cryptography - Find point and elliptic curve given the public key -

i'm trying resolve problem. once public key known, want know point , elliptic curve used generate public key.

for example, given ecc public key:

04 6b fb ee c6 9d e7 2c 66 a6 68 ec e1 aa f1 a2 64 a3 c9 b2 88 fb 32 d0 59 e9 2c 3e 5d 5b d4 d7 b5 01 48 78 f4 47 9c 13 c8 83 d0 54 55 5c d9 0e cd 13 6e c4 cc 34 64 89 cd d6 4e 69 43 f3 33 86 4a b9 df e4 42 dc bf 8f 69 c1 9e 71 d0 35 ff 31 7f c0 32 fc 21 55 ca ea a6 5b 49 3d 19 1d 39 9a c0

how possible know point , elliptic curve used generate ecc public key?

if elliptic curve 1 of recommended elliptic curves federal government use can find out domain parameters (p,a,b,g,n,h) g base point , bit length of public key tell curve name.

the ec public key point on curve, this: y^2 = x^3 + ax + b (mod p) p prime modulus.

the point represented octet string in compressed or uncompressed forms per ansi x9.62.

so sample public key mention consist of x-coordinate , y-coordinate:

public key = tag + x co-ordinate + y co-ordinate

the uncompressed form indicated tag = 0x04 , compressed form indicated either tag = 0x02 or tag = 0x03 (see section 2.2)

now, sample public key can written as:

04
6bfbeec69de72c66a668ece1aaf1a264a3c9b288fb32d059e92c3e5d5bd4d7b5014878f4479c13c883d054555cd90ecd
136ec4cc346489cdd64e6943f333864ab9dfe442dcbf8f69c19e71d035ff317fc032fc2155caeaa65b493d191d399ac0

the length of each co-ordinate 48 bytes or 384 bits. 'seems that' sample public key ec p-384 curve.