One reason bitcoin can be confusing for beginners is that the technology behind it redefines the concept of ownership. To own something in the traditional sense, be it a house or a sum of money, means either having personal custody of the thing or granting custody to a trusted entity such as a bank.
With bitcoin the case is different. Bitcoins themselves are not stored either centrally or locally and so no one entity is their custodian. They exist as records on a distributed ledger called the block chain, copies of which are shared by a volunteer network of connected computers.
To “own” a bitcoin simply means having the ability to transfer control of it to someone else by creating a record of the transfer in the block chain. What grants this ability? Access to an ECDSA private and public key pair. What does that mean and how does that secure bitcoin?
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A protocol such as bitcoin selects a set of parameters for the elliptic curve and its finite field representation that is fixed for all users of the protocol. The parameters include the equation used, the prime modulo of the field, and a base point that falls on the curve.
The order of the base point, which is not independently selected but is a function of the other parameters, can be thought of graphically as the number of times the point can be added to itself until its slope is infinite, or a vertical line. The base point is selected such that the order is a large prime number.
Bitcoin uses very large numbers for its base point, prime modulo, and order. In fact, all practical applications of ECDSA use enormous values. The security of the algorithm relies on these values being large, and therefore impractical to brute force or reverse engineer.
Bitcoin Financial News
the private key is an unpredictably chosen number between 1 and the order. The public key is derived from the private key by scalar multiplication of the base point a number of times equal to the value of the private key. Expressed as an equation: public key = private key * base point.
This shows that the maximum possible number of private keys (and thus bitcoin addresses) is equal to the order. Hence, bitcoins are inherently tough and secure systems of digital currencies.
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