curve nesf hast yani private key 1 va N-1 joftesh 1 x dare.

privatekey * lmda % N =private key 2
privatekey2 * lmda % N =private key 3
private key 3  * lmda % N = privatekey


vase x.
x*beta% P=x1
x1*beta% P=x2
x2*beta% P=x

inja ye group shekl migire har private key be x khodesh to p map mishe .

lmda=37718080363155996902926221483475020450927657555482586988616620542887997980018
beta =55594575648329892869085402983802832744385952214688224221778511981742606582254

farz kon private key 1 :
1* lmda % N =37718080363155996902926221483475020450927657555482586988616620542887997980018
         
37718080363155996902926221483475020450927657555482586988616620542887997980018* lmda % N =78074008874160198520644763525212887401909906723592317393988542598630163514318

78074008874160198520644763525212887401909906723592317393988542598630163514318  * lmda % N = 1

x= 55066263022277343669578718895168534326250603453777594175500187360389116729240
.

55066263022277343669578718895168534326250603453777594175500187360389116729240*beta% P=85340279321737800624759429340272274763154997815782306132637707972559913914315

85340279321737800624759429340272274763154997815782306132637707972559913914315*beta% P=91177636130617246552803821781935006617134368061721227770777272682868638699771

91177636130617246552803821781935006617134368061721227770777272682868638699771*beta% P=x

3 ta private key k sum up to N or 2N  , 3ta x k sum up to P or 2P.

emtehan kon har addad k to N hast private key to P hast . lmda va beta constent hastan . vase hame curve kar mikone.

hala man mikham N to P vasl konam ba mod (N+P)/2

yani (privatekey * constant)%(N+P)/2 = x

PUZZLE brute force hast . man daram trap door curve migam . algorithm k curve beshkane . P=NP hard.
vase hame chizayi ham k migam proof daram with example . hamash math hast namitoni ba hex befahmi .

do you know the exact release date ?