https://en.bitcoin.it/w/api.php?action=feedcontributions&feedformat=atom&user=WjmelementsBitcoin Wiki - User contributions [en]2026-04-19T01:12:57ZUser contributionsMediaWiki 1.43.8https://en.bitcoin.it/w/index.php?title=Secp256k1&diff=65599Secp256k12018-07-19T22:24:43Z<p>Wjmelements: added list of currencies using secp256k1</p>
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<div>[[File:Secp256k1.png|thumb |This is a graph of secp256k1's elliptic curve ''y<sup>2</sup> = x<sup>3</sup> + 7'' over the real numbers. Note that because secp256k1 is actually defined over the field Z<sub>p</sub>, its graph will in reality look like random scattered points, not anything like this.]]<br />
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'''secp256k1''' refers to the parameters of the [[ECDSA]] curve used in Bitcoin, and is defined in ''Standards for Efficient Cryptography (SEC)'' (Certicom Research, http://www.secg.org/sec2-v2.pdf).<br />
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secp256k1 was almost never used before Bitcoin became popular, but it is now gaining in popularity due to its several nice properties. Most commonly-used curves have a random structure, but secp256k1 was constructed in a special non-random way which allows for especially efficient computation. As a result, it is often more than 30% faster than other curves if the implementation is sufficiently optimized. Also, unlike the popular NIST curves, secp256k1's constants were selected in a predictable way, which significantly reduces the possibility that the curve's creator inserted any sort of backdoor into the curve.<br />
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=== Technical details ===<br />
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As excerpted from ''Standards'': <br />
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The elliptic curve domain parameters over F''<sub>p</sub>'' associated with a Koblitz curve secp256k1 are specified<br />
by the sextuple T = (''p,a,b,G,n,h'') where the finite field F''<sub>p</sub>'' is defined by:<br />
* ''p'' = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F<br />
* = 2<sup>256</sup> - 2<sup>32</sup> - 2<sup>9</sup> - 2<sup>8</sup> - 2<sup>7</sup> - 2<sup>6</sup> - 2<sup>4</sup> - 1<br />
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The curve ''E'': ''y<sup>2</sup> = x<sup>3</sup>+ax+b'' over F''<sub>p</sub>'' is defined by:<br />
* ''a'' = 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000<br />
* ''b'' = 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000007<br />
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The base point G in compressed form is:<br />
* ''G'' = 02 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798<br />
and in uncompressed form is:<br />
* ''G'' = 04 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8<br />
Finally the order ''n'' of ''G'' and the cofactor are:<br />
* ''n'' = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141<br />
* ''h'' = 01<br />
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=== Properties ===<br />
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* secp256k1 has characteristic ''p'', it is defined over the prime field ℤ<sub>''p''</sub>. Some other curves in common use have characteristic ''2'', and are defined over a binary Galois field ''GF(2<sup>n</sup>)'', but secp256k1 is not one of them.<br />
* As the ''a'' constant is zero, the ''ax'' term in the curve equation is always zero, hence the curve equation becomes ''y<sup>2</sup> = x<sup>3</sup> + 7''.<br />
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=== Cryptocurrencies ===<br />
This list is incomplete. You can help by expanding it.<br />
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* Bitcoin<br />
* Ethereum<br />
* EOS<br />
* Litecoin<br />
* Dash<br />
* Dogecoin<br />
* Zcash<br />
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== See also ==<br />
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* [https://bitcoin.stackexchange.com/questions/21907/what-does-the-curve-used-in-bitcoin-secp256k1-look-like What does secp256k1 look like] (Bitcoin stack exchange answer by Pieter Wuille)<br />
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[[es:Secp256k1]]<br />
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[[Category:Technical]]</div>Wjmelements