Secp256k1 - Revision history

NotATether: add graph of sampled points

2025-12-14T15:17:22Z

add graph of sampled points

← Older revision		Revision as of 15:17, 14 December 2025
Line 6:		Line 6:

	=== Technical details ===		=== Technical details ===

			[[File:Secp256k1-many.png\|thumb \|A sample of many points from a graph of a smaller elliptic curve similar to secp256k1. Image by [https://bitcoin.stackexchange.com/a/21911 Pieter Wuille].]]

	As excerpted from ''Standards'':		As excerpted from ''Standards'':

Luke-jr: Delete scamcoin promotion section /* Cryptocurrencies */

2019-04-24T00:14:19Z

Delete scamcoin promotion section Cryptocurrencies

@@ Line 30: / Line 30: @@
 * 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.
 * 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''.
 == See also ==

Theymos: Clarify that secp256k1 is independent of ECDSA

2018-07-19T23:33:32Z

Clarify that secp256k1 is independent of ECDSA

← Older revision		Revision as of 23:33, 19 July 2018
Line 1:		Line 1:
	[[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.]]		[[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.]]

	'''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).		'''secp256k1''' refers to the parameters of the elliptic curve used in Bitcoin's public-key cryptography, and is defined in ''Standards for Efficient Cryptography (SEC)'' (Certicom Research, http://www.secg.org/sec2-v2.pdf). Currently Bitcoin uses secp256k1 with the [[ECDSA]] algorithm, though the same curve with the same public/private keys can be used in some other algorithms such as [[Schnorr]].

	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.		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.

Wjmelements: added list of currencies using secp256k1

2018-07-19T22:24:43Z

added list of currencies using secp256k1

@@ Line 30: / Line 30: @@
 * 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.
 * 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''.
 == See also ==

Belcher: added to category technical

2017-12-23T21:07:46Z

added to category technical

← Older revision		Revision as of 21:07, 23 December 2017
Line 36:		Line 36:

	[[es:Secp256k1]]		[[es:Secp256k1]]

			[[Category:Technical]]

Wumpus: add some basic information on our favourite elliptic curve

2016-08-04T08:48:11Z

add some basic information on our favourite elliptic curve

← Older revision		Revision as of 08:48, 4 August 2016
Line 25:		Line 25:
	* ''n'' = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141		* ''n'' = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141
	* ''h'' = 01		* ''h'' = 01

			=== Properties ===

			* 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.
			* 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''.

			== See also ==

			* [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)

	[[es:Secp256k1]]		[[es:Secp256k1]]

Theymos: Update SEC 2 link to the official site, which is back up again

2015-03-30T02:43:49Z

Update SEC 2 link to the official site, which is back up again

← Older revision		Revision as of 02:43, 30 March 2015
Line 1:		Line 1:
	[[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.]]		[[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.]]

	'''secp256k1''' refers to the parameters of the [[ECDSA]] curve used in Bitcoin, and is defined in ''Standards for Efficient Cryptography (SEC)'' (Certicom Research, http://~~perso~~.~~univ-rennes1~~.fr/~~sylvain.duquesne/master/standards/sec2_final~~.pdf).		'''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).

	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.		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.

Timmattison: Fixed broken link to SEC PDF. I'm not happy about where it is coming from now but at least it is a link that works.

2014-09-26T13:26:55Z

Fixed broken link to SEC PDF. I'm not happy about where it is coming from now but at least it is a link that works.

← Older revision		Revision as of 13:26, 26 September 2014
Line 1:		Line 1:
	[[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.]]		[[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.]]

	'''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~~/~~collateral~~/sec2_final.pdf).		'''secp256k1''' refers to the parameters of the [[ECDSA]] curve used in Bitcoin, and is defined in ''Standards for Efficient Cryptography (SEC)'' (Certicom Research, http://perso.univ-rennes1.fr/sylvain.duquesne/master/standards/sec2_final.pdf).

	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.		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.

Theymos: Added an image of the curve

2014-06-30T18:09:12Z

Added an image of the curve

← Older revision		Revision as of 18:09, 30 June 2014
Line 1:		Line 1:
			[[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.]]

	'''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/collateral/sec2_final.pdf).		'''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/collateral/sec2_final.pdf).

Theymos: Add a paragraph about this curve's good properties

2014-06-30T02:38:44Z

Add a paragraph about this curve's good properties

← Older revision		Revision as of 02:38, 30 June 2014
Line 1:		Line 1:
	'''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/collateral/sec2_final.pdf).		'''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/collateral/sec2_final.pdf).

			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.

			=== Technical details ===

	As excerpted from ''Standards'':		As excerpted from ''Standards'':