§ 1. История создания и предпосылки криптовалюты переходящей в цифровой рубль
Криптовалюты с технологической точки зрения – это математический код, обращающийся в системе распределенного реестра – учетной записи, подтверждающей наличие криптовалюты. Она является представителем нового поколения валют крипто-цифровой формы стал биткоин. Криптовалюты представляют собой электронные деньги или цифровые активы в виде кода в специальном кошельке, создаваемые частными компьютерными системами без контроля центральных банков. Идея создателей криптовалют заключалась в попытке построить децентрализованную монетарную систему, которая бы не зависела от правительств и обладала высокой гибкостью. Поэтому исследование криптографии достаточно актуальное направление деятельности. В основе работы криптосистемы лежат эллиптические кривые. Эллиптическая кривая – это большое количество точек, описываемое уравнением (1) и условием (2), (это необходимо, чтобы исключить особые кривые, т.е. где функция не определена или имеет нерегулярное поведение.)
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)
Эллиптические кривые имеют некоторые полезные свойства. Например, не вертикальная прямая, пересекающая кривую в двух точках, всегда будет пересекать ее и в третьей точке, лежащей на кривой. Другим свойством является то, что если не вертикальная прямая является касательной к кривой в одной из точек, то она обязательно пересекает кривую еще ровно в одной точке [1].
Эти свойства можно использовать, чтобы определить две операции над точками, составляющими кривую: сложение точек и удвоение.
Для сложения точек P + Q = R мы проводим через точки P и Q прямую, которая, по свойствам эллиптических кривых, пересекает кривую в некоторой третьей точке R‘. Затем мы находим точку на кривой, симметричную точке R‘ относительно оси X. Именно эта точка R и будет считаться суммой P и Q (рис. 2).
Операция удвоения точки P + P = R. При удвоении мы проводим прямую, касательную к данной эллиптической кривой в точке P, которая, согласно свойствам кривой, должна пересекать ее еще в одной точке R‘. Точка R, симметричная R‘ относительно оси X, и будет считаться точкой удвоения P (рис. 3)
Важным элементом криптовалюты является подпись, но не обычная подпись, которую легко подделать, а цифровая (электронная) подпись, которая защищается ключом. А для этого применяется шифрование – один из наиболее важных инструментов, используемых в криптографии. Это средство, с помощью которого сообщение превращается в нечитаемый набор символов, если его непреднамеренно кто-то прочитает.
Ключ выводится математически из приватного ключа. В основе вычисления публичного ключа лежат операции удвоения точек и сложения точек, начиная с базовой точки. Нахождение суммы точек r будет определяться покомпонентно по следующим формулам: