E ;B ;B B''L
1b
!
!F ub))J!mmO
&
&'A'A'C'C'2<'@'@'26':':'2:'>'>'/L0A0A'B'B'2;r??'C'C ) )F J?&HIII?..00'2IJJG '!**!**%.."++"++' ' D NN4==T2233333r0 )p224
NIST P-224zP-224
prime224v1 secp224r1nistp224c T d} d}d}d}d}t | d }t |d }t |d }t }t | t | t | t | t
t | t t d } | rt d| z t | t j
}
t t | t | t | t | t | d d d
|
d d d
} t t$ t( | d S )Nl ?l F eY8 w-X"PVd/%PP!-l =*8% (?l ! "X!#BXtJ9!'|%VA-l 4~
f&Dv@h!fE0m 9_ qlM/ r9 z#Error %d initializing P-224 context z 1.3.132.0.33rR zecdsa-sha2-nistp224rQ )r r r* r; r< r r r= r r r> r r? r@ r1 r rA rB rC rD
p224_names) rF rG rH rI rJ p224_modulusp224_b
p224_orderec_p224_contextr- rO rQ s r. init_p224r^ sn BABA FE CB CB B''L
1b
!
!F ub))J!mmO
&
&'A'A'C'C'2<'@'@'26':':'2:'>'>'/L0A0A'B'B'2;r??'C'C ) )F J?&HIII?..00'2IJJG '!**!**%.."++"++ ' D NN4==T2233333r0 )p256
NIST P-256zP-256
prime256v1 secp256r1nistp256c T d} d}d}d}d}t | d }t |d }t |d }t }t | t | t | t | t
t | t t d } | rt d| z t | t j
}
t t | t | t | t | t | d d d
|
d d d
} t t$ t( | d S )Nl ? @ l K`Opq^cv
3,e<
1U]>{|R*Zl Q%x + Ohbi+}s @ l B11e %:f=K`wrH7gHK8hkl Q~o]l+fUg+< )Z?8O?q!O r9 z#Error %d initializing P-256 context z1.2.840.10045.3.1.7r` zecdsa-sha2-nistp256r_ )r r r* r; r< r r r= r r r> r r? r@ r1 r rA rB rC rD
p256_names) rF rG rH rI rJ p256_modulusp256_b
p256_orderec_p256_contextr- rO r_ s r. init_p256rl sn JAJA NE KB KB B''L
1b
!
!F ub))J!mmO
&
&'A'A'C'C'2<'@'@'26':':'2:'>'>'/L0A0A'B'B'2;r??'C'C ) )F J?&HIII?..00'2IJJG '!**!**%.."++"++' ' D NN4==T2233333r0 )p384
NIST P-384zP-384
prime384v1 secp384r1nistp384c T d} d}d}d}d}t | d }t |d }t |d }t }t | t | t | t | t
t | t t d } | rt d| z t | t j
}
t t | t | t | t | t | d d d
|
d d d
} t t$ t( | d S )Nl ~l *'#.TEbc +Z'@=D 1 "(?7N 2Z_+|S/1fl s)e`gwl
X_[nlv|l
dxRjoyU8T( :ss" nZL8 k&"_Ul _!uR/sX0
@qaNQNB&JxS8KJEY
K%l 0 r9 z#Error %d initializing P-384 contexti z 1.3.132.0.34rn zecdsa-sha2-nistp384rm )r r r* r; r< r r r= r r r> r r? r@ r1 r rA rB rC rD
p384_names) rF rG rH rI rJ p384_modulusp384_b
p384_orderec_p384_contextr- rO rm s r. init_p384ry 0 sn jAjA nE kB kB B''L
1b
!
!F ub))J!mmO
&
&'A'A'C'C'2<'@'@'26':':'2:'>'>'/L0A0A'B'B'2;r??'C'C ) )F J?&HIII?..00'2IJJG '!**!**%.."++"++ ' D NN4==T2233333r0 )p521
NIST P-521zP-521
prime521v1 secp521r1nistp521c T d} d}d}d}d}t | d }t |d }t |d }t }t | t | t | t | t
t | t t d } | rt d| z t | t j
}
t t | t | t | t | t | d d d
|
d d d
} t t$ t( | d S )Nl# l# ?VQ(z O%b95~cte1oR { V;LH w>l-rZE]"Sr&Ga9}*Fl# dp"z\}[z3"nZ;PK#
`7roCQl# f=xK)H-apY$3^Q n%k{;/K!u{4-{?$O d8V 1l3s: l# Pf?QE$XN!8 5aZU WL9YL hz
f$Du13otc!% p MxjRr`B r9 z#Error %d initializing P-521 contexti z 1.3.132.0.35r{ zecdsa-sha2-nistp521rz )r r r* r; r< r r r= r r r> r r? r@ r1 r rA rB rC rD
p521_names) rF rG rH rI rJ p521_modulusp521_b
p521_orderec_p521_contextr- rO rz s r. init_p521r _ s} SA SA
WE
TB
TB B''L
1b
!
!F ub))J!mmO
&
&'A'A'C'C'2<'@'@'26':':'2:'>'>'/L0A0A'B'B'2;r??'C'C ) )F J?&HIII?..00'2IJJG '!**!**%.."++"++ ' D NN4==T2233333r0 ed25519r c " d} d}d}d}t t | d t | t | t | d ddd ddd }t t t | d S )
N l S9i @eM^w|o l UK 5J,{$%Xci\-G'
lJ[sii!l XfL33ffL33ffL33ffL33ff 1.3.101.112r ssh-ed25519r )r1 r rA rB rC rD
ed25519_names)rF rH rI rJ r s r. init_ed25519r s JA NE KB KBWQZZ U^^ R[[ R[[" " G NN4== 8899999r0 ed448r" c d} d}d}d}t }t | }|rt d|z t | t j }t t | d t | t | t | d dd|dd d }t t
t | d S )
N ? l DVJ
Ru8 a6!m,&vD }D2_l ^@ 518`b8 Cl\p*At(qmj.< +FaS[/S DZ74_3 l zadoeC@
ZK^Dsxs sZhNx02>Ilq2 vIZu gt'
z#Error %d initializing Ed448 contexti 1.3.101.113r" r )r r) ed448_new_contextr< r> r r? ed448_free_contextr1 r rA rB rC rD ed448_names)rF rH rI rJ
ed448_contextr- rO r s r.
init_ed448r s zA ~E {B {B MMM
)
)-*B*B*D*D
E
EF
J?&HIII=,,..
0MNNG 71::5>>2;;2;;
E NN4==e4455555r0 c e Zd ZdS )UnsupportedEccFeatureN)__name__
__module__ __qualname__ r0 r. r r s Dr0 r c e Zd ZdZddZd Zd Zd Zd Zd Z d Z
d
Z d Z e
d Ze
d
Ze
d Zd Zd Zd Zd Zd Zd Zd Zd ZdS )EccPointaP A class to model a point on an Elliptic Curve.
The class supports operators for:
* Adding two points: ``R = S + T``
* In-place addition: ``S += T``
* Negating a point: ``R = -T``
* Comparing two points: ``if S == T: ...`` or ``if S != T: ...``
* Multiplying a point by a scalar: ``R = S*k``
* In-place multiplication by a scalar: ``T *= k``
:ivar x: The affine X-coordinate of the ECC point
:vartype x: integer
:ivar y: The affine Y-coordinate of the ECC point
:vartype y: integer
:ivar xy: The tuple with affine X- and Y- coordinates
r_ c t | | _ n-# t $ r t dt | z w xY w|| _ | }t || }t || }t | |k st | |k rt d t | d }t | d }t | _ | j j
} n# t $ r
t } Y nw xY w || j t# | t# | t% | | }
|
r'|
dk rt d t d|
z t' | j
| | _ d S )NzUnknown curve name %szIncorrect coordinate length new_point
free_point z)The EC point does not belong to the curvez(Error %d while instantiating an EC point)rA r% KeyError
ValueErrorstr _curve_name
size_in_bytesr r= r/ r _pointrO r? AttributeErrorr r< r r r ) selfxycurve
modulus_bytesxbybr free_funcrO r- s r. __init__zEccPoint.__init__ s C!%.DKK C C C 4s5zz ABB B C **,,
1m
,
,
1m
,
, r77m # #s2ww-'?'? :;; ; T;// T<00 !mm #k)--//GG # # #"GGG #4;1133&r??&r??#M22" $ $ R|| !LMMM G& PQQ Q #4;??#4#4i@@ s *?& D DDc ` t | d }t | d }t | _ || j |j }|rt d|z t
| j | | _ | S )Ncloner z"Error %d while cloning an EC point)r/ r r r< r? r r )r pointr r r- s r. setz EccPoint.set
s w'' T<00 !mm t{--// |''))+ + L AF JKK K"4;??#4#4i@@ r0 c t |t sdS t | d }d || j |j k S )NFcmpr )
isinstancer r/ r r? )r r cmp_funcs r. __eq__zEccPoint.__eq__ sY %** 5D%((HHT[__ . . 0@0@0B0BCCCCr0 c | |k S Nr )r r s r. __ne__zEccPoint.__ne__ s 5= r0 c t | d }| } ||j }|rt d|z |S )Nnegz$Error %d while inverting an EC point)r/ copyr r? r )r neg_funcnpr- s r. __neg__zEccPoint.__neg__# sY D%((
YY[[")--//** N Cf LMM M r0 c F | j \ }}t ||| j }|S )z Return a copy of this point.)xyr r )r r r r s r. r z
EccPoint.copy+ s& w1
aD ,
-
- r0 c | j j dv S )Nr r )r% namer s r. _is_eddsazEccPoint._is_eddsa1 { #777r0 c V | r | j dk S | j dk S )z,``True`` if this is the *point-at-infinity*.r )r r )r r r r s r. is_point_at_infinityz EccPoint.is_point_at_infinity4 s/ >> %6Q; 7f$ $r0 c | rt dd| j S t dd| j S )z-Return the *point-at-infinity* for the curve.r )r r r r s r. point_at_infinityzEccPoint.point_at_infinity< s@ >> 4Aq$"233 3Aq$"233 3r0 c | j d S )Nr r r s r. r z
EccPoint.xD wqzr0 c | j d S )Nr r r s r. r z
EccPoint.yH r r0 c | }t | }t | }t | d } |t | t | t | | j }|rt d|z t t | t t | fS )Nget_xyz#Error %d while encoding an EC point)
r bytearrayr/ r r r r? r r r
)r r r r r r- s r. r z EccPoint.xyL s **,,
}
%
%
}
%
%$)) B#B // ))+ + M BV KLL L
b))**GM"4E4E,F,FGGr0 c 6 | dz dz S )z"Size of each coordinate, in bytes. ) size_in_bitsr s r. r zEccPoint.size_in_bytes[ s !!##a'A--r0 c | j j S )z!Size of each coordinate, in bits.)r% modulus_bitsr s r. r zEccPoint.size_in_bits_ s
{''r0 c t | d } || j }|rt d|z | S )zuDouble this point (in-place operation).
Returns:
This same object (to enable chaining).
doublez#Error %d while doubling an EC pointr/ r r? r )r double_funcr- s r. r zEccPoint.doublec sP tX.. T[__ . .// M BV KLL L r0 c t | d } || j |j }|r'|dk rt d t d|z | S )z Add a second point to this oneadd z#EC points are not on the same curvez#Error %d while adding two EC pointsr )r r add_funcr- s r. __iadd__zEccPoint.__iadd__p sx D%(($+//++U\-=-=-?-?@@ M|| !FGGG BV KLL L r0 c 8 | }||z
}|S )z8Return a new point, the addition of this one and anotherr )r r r s r. __add__zEccPoint.__add__{ s YY[[
e r0 c
b t | d }|dk rt d t | } || j t | t
t | t t d }|rt d|z | S )z Multiply this point by a scalarscalarr z?Scalar multiplication is only defined for non-negative integersr9 z%Error %d during scalar multiplication)
r/ r r r r? r r r= r r )r r scalar_funcsbr- s r. __imul__zEccPoint.__imul__ s tX.. A:: ^__ _
6
"
" T[__ . . (__ %c"gg . . (R 9 9; ; O Dv MNN N r0 c 8 | }||z }|S )z2Return a new point, the scalar product of this oner )r r r s r. __mul__zEccPoint.__mul__ s YY[[
f r0 c , | | S r )r )r left_hands r. __rmul__zEccPoint.__rmul__ s ||I&&&r0 N)r_ )r r r __doc__r r r r r r r r r propertyr r r r r r r r r r r r r0 r. r r s~ ($A $A $A $AL D D D! ! ! 8 8 8% % %4 4 4 X X H H X H . . .( ( (
' ' ' ' 'r0 r r2 )GrQ r_ rm rz c e Zd ZdZd Zd Zd Zd Zd Zd Z d Z
e d Z e d
Z
e d Zd Zd
Zd Zd ZddZd Zd Zd Zd Zd Zd Zd ZdS )EccKeya Class defining an ECC key.
Do not instantiate directly.
Use :func:`generate`, :func:`construct` or :func:`import_key` instead.
:ivar curve: The name of the curve as defined in the `ECC table`_.
:vartype curve: string
:ivar pointQ: an ECC point representating the public component.
:vartype pointQ: :class:`EccPoint`
:ivar d: A scalar that represents the private component
in NIST P curves. It is smaller than the
order of the generator point.
:vartype d: integer
:ivar seed: A seed that representats the private component
in EdDSA curves
(Ed25519, 32 bytes; Ed448, 57 bytes).
:vartype seed: bytes
c t | }| dd }| dd | _ | dd | _ | dd | _ || j r | j j }|r t
dt | z |t vrt d|z t | | _
| j
j | _ t | j du t | j du z }|dk r| j t d dS |d
k rt d | s^| j t d t | j | _ d
| j cxk r| j
j k sn t d dS | j t d | j
j dk rt% | j dk rt d t' j | j }|dd | _ t/ |dd }|dxx dz cc< |d dz dz |d< n| j
j dk rt% | j dk rt d t1 j | j d }|dd | _ t/ |dd }|dxx dz cc< |d xx d z cc< d|d < t j |d | _ dS )!ai Create a new ECC key
Keywords:
curve : string
The name of the curve.
d : integer
Mandatory for a private key one NIST P curves.
It must be in the range ``[1..order-1]``.
seed : bytes
Mandatory for a private key on the Ed25519 (32 bytes)
or Ed448 (57 bytes) curve.
point : EccPoint
Mandatory for a public key. If provided for a private key,
the implementation will NOT check whether it matches ``d``.
Only one parameter among ``d``, ``seed`` or ``point`` may be used.
r Ndseedr Unknown parameters: zUnsupported curve (%s)r zGAt lest one between parameters 'point', 'd' or 'seed' must be specified z,Parameters d and seed are mutually exclusivez7Parameter 'seed' can only be used with Ed25519 or Ed448r z;Parameter d must be an integer smaller than the curve orderz/Parameter d can only be used with NIST P curvesr re z0Parameter seed must be 32 bytes long for Ed25519 r9 r 9 z.Parameter seed must be 57 bytes long for Ed448r 7 8 little byteorder)rC pop_d_seedr r TypeErrorr rA r r% r& r intr r rH r r= r newdigest_prefixr r read
from_bytes)r kwargskwargs_
curve_namecount seed_hashtmps r. r zEccKey.__init__ s- & v,, [[$//
++c4(( [[..
kk'400 $+ 0J C 2S\\ ABB B W $ $ 5
BCC C j) [%
DG4'((3tz/E+F+FF A::{" !jkkk F A:: KLL L ~~ Bz% !Z[[[ dg&&DG3333$+"33333 !^___ 43 w" !RSSS{ 9,,tz??b(($%WXXX "Jtz 2 2 9 9 ; ; (~ #2#//A$ r7T>T1B!W,,tz??b(($%UVVV $L 4 4 9 9# > > (~ #2#//A$B4B (AAADGGGr0 c | j j dv S )N)r r" )r% r& r s r. r zEccKey._is_eddsa# r r0 c t |t sdS | | k rdS |j | j k S )NF)r r has_privatepointQ)r others r. r z
EccKey.__eq__& sP %(( 5 $"2"2"4"4 4 45|t{**r0 c | rV| r*dt t j | j z }ndt
| j z }nd}| j j \ }}d| j
j |||fz S )Nz , seed=%sz, d=%d z,EccKey(curve='%s', point_x=%d, point_y=%d%s)) r r r binasciihexlifyr r r
r r r% r& )r extrar r s r. __repr__zEccKey.__repr__/ s ~~
0#eH,