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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).

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'':

The elliptic curve domain parameters over F''p'' associated with a Koblitz curve secp256k1 are specified
by the sextuple T = (''p,a,b,G,n,h'') where the finite field F''p'' is defined by:
* ''p'' = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F
* = 2256 - 232 - 29 - 28 - 27 - 26 - 24 - 1

The curve ''E'': ''y2 = x3+ax+b'' over F''p'' is defined by:
* ''a'' = 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
* ''b'' = 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000007

The base point G in compressed form is:
* ''G'' = 02 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798
and in uncompressed form is:
* ''G'' = 04 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8
Finally the order ''n'' of ''G'' and the cofactor are:
* ''n'' = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141
* ''h'' = 01

=== Properties ===

* secp256k1 has characteristic ''p'', it is defined over the prime field ℤ''p''. Some other curves in common use have characteristic ''2'', and are defined over a binary Galois field ''GF(2n)'', 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 ''y2 = x3 + 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)

==Source==

[http://bitcoin.it/ http://bitcoin.it/]

[[Category:Technology]]
[[Category:Cryptographic algorithms]]

Secp256k1 - Revision history

Admin: Created page with " '''secp256k1''' refers to the parameters of the ECDSA curve used in Bitcoin, and is defined in ''Standards for Efficient Cryptography (SEC)'' (Certicom Research, ht..."