title: Ð ÐµÐ³ÑÐ»ÑÑÐ¸Ð·Ð°ÑÐ¸Ñ Ð¾ÐºÐ¾Ð½Ð½ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ñ ÐºÑÐ°ÑÐ½Ð¾Ð¹ ÑÐ¾ÑÐºÐ¸ ÑÐ»Ð»Ð¸Ð¿ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÐºÑÐ¸Ð²Ð¾Ð¹
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Development of constant-time window point multiplication methods in an elliptic curve group
Creators: name: ÐÐµÑÑÑÐºÐ¾Ð², ÐÑÐºÐ°Ð´Ð¸Ð¹
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: 2020
Subjects: ÑÐ»Ð»Ð¸Ð¿ÑÐ¸ÑÐµÑÐºÐ¸Ðµ ÐºÑÐ¸Ð²ÑÐµ
ÐºÑÐ¸Ð¿ÑÐ¾Ð³ÑÐ°ÑÐ¸Ñ Ð½Ð° ÑÐ»Ð»Ð¸Ð¿ÑÐ¸ÑÐµÑÐºÐ¸Ñ ÐºÑÐ¸Ð²ÑÑ
ÑÐµÐ³ÑÐ»ÑÑÐ½Ð¾Ðµ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ðµ ÐºÑÐ°ÑÐ½Ð¾Ð¹ ÑÐ¾ÑÐºÐ¸
ÑÐµÐ³ÑÐ»ÑÑÐ½ÑÐµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ñ
Ð¼ÐµÑÐ¾Ð´ ÑÐºÐ¾Ð»ÑÐ·ÑÑÐµÐ³Ð¾ Ð¾ÐºÐ½Ð°
Ð¾ÐºÐ¾Ð½Ð½ÑÐ¹ naf Ð¼ÐµÑÐ¾Ð´
elliptic curves
elliptic curve cryptography (ecc)
regular point multiplication
constant time algorithms
sliding window method
window naf method

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description: This work is devoted to analysis of methods of point multiplication methods in an elliptic curve group and development of constant-time window algorithms of point multiplication in order to protect calculations from a simple side-channel attack. The following tasks were solved in scope of this work: - conducting a comparative analysis of point multiplication methods in an elliptic curve group; - development of constant-time window algorithms of point multiplication and theoretical justification of their regularity; - evaluation of the developed algorithms complexity and selection of optimal parameters for them; - implementation of the developed algorithms. In scope of this work, a comparative analysis of point multiplication methods in an elliptic curve group was carried out and two constant-time window methods of point multiplication were proposed. Algorithm that uses CLNW and VLNW method, and algorithm that uses a modified signed binary representation of an integer. Theoretically proved that the developed algorithms require a constant number of point additions and point doublings. The developed algorithms have been implemented in the C language using open source cryptographic library OpenSSL.