P-384

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.^[a] Its binary representation has 384 bits, with a simple pattern.^[b] 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.^[c] 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

External links

• FIPS 186-4 standards where the curve is defined
• Commercial National Security Algorithm (CNSA) Suite Factsheet