@ -37,11 +37,13 @@ A private key is simply a number, picked at random. In practice, and to make man
((("Bitcoin (system)","public keys")))((("public keys")))Each private key has a corresponding _public key_, which is calculated from the private key, using scalar multiplication on the elliptic curve. In simple terms, with a private key _k_, we can multiply it with a constant _G_ to produce a public key _K_:
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_K_ = __k__*__G__
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++++
<ul class="simplelist">
<li><em>K</em> = <em>k</em>*<em>G</em></li>
</ul>
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It is impossible to reverse this calculation. Given a public key +K+, one cannot calculate the private key +k+. Division by +G+ is not possible in elliptic curve math. Instead, one would have to try all possible values of +k+ in an exhaustive process called a _brute-force attack_. Because +k+ is a 256-bit number, exhausting all possible values with any classical computer would require more time and energy than available in this universe.
It is impossible to reverse this calculation. Given a public key _K_, one cannot calculate the private key _k_. Division by _G_ is not possible in elliptic curve math. Instead, one would have to try all possible values of _k_ in an exhaustive process called a _brute-force attack_. Because _k_ is a 256-bit number, exhausting all possible values with any classical computer would require more time and energy than available in this universe.
kristen@oreilly.com
3 years ago