title: Ð¡Ñ ÐµÐ¼Ð° Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ²ÐµÐ½Ð½Ð¾Ð¹ Ð¿Ð¾Ð´Ð¿Ð¸ÑÐ¸ Ð½Ð° Ð¸Ð·Ð¾Ð³ÐµÐ½Ð¸ÑÑ ÑÐ»Ð»Ð¸Ð¿ÑÐ¸ÑÐµÑÐºÐ¸Ñ ÐºÑÐ¸Ð²ÑÑ Ñ Ð°ÑÑÐµÐ½ÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸ÐµÐ¹ ÑÑÐ°ÑÑÐ½Ð¸ÐºÐ¾Ð²
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° ÑÐ¿ÐµÑÐ¸Ð°Ð»Ð¸ÑÑÐ°
titleType: Subtitle
title: Group signature scheme based on isogenies of elliptic curves with an ability for participants authentication
Creators: name: ÐÐ¾ÑÑÐ¸Ð½, Ð¡ÐµÑÐ³ÐµÐ¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2025
Subjects: Ð¿Ð¾ÑÑÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð°Ñ ÐºÑÐ¸Ð¿ÑÐ¾Ð³ÑÐ°ÑÐ¸Ñ
ÑÑÐ¿ÐµÑÑÐ¸Ð½Ð³ÑÐ»ÑÑÐ½ÑÐµ ÑÐ»Ð»Ð¸Ð¿ÑÐ¸ÑÐµÑÐºÐ¸Ðµ ÐºÑÐ¸Ð²ÑÐµ
Ð¸Ð·Ð¾Ð³ÐµÐ½Ð¸Ð¸
Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ²ÐµÐ½Ð½Ð°Ñ Ð¿Ð¾Ð´Ð¿Ð¸ÑÑ
postquantum cryptography
supersingular elliptic curves
isogenies
group signature

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description: The purpose of the study is to develop a protocol for multiple signature formation, based on the problem of searching elliptic curve isogenies, which eliminates previously found attacks and vulnerabilities of this apparatus. The subject of the work is the mechanism of digital signature formation resistant to attacks on a quantum computer. The research sets the following goals: Â  Â  1. Analysis of post-quantum schemes based on isogenies of elliptic curves. Â  Â  2. Analysis of vulnerabilities present in the post-quantuum schemes based on isogenies of elliptic curves. Â  Â  3. Develop a multiple signature scheme based on isogenies of elliptic curve. Â  Â  4. Security evaluation of the developed scheme. Â  Â  5. Software implementation of the developed method. Â  Â  The given work resulted in the development of multiple signature schemes based on isogenies of elliptic curves. The efficacy and safety of the resulting scheme has been demonstrated. The study points to the conclusion that security of such schemes still requires additional study and research before their application in production system. The results could be used as a basis for designing cryptographic protocols for digital signature, electronic document management systems, IoT, as well as in such technologies as blockchain.