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CH04::pubkeys: move-only

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David A. Harding 2023-02-08 21:12:58 -10:00
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@ -182,32 +182,6 @@ large number. It is approximately 10^77^ in decimal. For comparison, the
visible universe is estimated to contain 10^80^ atoms. visible universe is estimated to contain 10^80^ atoms.
==== ====
[[pubkey]]
==== Public Keys
((("keys and addresses", "overview of", "public key
calculation")))((("generator point")))The public key is calculated from
the private key using elliptic curve multiplication, which is
irreversible: _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.
[TIP]
====
Elliptic curve multiplication is a type of function that cryptographers
call a "trap door" function: it is easy to do in one direction
(multiplication) and impossible to do in the reverse direction
(division). Someone with a private key can easily create the public
key and then share it with the world knowing that no one can reverse the
function and calculate the private key from the public key. This
mathematical trick becomes the basis for unforgeable and secure digital
signatures that prove control over bitcoin funds.
====
[[elliptic_curve]] [[elliptic_curve]]
==== Elliptic Curve Cryptography Explained ==== Elliptic Curve Cryptography Explained
@ -339,7 +313,30 @@ that k is sometimes confusingly called an "exponent" in this case.((("",
startref="eliptic04")))((("", startref="Celliptic04"))) startref="eliptic04")))((("", startref="Celliptic04")))
[[public_key_derivation]] [[public_key_derivation]]
==== Generating a Public Key ==== Public Keys
((("keys and addresses", "overview of", "public key
calculation")))((("generator point")))The public key is calculated from
the private key using elliptic curve multiplication, which is
irreversible: _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.
[TIP]
====
Elliptic curve multiplication is a type of function that cryptographers
call a "trap door" function: it is easy to do in one direction
(multiplication) and impossible to do in the reverse direction
(division). Someone with a private key can easily create the public
key and then share it with the world knowing that no one can reverse the
function and calculate the private key from the public key. This
mathematical trick becomes the basis for unforgeable and secure digital
signatures that prove control over bitcoin funds.
====
((("keys and addresses", "overview of", "public key ((("keys and addresses", "overview of", "public key
generation")))((("generator point")))Starting with a private key in the generation")))((("generator point")))Starting with a private key in the