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 {{val|394|e=113}}.{{efn|p {{=}} {{gaps|394020|0619639447|9212279040|1001436138}}{{br}}{{gaps|0507973927|0465446667|9482934042|4572177149}}{{br}}{{gaps|6870329047|2660882589|3800186160|6973112319}}}} Its binary representation has 384 bits, with a simple pattern.{{efn|Explicitly: p {{=}}{{br}} {{gaps|11111111111111111111111111111111|11111111111111111111111111111111}}{{br}}

{{gaps|11111111111111111111111111111111|11111111111111111111111111111111}}{{br}}

{{gaps|11111111111111111111111111111111|11111111111111111111111111111111}}{{br}}

{{gaps|11111111111111111111111111111111|11111111111111111111111111111110}}{{br}}

{{gaps|11111111111111111111111111111111|00000000000000000000000000000000}}{{br}}

{{gaps|00000000000000000000000000000000|11111111111111111111111111111111}}₂,{{br}} that is, from the most significant bit: 255 '1's, 1 '0', 32 '1's, 64 '0's, 32 '1's.}} The curve is given by the equation {{math|y² {{=}} x³ − 3x + b}}, where {{math|b}} is given by a certain 384-bit number. The curve has order less than the field size.{{efn|n {{=}} {{gaps|394020|0619639447|9212279040|1001436138}}{{br}}{{gaps|0507973927|0465446667|9469052796|2765939911}}{{br}}{{gaps|3263569398|9563081522|9491355443|3653942643}}}} The bit-length of a key is considered to be that of the order of the curve, which is also 384 bits.