Secp256k1

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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[edit]

As excerpted from Standards:

The elliptic curve domain parameters over Fp associated with a Koblitz curve secp256k1 are specified by the sextuple T = (p,a,b,G,n,h) where the finite field Fp 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 Fp 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[edit]

  • secp256k1 has characteristic p, it is defined over the prime field ℤp. 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 on BitcoinWiki[edit]

Source[edit]

http://bitcoin.it/