bache ha kasi inja mitoone ye hint be man bede vase koblitz curve ya hamoon secp256k .

fasele beyn 2ta x coordinate dakhel range 50*10^77 ta 59*10^77 sabet hast.

mesal :  1 , 55066263022277343669578718895168534326250603453777594175500187360389116729240

privatekey ,55066263022277343669578718895168534326250603453777594175500187360389116729241
privatekey ,55066263022277343669578718895168534326250603453777594175500187360389116729239

fasle 2ta private key sabet hast vase hame addad ha to in range.

endomorphism ha sabet mikone k curve contant hast.
N + trace = P
N1 + N2 = N
P = Y1 +Y2
X coordinate generates Y1 and Y2
2 to 1 rabete beyn N va  X coordinate

Base point privKey = 1
Base point privkey = N -1
base point avaz namishe va faghi namikone Gx koja entekhab konim.
private key va ( N-private key )  to ye point hamo ghat mikonan k mishe x .

private key + ( N-private key ) = N point infinity

vaghti fasele 2 private key x va x+1 dashte basham , mitonam fasle hameye private key to rang ro hesab konam .

curve nesf hast , hameye privatekey az N/2+1 ta N-1  tekrar mishe , mesl ayne .

N to P mapping az addad (N+P)/2 estefade mishe.

lmda+lmda2 =N-1
beta + beta 2 = P-1
P- N = trace-1

kheyli sade hast age kasi chizi midoone k mitoone be man komak kone lotfan bege. man deta daram k harfamo sabet mikone .