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math tweak check
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@ -117,7 +117,7 @@ use to pick that number does not matter as long as it is not predictable
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or repeatable. Bitcoin software uses cryptographically secure random
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or repeatable. Bitcoin software uses cryptographically secure random
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number generators to produce 256 bits of entropy.
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number generators to produce 256 bits of entropy.
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More precisely, the private key can be any number between 0 and n -
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More precisely, the private key can be any number between 0 and _n_ -
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1 inclusive, where _n_ is a constant (_n_ = 1.1578 × 10^77^, slightly less
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1 inclusive, where _n_ is a constant (_n_ = 1.1578 × 10^77^, slightly less
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than 2^256^) defined as the order of the elliptic curve used in Bitcoin
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than 2^256^) defined as the order of the elliptic curve used in Bitcoin
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(see <<elliptic_curve>>). To create such a key, we randomly pick a
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(see <<elliptic_curve>>). To create such a key, we randomly pick a
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@ -343,10 +343,10 @@ find the public key _K_:
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[source, python]
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[source, python]
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----
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----
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K = 1E99423A4ED27608A15A2616A2B0E9E52CED330AC530EDCC32C8FFC6A526AEDD * G
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K = 1E99423A4ED27608A15A2616A2B0E9E52CED330AC530EDCC32C8FFC6A526AEDD × G
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----
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----
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Public key _K_ is defined as a point K = (x, y):
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Public key _K_ is defined as a point _K_ = (_x_, _y_):
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[latexmath]
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[latexmath]
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++++
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++++
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@ -1085,9 +1085,9 @@ The "32" stands for the number of characters in the bech32 alphabet
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.Bech32 typo detection
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.Bech32 typo detection
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====
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====
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Address:
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Address:
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bc1p9nh05ha8wrljf7ru236awpass:[<u>n</u>]4t2x0d5ctkkywm**v**9sclnm4t0av2vgs4k3au7
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bc1p9nh05ha8wrljf7ru236awpass:[<u><em>n</em></u>]4t2x0d5ctkkywmpass:[<u><em>v</em></u>]9sclnm4t0av2vgs4k3au7
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Detected errors shown in bold. Generated using the
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Detected errors shown in bold and underlined. Generated using the
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https://oreil.ly/paWIx[bech32 address decoder demo].
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https://oreil.ly/paWIx[bech32 address decoder demo].
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====
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====
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@ -141,7 +141,7 @@ simply adding the same value to both sides of the equation:
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[latexmath]
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[latexmath]
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++++
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++++
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\begin{equation}
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\begin{equation}
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K + (123 \times G) =\!= (k + 123) \times G
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K + (123 \times G) =\!\!\!= (k + 123) \times G
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\end{equation}
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\end{equation}
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++++
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++++
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@ -845,8 +845,10 @@ Nonlinear::
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significantly slows down operations and which, in some cases, has
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significantly slows down operations and which, in some cases, has
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resulted in software accidentally leaking private keys.
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resulted in software accidentally leaking private keys.
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Looking at the math of ECDSA,
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==== ECDSA Algorithm
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signatures are created by a mathematical function _F_~_sig_~
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Let's look at the math of ECDSA.
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Signatures are created by a mathematical function _F_~_sig_~
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that produces a signature composed of two values. In ECDSA, those two
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that produces a signature composed of two values. In ECDSA, those two
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values are _R_ and _s_.
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values are _R_ and _s_.
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@ -858,7 +858,7 @@ is:
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++++
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++++
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<ul class="simplelist">
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<ul class="simplelist">
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<li>target = coefficient * 2<sup>(8*(exponent – 3))</sup></li>
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<li>target = coefficient × 2<sup>(8 × (exponent – 3))</sup></li>
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</ul>
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</ul>
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++++
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++++
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@ -870,7 +870,7 @@ Using that formula, and the difficulty bits value 0x1903a30c, we get:
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</ul>
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</ul>
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++++
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++++
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which in decimal is:
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which is:
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++++
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++++
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<ul class="simplelist">
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<ul class="simplelist">
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@ -941,7 +941,7 @@ resulting in a retargeting bias toward higher difficulty by 0.05%.
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<<retarget_code>> shows the code used in the Bitcoin Core client.
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<<retarget_code>> shows the code used in the Bitcoin Core client.
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[[retarget_code]]
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[[retarget_code]]
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.Retargeting the proof of work—[.plain]#++CalculateNextWorkRequired()++# in pow.cpp
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.Retargeting the proof of work[.plain]#—++CalculateNextWorkRequired()++# in pow.cpp
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====
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====
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[source,cpp]
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[source,cpp]
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----
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----
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@ -125,9 +125,11 @@ Watch us on YouTube: link:$$https://youtube.com/oreillymedia$$[].
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=== Contacting the Authors
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=== Contacting the Authors
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[role="align"]
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++++
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<p class="align">
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You can contact Andreas M. Antonopoulos on his personal site:
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You can contact Andreas M. Antonopoulos on his personal site:
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[.keep-together]#link:$$https://antonopoulos.com$$[].#
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<span class="keep-together"><a href="https://antonopoulos.com">https://antonopoulos.com</a>.</span></p>
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++++
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Follow Andreas on Facebook:
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Follow Andreas on Facebook:
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link:$$https://facebook.com/AndreasMAntonopoulos$$[].
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link:$$https://facebook.com/AndreasMAntonopoulos$$[].
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