U ê°Íbã@sddlmZGdd„dƒZdS)é)ÚPointc@sleZdZedd„ƒZedd„ƒZedd„ƒZedd„ƒZed d „ƒZed d „ƒZ ed d„ƒZ edd„ƒZ dS)ÚMathc Cs | | | |¡||||¡|¡S)aÉ Fast way to multily point and scalar in elliptic curves :param p: First Point to mutiply :param n: Scalar to mutiply :param N: Order of the elliptic curve :param P: Prime number in the module of the equation Y^2 = X^3 + A*X + B (mod p) :param A: Coefficient of the first-order term of the equation Y^2 = X^3 + A*X + B (mod p) :return: Point that represents the sum of First and Second Point )Ú _fromJacobianÚ_jacobianMultiplyÚ _toJacobian©ÚclsÚpÚnÚNÚAÚP©rúr/var/www/html/staging.mfahmagazine.net/magazine_api/magazine_env/lib/python3.8/site-packages/ellipticcurve/math.pyÚmultiplys ÿz Math.multiplycCs$| | | |¡| |¡||¡|¡S)a¡ Fast way to add two points in elliptic curves :param p: First Point you want to add :param q: Second Point you want to add :param P: Prime number in the module of the equation Y^2 = X^3 + A*X + B (mod p) :param A: Coefficient of the first-order term of the equation Y^2 = X^3 + A*X + B (mod p) :return: Point that represents the sum of First and Second Point )rÚ _jacobianAddr)rr Úqr r rrrÚadds ÿzMath.addc Csb|dkr dSd}d}||}|}|dkrZ||}|||}|||} |}|}| }|}q ||S)zÅ Extended Euclidean Algorithm. It's the 'division' in elliptic curves :param x: Divisor :param n: Mod for division :return: Value representing the division érr) rÚxr ZlmZhmÚlowÚhighÚrÚnmZnwrrrÚinv%s   zMath.invcCst|j|jdƒS)z• Convert point to Jacobian coordinates :param p: First Point you want to add :return: Point in Jacobian coordinates r)rrÚy)rr rrrrAszMath._toJacobiancCs>| |j|¡}|j|d|}|j|d|}t||dƒS)zô Convert point back from Jacobian coordinates :param p: First Point you want to add :param P: Prime number in the module of the equation Y^2 = X^3 + A*X + B (mod p) :return: Point in default coordinates éér)rÚzrrr)rr r rrrrrrrKs zMath._fromJacobianc Cs¦|jdkrtdddƒS|jd|}d|j||}d|jd||jd|}|dd||}|||d|d|}d|j|j|} t||| ƒS)ac Double a point in elliptic curves :param p: Point you want to double :param P: Prime number in the module of the equation Y^2 = X^3 + A*X + B (mod p) :param A: Coefficient of the first-order term of the equation Y^2 = X^3 + A*X + B (mod p) :return: Point that represents the sum of First and Second Point rréré)rrrr) rr r r ZysqÚSÚMÚnxÚnyÚnzrrrÚ_jacobianDoubleZs   zMath._jacobianDoublecCs|jdkr|S|jdkr|S|j|jd|}|j|jd|}|j|jd|}|j|jd|}||kr–||krˆtdddƒS| |||¡S||} ||} | | |} | | |} || |} | d| d| |}| | ||| |}| |j|j|}t|||ƒS)a• Add two points in elliptic curves :param p: First Point you want to add :param q: Second Point you want to add :param P: Prime number in the module of the equation Y^2 = X^3 + A*X + B (mod p) :param A: Coefficient of the first-order term of the equation Y^2 = X^3 + A*X + B (mod p) :return: Point that represents the sum of First and Second Point rrrr)rrrrr&)rr rr r ZU1ZU2ZS1ZS2ÚHÚRZH2ZH3ZU1H2r#r$r%rrrrps*      zMath._jacobianAddc Cs¨|jdks|dkrtdddƒS|dkr*|S|dks:||krP| ||||||¡S|ddkr|| | ||d|||¡||¡S| | | ||d|||¡||¡|||¡S)a½ Multily point and scalar in elliptic curves :param p: First Point to mutiply :param n: Scalar to mutiply :param N: Order of the elliptic curve :param P: Prime number in the module of the equation Y^2 = X^3 + A*X + B (mod p) :param A: Coefficient of the first-order term of the equation Y^2 = X^3 + A*X + B (mod p) :return: Point that represents the sum of First and Second Point rrr)rrrr&rrrrrr•s$   ÿÿzMath._jacobianMultiplyN) Ú__name__Ú __module__Ú __qualname__Ú classmethodrrrrrr&rrrrrrrs        $rN)ZpointrrrrrrÚs