Current File : //opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyc
�
�ac @ s d d l m Z y d d l m Z e Z WnE e k
rq y d d l m Z e Z Wn e k
rm e Z n Xn Xd d l m
Z
d d l m Z d d l
m Z e
d e f d � � Y� Z d e f d
� � YZ d e f d � � YZ e e e e � Z d
S( i����( t division( t mpz( t python_2_unicode_compatiblei ( t numbertheory( t RWLockt CurveFpc B sw e Z d Z e r! d d � Z n d d � Z d � Z d � Z d � Z d � Z d � Z
d � Z d � Z d
� Z
RS( s9 Elliptic Curve over the field of integers modulo a prime.c C s: t | � | _ t | � | _ t | � | _ | | _ d S( su
The curve of points satisfying y^2 = x^3 + a*x + b (mod p).
h is an integer that is the cofactor of the elliptic curve domain
parameters; it is the number of points satisfying the elliptic curve
equation divided by the order of the base point. It is used for selection
of efficient algorithm for public point verification.
N( R t _CurveFp__pt _CurveFp__at _CurveFp__bt _CurveFp__h( t selft pt at bt h( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt __init__; s c C s( | | _ | | _ | | _ | | _ d S( su
The curve of points satisfying y^2 = x^3 + a*x + b (mod p).
h is an integer that is the cofactor of the elliptic curve domain
parameters; it is the number of points satisfying the elliptic curve
equation divided by the order of the base point. It is used for selection
of efficient algorithm for public point verification.
N( R R R R ( R
R R R
R ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR K s c C sG t | t � rC | j | j k oB | j | j k oB | j | j k St S( N( t
isinstanceR R R R t NotImplemented( R
t other( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt __eq__Y s
c C s t | j | j | j f � S( N( t hashR R R ( R
( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt __hash__a s c C s | j S( N( R ( R
( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR d s c C s | j S( N( R ( R
( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR g s c C s | j S( N( R ( R
( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR
j s c C s | j S( N( R ( R
( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt cofactorm s c C s/ | | | | | j | | j | j d k S( s! Is the point (x,y) on this curve?i ( R R R ( R
t xt y( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt contains_pointp s c C s d | j | j | j | j f S( Ns CurveFp(p=%d, a=%d, b=%d, h=%d)( R R R R ( R
( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt __str__t s N( t __name__t
__module__t __doc__t GMPYt NoneR R R R R R
R R R ( ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR 6 s t PointJacobic B s e Z d Z d e d � Z d � Z d � Z d � Z d � Z d � Z
d � Z d � Z e
e d � � Z d
� Z d � Z d � Z d
� Z d � Z d � Z d � Z d � Z d � Z d � Z d � Z d � Z e
d � � Z d � Z e
d � � Z d � Z d � Z RS( s�
Point on an elliptic curve. Uses Jacobi coordinates.
In Jacobian coordinates, there are three parameters, X, Y and Z.
They correspond to affine parameters 'x' and 'y' like so:
x = X / Z²
y = Y / Z³
c C sK | | _ t � | _ t r` t | � | _ t | � | _ t | � | _ | oW t | � | _ n$ | | _ | | _ | | _ | | _ g | _ | rG| s� t
� d } | d 9} t | | | | | � } | d 9} | j j | j
� | j � f � xQ | | k rC| d 9} | j � j � } | j j | j
� | j � f � q� Wn d S( s
Initialise a point that uses Jacobi representation internally.
:param CurveFp curve: curve on which the point resides
:param int x: the X parameter of Jacobi representation (equal to x when
converting from affine coordinates
:param int y: the Y parameter of Jacobi representation (equal to y when
converting from affine coordinates
:param int z: the Z parameter of Jacobi representation (equal to 1 when
converting from affine coordinates
:param int order: the point order, must be non zero when using
generator=True
:param bool generator: the point provided is a curve generator, as
such, it will be commonly used with scalar multiplication. This will
cause to precompute multiplication table for it
i i N( t _PointJacobi__curveR t _scale_lockR R t _PointJacobi__xt _PointJacobi__yt _PointJacobi__zt _PointJacobi__ordert _PointJacobi__precomputet AssertionErrorR t appendR R t doublet scale( R
t curveR R t zt ordert generatort it doubler( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR � s.
"
c C sf zL | j j � | t k r. | j p- | j S| j | j | j } } } Wd | j j � Xt | t � r� | j � | j
� d } } } nU t | t � r� z. | j j � | j | j | j } } } Wd | j j � Xn t S| j
| j � k r� t S| j
j � } | | | } | | | }
| |
| | | d k oe| |
| | | | | d k S( s# Compare two points with each-other.Ni i ( R" t reader_acquiret INFINITYR$ R% R# t reader_releaseR t PointR R R R R! R, t FalseR ( R
R t x1t y1t z1t x2t y2t z2R t zz1t zz2( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR � s*
!#
! c C s | j S( sE Return the order of the point.
None if it is undefined.
( R& ( R
( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR. � s c C s | j S( s- Return curve over which the point is defined.( R! ( R
( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR, � s c C s{ z9 | j j � | j d k r& | j S| j } | j } Wd | j j � X| j j � } t j | | � } | | d | S( s7
Return affine x coordinate.
This method should be used only when the 'y' coordinate is not needed.
It's computationally more efficient to use `to_affine()` and then
call x() and y() on the returned instance. Or call `scale()`
and then x() and y() on the returned instance.
i Ni ( R" R2 R% R# R4 R! R R t inverse_mod( R
R R- R ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR � s
c C s{ z9 | j j � | j d k r& | j S| j } | j } Wd | j j � X| j j � } t j | | � } | | d | S( s7
Return affine y coordinate.
This method should be used only when the 'x' coordinate is not needed.
It's computationally more efficient to use `to_affine()` and then
call x() and y() on the returned instance. Or call `scale()`
and then x() and y() on the returned instance.
i Ni ( R" R2 R% R$ R4 R! R R R? ( R
R R- R ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR � s
c C s� z$ | j j � | j d k r# | SWd | j j � Xzx | j j � | j j � } t j | j | � } | | | } | j | | | _ | j
| | | | _
d | _ Wd | j j � X| S( s_
Return point scaled so that z == 1.
Modifies point in place, returns self.
i N( R" R2 R% R4 t writer_acquireR! R R R? R# R$ t writer_release( R
R t z_invt zz_inv( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR+ s
c C sA | j s | j r t S| j � t | j | j | j | j � S( s Return point in affine form.( R$ R% R3 R+ R5 R! R# R& ( R
( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt to_affine" s
c C s1 t | j � | j � | j � d | j � | � S( s Create from an affine point.
:param bool generator: set to True to make the point to precalculate
multiplication table - useful for public point when verifying many
signatures (around 100 or so) or for generator points of a curve.
i ( R R, R R R. ( t pointR/ ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt from_affine+ s !c
C s� | | | | | | } } | s' d S| | | } d | | d | | | } d | | } | | d | | }
| | |
d | | } d | | } |
| | f S( s" Add a point to itself with z == 1.i i i i i ( i i i ( (
R
t X1t Y1R R t XXt YYt YYYYt St Mt Tt Y3t Z3( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt _double_with_z_1@ s c C s� | d k r" | j | | | | � S| s, d S| | | | | | } } | sS d S| | | } | | | } d | | d | | | }
d | | | | | } | | d |
| } | |
| d | | }
| | d | | | } | |
| f S( s# Add a point to itself, arbitrary z.i i i i i ( i i i ( i i i ( RQ ( R
RG RH t Z1R R RI RJ RK t ZZRL RM RN RO RP ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt _doubleP s c C s� | j s
t S| j j � | j j � } } z. | j j � | j | j | j } } } Wd | j j � X| j
| | | | | � \ } } } | s� | r� t St | j | | | | j � S( s Add a point to itself.N(
R$ R3 R! R R R" R2 R# R% R4 RT R R& ( R
R R RG RH RR t X3RO RP ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR* f s
!$c C s� | | } | | } d | | } | | } d | | }
| rg |
rg | j | | | | j j � � S| | } |
d | d | | } |
| | d | | | }
d | | } | |
| f S( s& add points when both Z1 and Z2 equal 1i i ( RQ R! R ( R
RG RH t X2t Y2R t Ht HHt It Jt rt VRU RO RP ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt
_add_with_z_1y s
c C s� | | d | } | | | } | | } | | d | }
| rl |
rl | j | | | | | j j � � S|
| | | } | | | | | | | | } | | | | }
| | |
f S( s add points when Z1 == Z2i ( RT R! R ( R
RG RH RR RV RW R t At Bt Ct DRU RO RP ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt _add_with_z_eq� s
""c C s | | | } | | | | | | | } } | | | }
|
|
| } d | | } |
| }
d | | | } | r� |
r� | j | | | | j j � � S| | } | | |
d | | } | | | d | |
| } | |
d | | | } | | | f S( s add points when Z2 == 1i i ( RQ R! R ( R
RG RH RR RV RW R t Z1Z1t U2t S2RX RY RZ R[ R\ R] RU RO RP ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt _add_with_z2_1� s !
c C s5 | | | } | | | } | | | }
| | | } | | | | } | | | | }
| |
} d | | | } | | | } d |
| | } | r� | r� | j | | | | | j j � � S|
| } | | | d | | } | | | d | | | } | | d | | | | } | | | f S( s add points with arbitrary zi i ( RT R! R ( R
RG RH RR RV RW t Z2R Rd t Z2Z2t U1Re t S1Rf RX RZ R[ R\ R] RU RO RP ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt _add_with_z_ne� s"
"
c C s | | S( s Add other to self.( ( R
R ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt __radd__� s c C s� | s | r | | | f S| s) | r6 | | | f S| | k r� | d k rg | j | | | | | � S| j | | | | | | � S| d k r� | j | | | | | | � S| d k r� | j | | | | | | � S| j | | | | | | | � S( s& add two points, select fastest method.i ( R^ Rc Rg Rl ( R
RG RH RR RV RW Rh R ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt _add� s
c C sG | t k r | S| t k r | St | t � rA t j | � } n | j | j k rb t d � � n | j j � } z. | j j � | j
| j | j } } } Wd | j j
� Xz. | j j � | j
| j | j } } } Wd | j j
� X| j | | | | | | | � \ } }
} |
s'| r+t St | j | |
| | j � S( s! Add two points on elliptic curve.s% The other point is on different curveN( R3 R R5 R RF R! t
ValueErrorR R" R2 R# R$ R% R4 Rn R& ( R
R R RG RH RR RV RW Rh RU RO RP ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt __add__� s*
!
!*c C s | | S( s Multiply point by an integer.( ( R
R ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt __rmul__� s c C s
d d d | j j � f \ } } } } | j } x� | j D]� \ } } | d r� | d d k r� | d d } | | | | | | d | � \ } } } q� | d d } | | | | | | d | � \ } } } q: | d } q: W| s� | r� t St | j | | | | j � S( s4 Multiply point by integer with precomputation table.i i i i ( R! R Rn R' R3 R R& ( R
R RU RO RP R Rn RV RW ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt _mul_precompute� s '
+*c C su g } xh | rp | d rV | d } | d k r< | d } n | | g 7} | | 8} n
| d g 7} | d } q W| S( s& Calculate non-adjacent form of number.i i i ( ( t multt rett nd( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt _naf
s
c C s� | j s | r t S| d k r% | S| j rB | | j d } n | j rX | j | � S| j � } | j | j } } d \ } } } | j j � | j j � } } | j
} | j }
x� t | j
| � � D]� } | | | | | | � \ } } } | d k r+|
| | | | | d | � \ } } } q� | d k r� |
| | | | | d | � \ } } } q� q� W| ss| rwt St | j | | | | j � S( s Multiply point by an integer.i i i ( i i i ( R$ R3 R& R' Rr R+ R# R! R R RT Rn t reversedRv R ( R
R RV RW RU RO RP R R RT Rn R0 ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt __mul__ s.
! + .c C s= | d k s t � d } x | | k r4 d | } q W| d S( sC Return integer with the same magnitude as x but hamming weight of 1i i i ( R( ( R t result( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt
_leftmost_bit; s
c C sl | t k s | d k r | | S| d k r4 | | St | t � sU t j | � } n | j rw | j rw | | | | S| j r� | | j } | | j } n | j t | | � � d } d \ } } } | j j � | j j
� } } | j � } | j | j
}
} | j � } | j | j
} }
| | j � } | j | j
} } | j } | j } x� | d k r=| | | | | | � \ } } } | d } | | @r�| | @r�| | | | | | d | � \ } } } q]| | @r| | | | |
| d | � \ } } } q]| | @r]| | | | | |
d | � \ } } } q]q]W| sL| rPt St | j | | | | j � S( su
Do two multiplications at the same time, add results.
calculates self*self_mul + other*other_mul
i i i ( i i i ( R3 R R RF R' R& Rz t maxR! R R R+ R# R$ RT Rn ( R
t self_mulR t other_mulR0 RU RO RP R R RG RH RV RW t botht X4t Y4RT Rn ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt mul_addD sD
!
*
*
.c C sL z7 | j j � t | j | j | j | j | j � SWd | j j � Xd S( s Return negated point.N( R" R2 R R! R# R$ R% R& R4 ( R
( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt __neg__u s
N( R R R R R6 R R R. R, R R R+ RD t staticmethodRF RQ RT R* R^ Rc Rg Rl Rm Rn Rp Rq Rr Rv Rx Rz R� R� ( ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR y s8 - ! 1R5 c B s} e Z d Z d
d � Z d � Z d � Z d � Z d � Z d � Z d � Z
d � Z d � Z d
� Z
d � Z d � Z RS( ss A point on an elliptic curve. Altering x and y is forbidding,
but they can be read by the x() and y() methods.c C s� | | _ t rQ | o t | � | _ | o3 t | � | _ | oH t | � | _ n | | _ | | _ | | _ | j r� | j j | | � s� t � n | r� | j � d k r� | r� | | t k s� t � n d S( s@ curve, x, y, order; order (optional) is the order of this point.i N(
t
_Point__curveR R t _Point__xt _Point__yt
_Point__orderR R( R R3 ( R
R, R R R. ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR � s c C sG t | t � rC | j | j k oB | j | j k oB | j | j k St S( s9 Return True if the points are identical, False otherwise.( R R5 R� R� R� R ( R
R ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR � s
c C s& t | j | j | j j � | j � S( N( R5 R� R� R R� ( R
( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR� � s c C s t | t � s t S| t k r# | S| t k r3 | S| j | j k sK t � | j | j k r� | j | j | j j � d k r� t S| j � Sn | j j � } | j | j t
j | j | j | � | } | | | j | j | } | | j | | j | } t | j | | � S( s Add one point to another point.i ( R R5 R R3 R� R( R� R� R R* R R? ( R
R R t lt x3t y3( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyRp � s" #
! c C s* d � } | } | d k s7 | j r; | | j d k r; t S| t k rK t S| d k ra | | Sd | } t | j | j | j | j � } | | � d } | } x� | d k r%| j � } | | @d k r� | | @d k r� | | } n | | @d k r| | @d k r| | } n | d } q� W| S( s Multiply a point by an integer.c S s= | d k s t � d } x | | k r4 d | } q W| d S( Ni i i ( R( ( R Ry ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt leftmost_bit� s
i i i i ( R� R3 R5 R� R� R� R* ( R
R R� t et e3t
negative_selfR0 Ry ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyRx � s( (
"
c C s | | S( s Multiply a point by an integer.( ( R
R ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyRq � s c C s$ | t k r d Sd | j | j f S( Nt infinitys (%d,%d)( R3 R� R� ( R
( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR � s c C s� | t k r t S| j j � } | j j � } d | j | j | t j d | j | � | } | | d | j | } | | j | | j | } t | j | | � S( s) Return a new point that is twice the old.i i ( R3 R� R R R� R R? R� R5 ( R
R R R� R� R� ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR* � s c C s | j S( N( R� ( R
( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR � s c C s | j S( N( R� ( R
( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR s c C s | j S( N( R� ( R
( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR, s c C s | j S( N( R� ( R
( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR. s N( R R R R R R R� Rp Rx Rq R R* R R R, R. ( ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyR5 s $ N( t
__future__R t gmpy2R t TrueR t ImportErrort gmpyR6 t sixR t R t _rwlockR t objectR R R5 R R3 ( ( ( sH /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/ellipticcurve.pyt <module>$ s&
B� � �
Mini Shell