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mirror of https://github.com/bitcoinbook/bitcoinbook synced 2024-11-29 03:18:33 +00:00

math tweak check

This commit is contained in:
Clare Laylock 2023-10-25 14:17:02 -04:00
parent b4576263bb
commit 78ec958c82
5 changed files with 17 additions and 13 deletions

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@ -117,7 +117,7 @@ use to pick that number does not matter as long as it is not predictable
or repeatable. Bitcoin software uses cryptographically secure random or repeatable. Bitcoin software uses cryptographically secure random
number generators to produce 256 bits of entropy. number generators to produce 256 bits of entropy.
More precisely, the private key can be any number between 0 and n - More precisely, the private key can be any number between 0 and _n_ -
1 inclusive, where _n_ is a constant (_n_ = 1.1578 × 10^77^, slightly less 1 inclusive, where _n_ is a constant (_n_ = 1.1578 × 10^77^, slightly less
than 2^256^) defined as the order of the elliptic curve used in Bitcoin than 2^256^) defined as the order of the elliptic curve used in Bitcoin
(see <<elliptic_curve>>). To create such a key, we randomly pick a (see <<elliptic_curve>>). To create such a key, we randomly pick a
@ -343,10 +343,10 @@ find the public key _K_:
[source, python] [source, python]
---- ----
K = 1E99423A4ED27608A15A2616A2B0E9E52CED330AC530EDCC32C8FFC6A526AEDD * G K = 1E99423A4ED27608A15A2616A2B0E9E52CED330AC530EDCC32C8FFC6A526AEDD × G
---- ----
Public key _K_ is defined as a point K = (x, y): Public key _K_ is defined as a point _K_ = (_x_, _y_):
[latexmath] [latexmath]
++++ ++++
@ -1085,9 +1085,9 @@ The "32" stands for the number of characters in the bech32 alphabet
.Bech32 typo detection .Bech32 typo detection
==== ====
Address: Address:
bc1p9nh05ha8wrljf7ru236awpass:[<u>n</u>]4t2x0d5ctkkywm**v**9sclnm4t0av2vgs4k3au7 bc1p9nh05ha8wrljf7ru236awpass:[<u><em>n</em></u>]4t2x0d5ctkkywmpass:[<u><em>v</em></u>]9sclnm4t0av2vgs4k3au7
Detected errors shown in bold. Generated using the Detected errors shown in bold and underlined. Generated using the
https://oreil.ly/paWIx[bech32 address decoder demo]. https://oreil.ly/paWIx[bech32 address decoder demo].
==== ====

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@ -141,7 +141,7 @@ simply adding the same value to both sides of the equation:
[latexmath] [latexmath]
++++ ++++
\begin{equation} \begin{equation}
K + (123 \times G) =\!= (k + 123) \times G K + (123 \times G) =\!\!\!= (k + 123) \times G
\end{equation} \end{equation}
++++ ++++

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@ -845,8 +845,10 @@ Nonlinear::
significantly slows down operations and which, in some cases, has significantly slows down operations and which, in some cases, has
resulted in software accidentally leaking private keys. resulted in software accidentally leaking private keys.
Looking at the math of ECDSA, ==== ECDSA Algorithm
signatures are created by a mathematical function _F_~_sig_~
Let's look at the math of ECDSA.
Signatures are created by a mathematical function _F_~_sig_~
that produces a signature composed of two values. In ECDSA, those two that produces a signature composed of two values. In ECDSA, those two
values are _R_ and _s_. values are _R_ and _s_.

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@ -858,7 +858,7 @@ is:
++++ ++++
<ul class="simplelist"> <ul class="simplelist">
<li>target = coefficient * 2<sup>(8*(exponent 3))</sup></li> <li>target = coefficient × 2<sup>(8 × (exponent 3))</sup></li>
</ul> </ul>
++++ ++++
@ -870,7 +870,7 @@ Using that formula, and the difficulty bits value 0x1903a30c, we get:
</ul> </ul>
++++ ++++
which in decimal is: which is:
++++ ++++
<ul class="simplelist"> <ul class="simplelist">
@ -941,7 +941,7 @@ resulting in a retargeting bias toward higher difficulty by 0.05%.
<<retarget_code>> shows the code used in the Bitcoin Core client. <<retarget_code>> shows the code used in the Bitcoin Core client.
[[retarget_code]] [[retarget_code]]
.Retargeting the proof of work[.plain]#++CalculateNextWorkRequired()++# in pow.cpp .Retargeting the proof of work[.plain]#++CalculateNextWorkRequired()++# in pow.cpp
==== ====
[source,cpp] [source,cpp]
---- ----

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@ -125,9 +125,11 @@ Watch us on YouTube: link:$$https://youtube.com/oreillymedia$$[].
=== Contacting the Authors === Contacting the Authors
[role="align"] ++++
<p class="align">
You can contact Andreas M. Antonopoulos on his personal site: You can contact Andreas M. Antonopoulos on his personal site:
[.keep-together]#link:$$https://antonopoulos.com$$[].# <span class="keep-together"><a href="https://antonopoulos.com">https://antonopoulos.com</a>.</span></p>
++++
Follow Andreas on Facebook: Follow Andreas on Facebook:
link:$$https://facebook.com/AndreasMAntonopoulos$$[]. link:$$https://facebook.com/AndreasMAntonopoulos$$[].