Secp256k1

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:

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