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Describe Uncompressed And Compressed Public Keys
A quick little subsection the two different public key formats possible in Bitcoin.
This commit is contained in:
David A. Harding
parent
87e31affba
commit
968d9c1f64
5 changed files with 491 additions and 6 deletions
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@ -266,15 +266,19 @@ In order to make copying of private keys less prone to error, [Wallet Import For
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2. Add a 0x80 byte in front of it for mainnet addresses or 0xef for testnet addresses.
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3. Perform a SHA-256 hash on the extended key.<!--noref-->
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3. Append a 0x01 byte after it if it should be used with compressed
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public keys (described in a later subsection). Nothing is appended if
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it is used with uncompressed public keys.
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4. Perform a SHA-256 hash on result of SHA-256 hash.
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4. Perform a SHA-256 hash on the extended key.<!--noref-->
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5. Take the first four bytes of the second SHA-256 hash; this is the checksum.
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5. Perform a SHA-256 hash on result of SHA-256 hash.
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6. Add the four checksum bytes from point 5 at the end of the extended key<!--noref--> from point 2.
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6. Take the first four bytes of the second SHA-256 hash; this is the checksum.
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7. Convert the result from a byte string into a Base58 string using Base58Check encoding.
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7. Add the four checksum bytes from point 5 at the end of the extended key<!--noref--> from point 2.
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8. Convert the result from a byte string into a Base58 string using Base58Check encoding.
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The process is easily reversible, using the Base58 decoding function, and removing the padding.
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@ -302,6 +306,64 @@ address utility].
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{% endautocrossref %}
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#### Public Key Formats
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{% autocrossref %}
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Bitcoin ECDSA public keys represent a point on a particular Elliptic
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Curve (EC) defined in secp256k1. In their traditional "uncompressed" form,
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public keys contain an identification byte, a 32-byte X coordinate, and
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a 32-byte Y coordinate. The extremely simplified illustration below
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shows such a point on the elliptic curve used by Bitcoin,
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x<sup>2</sup> = y<sup>3</sup> + 7, over a field of
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contiguous numbers.
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(Secp256k1 actually modulos coordinates by a large prime, which produces a
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field of non-contiguous integers and a significantly less clear plot,
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although the principles are the same.)
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An almost 50% reduction in public key size can be realized without
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changing any fundamentals by dropping the Y coordinate. This is possible
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because only two points along the curve share any particular X
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coordinate, so the 32-byte Y coordinate can be replaced with a single
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bit indicating whether the point is on what appears in the illustration
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as the "top" side or the "bottom" side.
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No data is lost by creating these compressed public keys---only a small
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amount of CPU is necessary to reconstruct the Y coordinate and access
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the uncompressed public key. Both uncompressed and compressed public
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keys are supported by default in OpenSSL, the library Bitcoin Core and
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many other Bitcoin programs use.
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Because they're easy to use, and because they reduce almost by half
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the block chain space used to store public keys for every spent output,
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compressed public keys are the default in Bitcoin Core and are the
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recommended default for all Bitcoin software.
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However, Bitcoin Core prior to 0.6 used uncompressed keys. This creates
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a few complications, as the hashed form of an uncompressed key is
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different than the hashed form of a compressed key, so the same key
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works with two different P2PKH addresses. This also means that the key
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must be submitted in the correct format in the input scriptSig so it
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matches the hash in the previous output script.
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For this reason, Bitcoin Core uses several different identifier bytes to
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help programs identify how keys should be used:
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* Private keys meant to be used with compressed public keys have 0x01
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appended to them before being Base-58 encoded. (See the private key
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encoding section above.)
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* Uncompressed public keys start with 0x04; compressed public keys begin
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with 0x03 or 0x02 depending on what side of the curve they're on.
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{% endautocrossref %}
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#### Hierarchical Deterministic Key Creation
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<!--
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@ -1,4 +1,6 @@
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The images are generated using dot from the graphviz package. For
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## Files Ending In .dot, .neato, .circo
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Many of the images are generated using dot from the graphviz package. For
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assistance with these files, feel free to contact dave@dtrt.org.
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The following examples generate a .png or .svg file from a .dot file:
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@ -34,3 +36,23 @@ near the top of the file:
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Also, splines=ortho should not be used in new or updated files until
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Graphviz fixes its post-2.26.3 ortho code.
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## Files Ending In .gnuplot
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Some images are generated using gnuplot. As of this writing, you can
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generate both the SVG and PNG output for any of these files by running
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the following command:
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gnuplot <filename.gnuplot>
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After generating, you should use optipng to reduce the PNG filesize.
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(Reductions here tend to be small, ~10%):
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optipng -o7 <filename.png>
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If your plot has a high sample rate, you can reduce the SVG filesize by
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opening it in Inkscape, ungrouping the graphic, selecting plot lines,
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and using Path->Simplify. Then select all, regroup, and save. Be sure
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to double-check your work---if you simplify text, it becomes unreadable.
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(Reductions here tend to be large, I've seen ~80%.)
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15
img/dev/en-ecdsa-compressed-public-key.gnuplot
Normal file
15
img/dev/en-ecdsa-compressed-public-key.gnuplot
Normal file
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@ -0,0 +1,15 @@
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set samples 1000000
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set yrange [-4:4]
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set terminal svg size 600,200 font "Sans,12"
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set output "en-ecdsa-compressed-public-key.svg"
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plot [-3:8] sqrt(x**3+7) \
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,-sqrt(x**3+7) \
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,"< echo 1 2.83" u 1:2 title "x,y=1.00,2.83" with points
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## Remember to run optipng -o7 on output before commiting
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set terminal png size 600,200 font "Sans,12"
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set output "en-ecdsa-compressed-public-key.png"
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replot
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BIN
img/dev/en-ecdsa-compressed-public-key.png
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BIN
img/dev/en-ecdsa-compressed-public-key.png
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Binary file not shown.
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After Width: | Height: | Size: 2.9 KiB |
386
img/dev/en-ecdsa-compressed-public-key.svg
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386
img/dev/en-ecdsa-compressed-public-key.svg
Normal file
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@ -0,0 +1,386 @@
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<dc:format>image/svg+xml</dc:format>
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<dc:type
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rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
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</cc:Work>
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xlink:href="#gpPt11" />
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</defs>
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</defs>
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<sodipodi:namedview
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pagecolor="#ffffff"
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bordercolor="#666666"
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borderopacity="1"
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objecttolerance="10"
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inkscape:window-width="1278"
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inkscape:zoom="1.7017703"
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inkscape:window-y="0"
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inkscape:window-maximized="0"
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inkscape:current-layer="svg2" />
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||||
<title
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id="title4">Gnuplot</title>
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||||
<desc
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id="desc6">Produced by GNUPLOT 4.6 patchlevel 0 </desc>
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After Width: | Height: | Size: 13 KiB |
Loading…
Add table
Add a link
Reference in a new issue