The public key is calculated from the private key using elliptic curve multiplication, which is irreversible: latexmath:[\(K = k * G\)] where +k+ is the private key, +G+ is a constant point called the _Generator Point_ and +K+ is the resulting public key. The reverse operation, known as "finding the discrete logarithm" -- calculating +k+ if you know +K+ -- is as difficult as trying all possible values of +k+, i.e., a brute-force search. Before we demonstrate how to generate a public key from a private key, let's look at Elliptic Curve Cryptography in a bit more detail.
The public key is calculated from the private key using elliptic curve multiplication, which is irreversible: latexmath:[\(K = k * G\)] where _k_ is the private key, _G_ is a constant point called the _generator point_ and _K_ is the resulting public key. The reverse operation, known as "finding the discrete logarithm"—calculating _k_ if you know _K_—is as difficult as trying all possible values of +k+, i.e., a brute-force search. Before we demonstrate how to generate a public key from a private key, let's look at elliptic curve cryptography in a bit more detail.
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