение задачи обратной к удвоению точки для кривой представленной в скрученной форме Эдвардса. Получены оценки сложности операции деления на два в сравнении с удвоением точки. Найдено одно из приложений свойств делимости точки на два для определения порядка точки в криптосистеме основаной на проблеме дискретного логарифма.Найдены необходимые и достаточные условия делимости точки кривой на 2. Исследовано возможность применения данных кривых для генерации криптостойкой последовательности большого периода. Важность операции делимости точки на 2 при криптоанализе уже частично замечена криптографами.Исследованы все возможные количества результатов от деления точки на два и зависимости этих количеств от делимой точки. Исследованы необходимые и достаточные условия существования 4 разных прообразов точки при делении ее на два. Спаривание на дружественных эллиптических кривых простого порядка или почти простого порядка есть очень существенным во многих криптографических протоколах вида короткой цифровой подписи длительного использования. Кам'янець-Подільський національний університет імені Івана Огієнка 2019-01-21 Article Article Рецензована Стаття application/pdf http://mcm-math.kpnu.edu.ua/article/view/174210 10.32626/2308-5878.2019-19.148-155 Mathematical and computer modelling. Series: Physical and mathematical sciences; 2019: Mathematical and computer modelling. Series: Physical and mathematical sciences. Issue 19; 148-155 Математичне та комп'ютерне моделювання. Серія: Фізико-математичні науки; 2019: Математичне та комп'ютерне моделювання. Серія: Фізико-математичні науки. Випуск 19; 148-155 2308-5878 10.32626/2308-5878.2019-19 ru http://mcm-math.kpnu.edu.ua/article/view/174210/174159 Авторське право (c) 2021 Руслан Вячеславович Скуратовский |
| spellingShingle | Скуратовский, Руслан Вячеславович A Solution of the Inverse Problem to Doubling of Twisted Edwards Curve Point |
| title | A Solution of the Inverse Problem to Doubling of Twisted Edwards Curve Point |
| title_alt | Решение обратной задачи к удвоению точки скрученной кривой Эдвардса над конечным полем |
| title_full | A Solution of the Inverse Problem to Doubling of Twisted Edwards Curve Point |
| title_fullStr | A Solution of the Inverse Problem to Doubling of Twisted Edwards Curve Point |
| title_full_unstemmed | A Solution of the Inverse Problem to Doubling of Twisted Edwards Curve Point |
| title_short | A Solution of the Inverse Problem to Doubling of Twisted Edwards Curve Point |
| title_sort | solution of the inverse problem to doubling of twisted edwards curve point |
| url | http://mcm-math.kpnu.edu.ua/article/view/174210 |
| work_keys_str_mv | AT skuratovskijruslanvâčeslavovič asolutionoftheinverseproblemtodoublingoftwistededwardscurvepoint AT skuratovskijruslanvâčeslavovič rešenieobratnojzadačikudvoeniûtočkiskručennojkrivojédvardsanadkonečnympolem AT skuratovskijruslanvâčeslavovič solutionoftheinverseproblemtodoublingoftwistededwardscurvepoint |