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ECDSA Private Keys Study of Security

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Document pages: 19 pages

Abstract: Cryptocurrencies are a mean of executing online transactions. They use a variety of cryptographic techniques to secure and verify these transactions, which are functionally supported by the Blockchain platform. Blockchain is a continuously growing, distributed ledger of files that contains all transactions between users of cryptocurrencies in a verifiable and permanent manner. It consists of blocks that are connected and secured cryptographically. Cryptocurrencies use algorithms to produce pairs of public and private keys. These pairs, cryptographically merged with a message between the participants, are the building blocks of the relevant transactions. Bitcoin uses the ECDSA algorithm to produce the above-mentioned keys. The purpose of our work is to present some useful motifs for the domain parameters of base point (P) and the order (n) of the subgroup produced by it, while choosing the elliptic curve and the Galois field on which we formulate the algorithm, in order to obtain safer private keys. The results of the research are experimental due to the limited infrastructure, but explanatory for the purpose of our work. The resulting conclusions highlight the value of the proper selection of the structural parameters of these algorithms and possible alternatives to the curve, field and domain parameters that can be used.

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