o wÔ+fyã@sddlmZGdd„dƒZdS)é)ÚPointc@sxeZdZedd„ƒZedd„ƒZedd„ƒZedd„ƒZed d „ƒZed d „ƒZ ed d„ƒZ edd„ƒZ edd„ƒZ dS)ÚMathcCst||dd|ƒS)Nré)Úpow)ÚclsÚvalueÚprime©r úE/var/www/html/venv/lib/python3.10/site-packages/ellipticcurve/math.pyÚmodularSquareRootszMath.modularSquareRootc 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©rÚpÚnÚNÚAÚPr r r Úmultiply s ÿz Math.multiplycCs$| | | |¡| |¡||¡|¡S)a¡ Fast way to add two points in elliptic curves :param p: First Point you want to add :param q: Second Point you want to add :param P: Prime number in the module of the equation Y^2 = X^3 + A*X + B (mod p) :param A: Coefficient of the first-order term of the equation Y^2 = X^3 + A*X + B (mod p) :return: Point that represents the sum of First and Second Point )r Ú _jacobianAddr)rrÚqrrr r r Úadds ÿzMath.addc Csh|dkrdSd}d}||}|}|dkr0||}|||}|||} |}|}| }|}|dks||S)zÅ Extended Euclidean Algorithm. It's the 'division' in elliptic curves :param x: Divisor :param n: Mod for division :return: Value representing the division érr ) rÚxrÚlmÚhmÚlowÚhighÚrÚnmÚnwr r r Úinv)s    ù zMath.invcCst|j|jdƒS)z• Convert point to Jacobian coordinates :param p: First Point you want to add :return: Point in Jacobian coordinates r)rrÚy)rrr r r rEszMath._toJacobiancCs>| |j|¡}|j|d|}|j|d|}t||dƒS)zô Convert point back from Jacobian coordinates :param p: First Point you want to add :param P: Prime number in the module of the equation Y^2 = X^3 + A*X + B (mod p) :return: Point in default coordinates éér)r"Úzrr#r)rrrr&rr#r r r r Os  zMath._fromJacobianc Cs¦|jdkr tdddƒS|jd|}d|j||}d|jd||jd|}|dd||}|||d|d|}d|j|j|} t||| ƒS)ac Double a point in elliptic curves :param p: Point you want to double :param P: Prime number in the module of the equation Y^2 = X^3 + A*X + B (mod p) :param A: Coefficient of the first-order term of the equation Y^2 = X^3 + A*X + B (mod p) :return: Point that represents the sum of First and Second Point rr$rr%é)r#rrr&) rrrrÚysqÚSÚMÚnxÚnyÚnzr r r Ú_jacobianDouble^s   zMath._jacobianDoublecCs|jdkr|S|jdkr|S|j|jd|}|j|jd|}|j|jd|}|j|jd|}||krK||krDtdddƒS| |||¡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 rr$r%r)r#rr&rr.)rrrrrÚU1ÚU2ÚS1ÚS2ÚHÚRÚH2ÚH3ÚU1H2r+r,r-r r r rts*       zMath._jacobianAddc Cs¨|jdks |dkrtdddƒS|dkr|S|dks||kr(| ||||||¡S|ddkr>| | ||d|||¡||¡S| | | ||d|||¡||¡|||¡S)a½ Multily point and scalar in elliptic curves :param p: First Point to mutiply :param n: Scalar to mutiply :param N: Order of the elliptic curve :param P: Prime number in the module of the equation Y^2 = X^3 + A*X + B (mod p) :param A: Coefficient of the first-order term of the equation Y^2 = X^3 + A*X + B (mod p) :return: Point that represents the sum of First and Second Point rrr$)r#rr r.rrr r r r ™s  ÿ$ÿzMath._jacobianMultiplyN) Ú__name__Ú __module__Ú __qualname__Ú classmethodr rrr"rr r.rr r r r r rs&        $rN)Úpointrrr r r r Ús