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QC1 and math check
This commit is contained in:
Clare Laylock
parent
48cd7ae0b1
commit
b4576263bb
@ -36,12 +36,12 @@ occurred in July 2010, long after Bitcoin’s initial release:
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- if (pindexNew->nHeight > nBestHeight)
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+ if (pindexNew->bnChainWork > bnBestChainWork)
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----
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* *Terminology change:* General CPUs were used to generate the POW for
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the earliest Bitcoin blocks, but POW generation today is mostly performed
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* *Terminology change:* General CPUs were used to generate the PoW for
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the earliest Bitcoin blocks, but PoW generation today is mostly performed
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by specialist Application Specific Integrated Circuits (ASICs), so
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instead of saying "CPU power" it is perhaps more correct to say
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"computational power" or, simply, "hash rate" for the hashing used
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in generating the POW.
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in generating the PoW.
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____
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"As long as a majority of CPU power is controlled by nodes that are not
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@ -133,7 +133,7 @@ computing, known as the "Byzantine Generals' Problem." Briefly, the
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problem consists of trying to get multiple participants without a leader
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to agree on a course of action by exchanging information over an
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unreliable and potentially compromised network. Satoshi Nakamoto's solution, which uses the concept of
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Proof-of-Work to achieve consensus _without a central trusted
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proof of work to achieve consensus _without a central trusted
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authority_, represents a breakthrough in distributed computing.
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****
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@ -14,8 +14,7 @@ transactions, the network, and mining.
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=== Bitcoin Overview
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In the ((("Bitcoin", "operational overview", id="bitcoin-operational-overview-ch2")))((("blockchain explorers", id="blockchain-explorers")))overview diagram shown in <<bitcoin-overview>>, we see that the
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Bitcoin system consists of users with wallets containing keys,
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The ((("Bitcoin", "operational overview", id="bitcoin-operational-overview-ch2")))((("blockchain explorers", id="blockchain-explorers")))Bitcoin system consists of users with wallets containing keys,
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transactions that are propagated across the network, and miners who
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produce (through competitive computation) the consensus blockchain,
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which is the authoritative journal of all transactions.
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@ -30,10 +29,6 @@ application that operates as a Bitcoin search engine, in that it allows
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you to search for addresses, transactions, and blocks and see the
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relationships and flows between them.
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[[bitcoin-overview]]
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.Bitcoin overview
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image::images/mbc3_0201.png["Bitcoin Overview"]
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Popular blockchain explorers include:
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* https://blockstream.info[Blockstream Explorer]
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@ -63,10 +63,10 @@ from the private key, so storing only the private key is also possible.
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A Bitcoin wallet contains a collection of key
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pairs, each consisting of a private key and a public key. The private
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key (k) is a number, usually derived from a number picked at random.
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key (_k_) is a number, usually derived from a number picked at random.
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From the private key, we
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use elliptic curve multiplication, a one-way cryptographic function, to
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generate a public((("public key cryptography", startref="pub-key")))((("key pairs", startref="key-pair"))) key (K).
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generate a public((("public key cryptography", startref="pub-key")))((("key pairs", startref="key-pair"))) key (_K_).
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.Why Use Asymmetric Cryptography (Public/Private Keys)?
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****
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@ -118,15 +118,15 @@ or repeatable. Bitcoin software uses cryptographically secure random
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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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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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(see <<elliptic_curve>>). To create such a key, we randomly pick a
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256-bit number and check that it is less than +n+. In programming terms,
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256-bit number and check that it is less than _n_. In programming terms,
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this is usually achieved by feeding a larger string of random bits,
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collected from a cryptographically secure source of randomness, into the
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SHA256 hash algorithm, which will conveniently produce a 256-bit value
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that can be interpreted as a number.
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If the result is less than +n+, we have a suitable private key.
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If the result is less than _n_, we have a suitable private key.
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Otherwise, we simply try again with another random number.
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[WARNING]
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@ -140,7 +140,7 @@ choose to make sure it is cryptographically secure. Correct
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implementation of the CSPRNG is critical to the security of the keys.
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====
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The following is a randomly generated private key (k) shown in
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The following is a randomly generated private key (_k_) shown in
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hexadecimal format (256 bits shown as 64 hexadecimal digits, each 4
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bits):
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@ -167,7 +167,7 @@ curve.
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by Bitcoin.
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[[ecc-curve]]
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[role="width-80"]
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[role="width-50"]
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.An elliptic curve
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image::images/mbc3_0402.png["ecc-curve"]
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@ -341,12 +341,10 @@ Implementing the elliptic curve multiplication, we take the private key
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_k_ generated previously and multiply it with the generator point _G_ to
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find the public key _K_:
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[latexmath]
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++++
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\begin{equation}
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{K = 1E99423A4ED27608A15A2616A2B0E9E52CED330AC530EDCC32C8FFC6A526AEDD \times G}
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\end{equation}
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++++
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[source, python]
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----
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K = 1E99423A4ED27608A15A2616A2B0E9E52CED330AC530EDCC32C8FFC6A526AEDD * G
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----
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Public key _K_ is defined as a point K = (x, y):
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@ -1087,7 +1085,7 @@ The "32" stands for the number of characters in the bech32 alphabet
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.Bech32 typo detection
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====
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Address:
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bc1p9nh05ha8wrljf7ru236aw**n**4t2x0d5ctkkywm**v**9sclnm4t0av2vgs4k3au7
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bc1p9nh05ha8wrljf7ru236awpass:[<u>n</u>]4t2x0d5ctkkywm**v**9sclnm4t0av2vgs4k3au7
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Detected errors shown in bold. Generated using the
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https://oreil.ly/paWIx[bech32 address decoder demo].
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@ -1633,7 +1631,7 @@ Once a vanity address matching the desired pattern is found, the private
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key from which it was derived can be used by the owner to spend bitcoins
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in exactly the same way as any other address. Vanity addresses are no
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less or more secure than any other address. They depend on the same
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elliptic curve cryptography (ECC) and SHA as any other address. You can
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elliptic curve cryptography (ECC) and secure hash algorithm (SHA) as any other address. You can
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no more easily find the private key of an address starting with a vanity
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pattern than you can any other address.
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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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++++
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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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++++
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@ -149,13 +149,13 @@ K + (123 \times G) == (k + 123) \times G
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[TIP]
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====
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In equations throughout this book, we use a single equals sign for
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operations such as K = k × G where the value of a variable is
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operations such as _K_ = _k_ × _G_ where the value of a variable is
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calculated. We use a double equals sign to show both sides of an
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equation are equivalent, or that an operation should return false (not
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true) if the two sides aren't equivalent.
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====
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An interesting consequence of this is that adding `123` to the public
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An interesting consequence of this is that adding 123 to the public
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key can be done using entirely public information. For example, Alice
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generates public key _K_ and gives it to Bob. Bob doesn't know the
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private key, but he does know the global constant _G_, so he can add any
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@ -1053,7 +1053,7 @@ hash is used to create a _master private key_ (m) and a _master chain
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code_ (c).
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The master private key (m) then generates a corresponding master public
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key (M) using the normal elliptic curve multiplication process __m × G__
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key (M) using the normal elliptic curve multiplication process m × _G_
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that we saw in <<public_key_derivation>>.
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The chain code (c) is used to introduce entropy in the function that
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@ -1318,11 +1318,6 @@ To export the xpub from his Trezor hardware signing device, Gabriel uses
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the web-based Trezor wallet application. The Trezor device must be plugged in
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for the public keys to be exported. Note that most hardware signing devices will
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never export private keys--those always remain on the device.
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<<export_xpub>> shows the web interface Gabriel uses to export the xpub.
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[[export_xpub]]
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.Exporting an xpub from a Trezor hardware signing device
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image::images/mbc3_0509.png["Exporting the xpub from the Trezor"]
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Gabriel copies the xpub to his web store's Bitcoin payment processing
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software, such as the widely used open source BTCPay Server.
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@ -228,22 +228,22 @@ unsigned integers:
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</thead>
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<tbody>
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<tr>
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<td><p>>= <code>0</code> && <= <code>252</code> (<code>0xfc</code>)</p></td>
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<td><p>≥ <code>0</code> && ≤ <code>252</code> (<code>0xfc</code>)</p></td>
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<td><p><code>1</code></p></td>
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<td><p><code>uint8_t</code></p></td>
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</tr>
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<tr>
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<td><p>>= <code>253</code> && <= <code>0xffff</code></p></td>
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<td><p>≥ <code>253</code> && ≤ <code>0xffff</code></p></td>
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<td><p>3</p></td>
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<td><p><code>0xfd</code> followed by the number as <code>uint16_t</code></p></td>
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</tr>
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<tr>
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<td><p>>= <code>0x10000</code> && <= <code>0xffffffff</code></p></td>
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<td><p>≥ <code>0x10000</code> && ≤ <code>0xffffffff</code></p></td>
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<td><p><code>5</code></p></td>
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<td><p><code>0xfe</code> followed by the number as <code>uint32_t</code></p></td>
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</tr>
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<tr>
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<td><p>>= <code>0x100000000</code> && <= <code>0xffffffffffffffff</code></p></td>
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<td><p>≥ <code>0x100000000</code> && ≤ <code>0xffffffffffffffff</code></p></td>
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<td><p><code>9</code></p></td>
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<td><p><code>0xff</code> followed by the number as <code>uint64_t</code></p></td>
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</tr>
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@ -276,7 +276,7 @@ control over bitcoins is assigned in transaction outputs, Alice _points_
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to the previous _output_ using an _outpoint_ field. Each input must
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contain a single outpoint.
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The outpoint contains a 32-byte transaction identifier (_txid_) for the
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The outpoint contains a 32-byte txid for the
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transaction where Alice received the bitcoins she now wants to spend.
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This txid is in Bitcoin's internal byte order for hashes; see
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<<internal_and_display_order>>.
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@ -325,7 +325,7 @@ Different approaches to tracking previous outputs have been tried by
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different full node implementations at various times. Bitcoin Core
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currently uses the solution believed to be most effective at retaining
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all necessary information while minimizing disk space: it keeps a
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database that stores every unspent transaction output (UTXO) and
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database that stores every UTXO and
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essential metadata about it (like its confirmation block height). Each
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time a new block of transactions arrives, all of the outputs they spend
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are removed from the UTXO database and all of the outputs they create
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@ -986,23 +986,23 @@ be received to witness programs and spent with the witness structure. The terms
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<tr>
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<th/>
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<th><p>Authorization</p></th>
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<th><p>Authentication</p></th>
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<th class="right"><p>Authentication</p></th>
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</tr></thead>
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<tbody>
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<tr>
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<td class="fakeheader"><p><strong>Whitepaper</strong></p></td>
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<td><p>Public key</p></td>
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<td><p>Signature</p></td>
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<td class="right"><p>Signature</p></td>
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</tr>
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<tr>
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<td class="fakeheader"><p><strong>Original (Legacy)</strong></p></td>
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<td><p>Output script</p></td>
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<td><p>Input script</p></td>
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<td class="right"><p>Input script</p></td>
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</tr>
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<tr>
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<td class="fakeheader"><p><strong>Segwit</strong></p></td>
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<td><p>Witness program</p></td>
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<td><p>Witness structure</p></td>
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<td class="right"><p>Witness structure</p></td>
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</tr>
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</tbody>
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</table>
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@ -1383,8 +1383,7 @@ satisfy that redeem script, all inside the transaction input:
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Now, let's look at how this entire example would be upgraded to segwit v0.
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If Mohammed's customers were using a segwit-compatible wallet, they
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would make a payment, creating a pay to witness script hash (P2WSH)
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output that would look like this:
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would make a payment, creating a P2WSH output that would look like this:
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.Example P2WSH output script
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----
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@ -409,7 +409,7 @@ brute force is easy; the numbers used in Bitcoin are much larger.
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Let's discuss some of the features of the interactive schnorr
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identity protocol that make it secure:
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The nonce ([.plain]#k#)::
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The nonce (k)::
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In step 1, ((("digital signatures", "schnorr signature algorithm", "security features")))((("schnorr signature algorithm", "security features")))Alice chooses a number that Bob doesn't
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know and can't guess and gives him the scaled form of that number,
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_kG_. At that point, Bob also already has her public key (_xG_),
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@ -424,7 +424,7 @@ In step 1, ((("digital signatures", "schnorr signature algorithm", "security fea
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be able to leverage that into figuring out Alice's private key. See
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<<nonce_warning>> for more details.
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The challenge scalar ([.plain]#e#)::
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The challenge scalar (e)::
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Bob waits to receive Alice's public nonce
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and then proceeds in step 2 to give her a number (the challenge
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scalar) that Alice didn't previously know and couldn't have guessed.
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@ -674,8 +674,7 @@ MuSig2::
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This only ((("MuSig2 protocol")))requires two rounds of communication and can sometimes allow
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one of the rounds to be combined with key exchange. This can
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significantly speed up signing for certain protocols, such as how
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scriptless multisignatures are planned to be used in the Lightning
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Network. MuSig2 is specified in BIP327 (the only scriptless
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scriptless multisignatures are planned to be used in the LN. MuSig2 is specified in BIP327 (the only scriptless
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multisignature protocol that has a BIP as of this writing).
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MuSig-DN::
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@ -903,7 +902,7 @@ the following DER-encoded signature:
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b9f039ff08df09cbe9f6addac960298cad530a863ea8f53982c09db8f6e381301
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----
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That signature is a serialized byte stream of the +R+ and _s_ values
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That signature is a serialized byte stream of the _R_ and _s_ values
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produced by the signer to prove control of the private key authorized
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to spend an output. The serialization format consists of nine elements
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as follows:
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@ -590,7 +590,7 @@ miners:
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[latexmath]
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++++
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\begin{equation}
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{Fees = Sum(Inputs) – Sum(Outputs)}
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{Fees = Sum(Inputs) - Sum(Outputs)}
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\end{equation}
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++++
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@ -385,7 +385,7 @@ transaction fees:
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[latexmath]
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++++
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\begin{equation}
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Total Fees = Sum(Inputs) - Sum(Outputs)
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Total\:Fees = Sum(Inputs) - Sum(Outputs)
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\end{equation}
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++++
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@ -858,7 +858,7 @@ is:
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++++
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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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++++
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@ -866,9 +866,7 @@ Using that formula, and the difficulty bits value 0x1903a30c, we get:
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++++
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<ul class="simplelist">
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<li>target = 0x03a30c * 2<sup>0x08*(0x19-0x03)</sup></li>
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<li>=> target = 0x03a30c * 2<sup>(0x08*0x16)</sup></li>
|
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<li>=> target = 0x03a30c * 2<sup>0xB0</sup></li>
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<li>target = 0x03a30c × 2<sup>0x08 × (0x19 - 0x03)</sup></li>
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</ul>
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++++
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@ -876,16 +874,15 @@ which in decimal is:
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++++
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<ul class="simplelist">
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<li>=> target = 238,348 * 2<sup>176</sup></li>
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<li>=> target = <br/>22,829,202,948,393,929,850,749,706,076,701,368,331,072,452,018,388,575,715,328</li>
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<li>22,829,202,948,393,929,850,749,706,076,701,368,331,072,452,018,388,575,715,328</li>
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</ul>
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++++
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switching back to hexadecimal:
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Or, in hexadecimal:
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++++
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<ul class="simplelist">
|
||||
<li>=> target = <br/>0x0000000000000003A30C00000000000000000000000000000000000000000000</li>
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<li>0x0000000000000003A30C00000000000000000000000000000000000000000000</li>
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</ul>
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++++
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@ -944,7 +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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|
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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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[source,cpp]
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----
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@ -339,9 +339,8 @@ Translated forwarding::
|
||||
support forwarding bitcoin payments.
|
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|
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Native forwarding is conceptually simpler but essentially requires a
|
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separate Lightning Network for every asset. Translated forwarding
|
||||
allows building on the economies of scale of the Bitcoin Lightning
|
||||
Network, but it may be vulnerable to a problem called((("free American call option"))) the _free American
|
||||
separate LN for every asset. Translated forwarding
|
||||
allows building on the economies of scale of the Bitcoin LN, but it may be vulnerable to a problem called((("free American call option"))) the _free American
|
||||
call option_, where a receiver may selectively accept or reject certain
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||||
payments depending on recent changes to the exchange rate in order to
|
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siphon money from the hop next to them. Although there's no known
|
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@ -712,8 +711,7 @@ Even though a transaction cannot be canceled, it can be constructed in
|
||||
such a way as to make it undesirable to use. The way we do that is by
|
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giving each party a _revocation key_ that can be used to punish the
|
||||
other party if they try to cheat. This mechanism for revoking prior
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||||
commitment transactions was first proposed as part of the Lightning
|
||||
Network.
|
||||
commitment transactions was first proposed as part of the LN.
|
||||
|
||||
To explain revocation keys, we will construct a more complex payment
|
||||
channel between two exchanges run by Hitesh and Irene. Hitesh and Irene
|
||||
@ -909,8 +907,7 @@ Asymmetric revocable commitments with relative time locks (+CSV+) are a
|
||||
much better way to implement payment channels and a very significant
|
||||
innovation in this technology. With this construct, the channel can
|
||||
remain open indefinitely and can have billions of intermediate
|
||||
commitment transactions. In implementations of Lightning
|
||||
Network, the commitment state is identified by a 48-bit index, allowing
|
||||
commitment transactions. In implementations of LN, the commitment state is identified by a 48-bit index, allowing
|
||||
more than 281 trillion (2.8 × 10^14^) state transitions in ((("payment channels", "asymmetric revocable commitments", startref="payment-channel-revoke")))((("asymmetric revocable commitments", startref="asymmetric-revoke-commit")))((("commitment transactions", "asymmetric revocable commitments", startref="commit-revoke")))((("revocable commitments", startref="revoke-commit")))any single
|
||||
channel.
|
||||
|
||||
@ -996,12 +993,11 @@ to Carol, Carol to Diana, and Diana to Eric. For simplicity let's assume
|
||||
each channel is funded with 2 bitcoins by each participant, for a total
|
||||
capacity of 4 bitcoins in each channel.
|
||||
|
||||
<<lightning_network_fig>> shows five participants in a Lightning
|
||||
Network, connected by bidirectional payment channels that can be linked
|
||||
<<lightning_network_fig>> shows five participants in an LN, connected by bidirectional payment channels that can be linked
|
||||
to make a payment from Alice to Eric (see <<lightning_network>>).
|
||||
|
||||
[[lightning_network_fig]]
|
||||
.A series of bidirectional payment channels linked to form a Lightning Network that can route a payment from Alice to Eric
|
||||
.A series of bidirectional payment channels linked to form an LN that can route a payment from Alice to Eric
|
||||
image::images/mbc3_1406.png["A series of bi-directional payment channels linked to form a Lightning Network"]
|
||||
|
||||
Alice wants to pay Eric 1 bitcoin. However, Alice is not connected to
|
||||
@ -1015,10 +1011,10 @@ payment from Alice to Eric, through a series of HTLC commitments on the
|
||||
payment channels connecting the participants.
|
||||
|
||||
[[ln_payment_process]]
|
||||
.Step-by-step payment routing through a Lightning Network
|
||||
.Step-by-step payment routing through an LN
|
||||
image::images/mbc3_1407.png["Step-by-step payment routing through a Lightning Network"]
|
||||
|
||||
Alice is running a Lightning Network (LN) node that is keeping track of
|
||||
Alice is running an LN node that is keeping track of
|
||||
her payment channel to Bob and has the ability to discover routes
|
||||
between payment channels. Alice's LN node also has the ability to
|
||||
connect over the internet to Eric's LN node. Eric's LN node creates a
|
||||
@ -1114,7 +1110,7 @@ with sufficient capacity. Nodes advertise routing information, including
|
||||
what channels they have open, how much capacity each channel has, and
|
||||
what fees they charge to route payments. The routing information can be
|
||||
shared in a variety of ways, and different pathfinding protocols have
|
||||
emerged as Lightning Network technology has advanced.
|
||||
emerged as LN technology has advanced.
|
||||
Current implementations of
|
||||
route discovery use a P2P model where nodes propagate channel
|
||||
announcements to their peers in a "flooding" model, similar to how
|
||||
@ -1132,15 +1128,15 @@ Carol's perspective, this looks like a payment from Bob to Diana. Carol
|
||||
does not know that Bob is actually relaying a payment from Alice. She
|
||||
also doesn't know that Diana will be relaying a payment to Eric.
|
||||
|
||||
This is a critical feature of the Lightning Network because it ensures
|
||||
This is a critical feature of the LN because it ensures
|
||||
privacy of payments and makes it difficult to apply surveillance,
|
||||
censorship, or blacklists. But how does Alice establish this payment
|
||||
path without revealing anything to the intermediary nodes?
|
||||
|
||||
The Lightning Network implements an onion-routed protocol based on a
|
||||
The LN implements an onion-routed protocol based on a
|
||||
scheme called https://oreil.ly/fuCiK[Sphinx]. This routing protocol
|
||||
ensures that a payment sender can construct and communicate a path
|
||||
through the Lightning Network such that:
|
||||
through the LN such that:
|
||||
|
||||
- Intermediate nodes can verify and decrypt their portion of route
|
||||
information and find the next hop.
|
||||
@ -1192,40 +1188,39 @@ hops to go.
|
||||
|
||||
==== Lightning Network Benefits
|
||||
|
||||
A((("payment channels", "Lightning Network", "benefits of", id="payment-channel-ln-benefits")))((("Lightning Network", "benefits of", id="lightning-benefits"))) Lightning Network is a
|
||||
An((("payment channels", "Lightning Network", "benefits of", id="payment-channel-ln-benefits")))((("Lightning Network", "benefits of", id="lightning-benefits"))) LN is a
|
||||
second-layer routing technology. It can be applied to any blockchain
|
||||
that supports some basic capabilities, such as multisignature
|
||||
transactions, timelocks, and basic smart contracts.
|
||||
|
||||
Lightning Network is layered on top of the Bitcoin network, giving
|
||||
LN is layered on top of the Bitcoin network, giving
|
||||
Bitcoin a significant increase in capacity, privacy,
|
||||
granularity, and speed, without sacrificing the principles of trustless
|
||||
operation without intermediaries:
|
||||
|
||||
Privacy:: Lightning Network payments are much more private than payments
|
||||
Privacy:: LN payments are much more private than payments
|
||||
on the Bitcoin blockchain, as they are not public. While participants in
|
||||
a route can see payments propagated across their channels, they do not
|
||||
know the sender or recipient.
|
||||
|
||||
Fungibility:: A Lightning Network makes it much more difficult to apply
|
||||
Fungibility:: An LN makes it much more difficult to apply
|
||||
surveillance and blacklists on Bitcoin, increasing the fungibility of
|
||||
the currency.
|
||||
|
||||
Speed:: Bitcoin transactions using Lightning Network are settled in
|
||||
Speed:: Bitcoin transactions using LN are settled in
|
||||
milliseconds, rather than minutes or hours, as HTLCs are cleared without
|
||||
committing transactions to a block.
|
||||
|
||||
Granularity:: A Lightning Network can enable payments at least as small
|
||||
Granularity:: An LN can enable payments at least as small
|
||||
as the Bitcoin "dust" limit, perhaps even smaller.
|
||||
|
||||
Capacity:: A Lightning Network increases the capacity of the Bitcoin
|
||||
Capacity:: An LN increases the capacity of the Bitcoin
|
||||
system by several orders of magnitude. The upper bound
|
||||
to the number of payments per second that can be routed over a Lightning
|
||||
Network depends only on the capacity and speed of each node.
|
||||
|
||||
Trustless Operation:: A Lightning Network uses Bitcoin transactions
|
||||
between nodes that operate as peers without trusting each other. Thus, a
|
||||
Lightning Network preserves the principles of the Bitcoin system, while
|
||||
Trustless Operation:: An LN uses Bitcoin transactions
|
||||
between nodes that operate as peers without trusting each other. Thus, an LN preserves the principles of the Bitcoin system, while
|
||||
expanding its operating parameters ((("Bitcoin", "as application platform", "routed payment channels (Lightning Network)", secondary-sortas="application platform", startref="bitcoin-app-platform-ln")))((("application platform, Bitcoin as", "routed payment channels (Lightning Network)", startref="app-platform-ln")))((("payment channels", "Lightning Network", startref="payment-channel-ln")))((("Lightning Network", startref="lightning")))((("payment channels", "Lightning Network", "benefits of", startref="payment-channel-ln-benefits")))((("Lightning Network", "benefits of", startref="lightning-benefits")))significantly.
|
||||
|
||||
We have examined just a few of the emerging applications that can be
|
||||
|
||||
@ -125,7 +125,7 @@ Watch us on YouTube: link:$$https://youtube.com/oreillymedia$$[].
|
||||
|
||||
=== Contacting the Authors
|
||||
|
||||
[.align]
|
||||
[role="align"]
|
||||
You can contact Andreas M. Antonopoulos on his personal site:
|
||||
[.keep-together]#link:$$https://antonopoulos.com$$[].#
|
||||
|
||||
|
||||
@ -5,3 +5,6 @@ td.fakeheader {
|
||||
background-color: Black !important;
|
||||
border: 0pt solid cmyk(0%,0%,0%,100%);
|
||||
}
|
||||
|
||||
/*--Table lines--*/
|
||||
table td.right, th.right { border-right: 0.25pt solid cmyk(0%,0%,0%,100%); }
|
||||
|
||||
@ -18,6 +18,10 @@ pre[data-type="programlisting"] {
|
||||
font-style: normal;
|
||||
}
|
||||
|
||||
/*--Table lines--*/
|
||||
table td.right, th.right { border-right: 0.25pt solid cmyk(0%,0%,0%,100%); }
|
||||
|
||||
|
||||
td.fakeheader {
|
||||
font-family: "MyriadPro-SemiboldCond" !important;
|
||||
font-weight: 600 !important;
|
||||
|
||||
Loading…
Reference in New Issue
Block a user