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    Cryptography How does elliptic curve domain parameters be chosen?

    July 01, 2018

    Cryptography How does elliptic curve domain parameters be chosen?

    How does elliptic curve domain parameters be chosen?

    Posted: 23 Jun 2018 02:07 AM PDT

    Lets's say secp256k1,

    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

    How and why these parameters be chosen ?

    submitted by /u/cyou2
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