danДоклады Национальной академии наук БеларусиDoklady of the National Academy of Sciences of Belarus1561-83232524-2431The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"dan-137Research ArticleМАТЕМАТИКАMATHEMATICSАНАЛОГ RSA-КРИПТОСИСТЕМЫ В КВАДРАТИЧНЫХ ФАКТОРИАЛЬНЫХ КОЛЬЦАХANALOGUE OF THE RSA-CRYPTOSYSTEM IN QUADRATIC UNIQUE FACTORIZATION DOMAINSВАСЬКОВСКИЙМ. М.VASKOUSKIM.vaskovskii@bsu.byКОДРАТЕНОКН. В.KONDRATYONOKN.nkondr2006@rambler.ruБелорусский государственный университет, МинскBelarusian State University, Minsk2015060620165951823Copyright © ВАСЬКОВСКИЙ М.М., КОДРАТЕНОК Н.В., 20162016ВАСЬКОВСКИЙ М.М., КОДРАТЕНОК Н.В.VASKOUSKI M., KONDRATYONOK N.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://doklady.belnauka.by/jour/article/view/137

Цель данной работы заключается в построении аналога RSA-криптосистемы в квадратичных факториальных кольцах. В работе предложен алгоритм построения электронной цифровой подписи. Доказан аналог поиска секретного ключа и факторизации модуля криптосистемы в случае, когда целые алгебраические элементы поля образуют Евклидово кольцо. Даны ограничения на параметры криптосистемы для защиты от метода повторного цифрования. Так же проведено исследование скорости работы и взлома полученной криптосистемы.

In the article, the analogue of a RSA-cryptosystem in general quadratic unique factorization domains is obtained. A scheme of digital signature on the basis of the generalized RSA cryptosystem is suggested. The analogue of Wiener’s theorem on low private key is obtained. We prove the equivalence of the problems of generalized RSA-modulus factorization and private key search when the domain of all algebraic integer elements of the quadratic field is Euclidean. A method to secure the generalized RSA-cryptosystem of the iterated encryption cracking is proposed.

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The authors declare that there are no conflicts of interest present.