Abstract
The article deals with the question of the creation and popularization of kriptovaljuty from a mathematical point of view. In particular it is a question of bitcoin, which is the most known kind of cryptocurrency today. This theme is important enough at present as in a society there is a demand for the decentralised alternative instrument of payment which irrespective of the state and on sense reminds system of the gold standard with the limited offer of currency. In the presented work the basic accent is made not only on occurrence history of bitcoin, but also on an action mathematical apparatus of cryptosystem. The elliptic curves are considered as the main tool of cryptography which is base at working out bitcoin. One of the basic properties of the given curves, and also a principle of their application are resulted at creation cryptocurrency. Mathematical formulas of calculation of a public key from a private key, process mining of bitcoins and their exchange for the goods and services are specified. The purposes of creation of specialised electronic stock exchanges on which bitcoins began to be on sale for the basic world currencies are described. The main reasons of use of the elliptic curves taken as a principle of work cryptosystem are allocated.
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