P-384 is the elliptic curve currently specified in Commercial National Security Algorithm Suite for the ECDSA and ECDH algorithms. It is a 384-bit curve over a finite field of prime order approximately 394×10113.[lower-alpha 1] Its binary representation has 384 bits, with a simple pattern.[lower-alpha 2] The curve is given by the equation y2 = x3 − 3x + b, where b is given by a certain 384-bit number. The curve has order less than the field size.[lower-alpha 3] The bit-length of a key is considered to be that of the order of the curve, which is also 384 bits.

Notes

  1. ↑ p = 394020061963944792122790401001436138
    0507973927046544666794829340424572177149
    6870329047266088258938001861606973112319
  2. ↑ Explicitly: p =
    1111111111111111111111111111111111111111111111111111111111111111
    1111111111111111111111111111111111111111111111111111111111111111
    1111111111111111111111111111111111111111111111111111111111111111
    1111111111111111111111111111111111111111111111111111111111111110
    1111111111111111111111111111111100000000000000000000000000000000
    00000000000000000000000000000000111111111111111111111111111111112,
    that is, from the most significant bit: 255 '1's, 1 '0', 32 '1's, 64 '0's, 32 '1's.
  3. ↑ n = 394020061963944792122790401001436138
    0507973927046544666794690527962765939911
    3263569398956308152294913554433653942643
  • FIPS 186-4 standards where the curve is defined
  • Commercial National Security Algorithm (CNSA) Suite Factsheet
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