eiddlmZddlmZGddeZGddeZGdd eZGd d eZed d d Z d S) )division) numbertheoryc6eZdZdZdZdZdZdZdZdZ dS) CurveFpz9Elliptic Curve over the field of integers modulo a prime.c0||_||_||_dS)z;The curve of points satisfying y^2 = x^3 + a*x + b (mod p).N _CurveFp__p _CurveFp__a _CurveFp__b)selfpabs j/var/www/html/volatility/venv/lib/python3.11/site-packages/ccxt/static_dependencies/ecdsa/ellipticcurve.py__init__zCurveFp.__init__+sc|jSN)r r s rrz CurveFp.p1 xrc|jSr)r rs rrz CurveFp.a4rrc|jSr)r rs rrz CurveFp.b7rrc\||z||z|z|j|zz|jzz |jzdkS)z!Is the point (x,y) on this curve?r)r r r )r xys rcontains_pointzCurveFp.contains_point:s7AQTX\1DH<=IQNNrc0d|j|j|jfzS)NzCurveFp(p=%d, a=%d, b=%d)r rs r__str__zCurveFp.__str__>s*dh$(-KKKrN) __name__ __module__ __qualname____doc__rrrrrrrrrr(s|CC OOOLLLLLrrcVeZdZdZddZdZdZdZdZdZ d Z d Z d Z d Z d ZdS)PointzsA point on an elliptic curve. Altering x and y is forbidding, but they can be read by the x() and y() methods.Nc||_||_||_||_|jr|j||sJ|r||zt ksJdSdS)z@curve, x, y, order; order (optional) is the order of this point.N) _Point__curve _Point__x _Point__y _Point__orderrINFINITY)r curverrorders rrzPoint.__init__Fss  < 5<..q!44 4 4 4  ,%<8++++ , ,++rcj|j|jkr"|j|jkr|j|jkrdSdS)z9Return True if the points are identical, False otherwise.TF)r(r)r*r others r__eq__z Point.__eq__Rs9 <5= ( (H ))H ))45rc2|tkr|S|tkr|S|j|jksJ|j|jkrH|j|jz|jzdkrtS|S|j}|j|jz t j|j|jz |z|z}||z|jz |jz |z}||j|z z|jz |z}t|j||S)zAdd one point to another point.r) r,r(r)r*rdoubler inverse_modr&)r r1rlx3y3s r__add__z Point.__add__[s H  K 8  L|u},,,, 8uy 59$ (8(88A=={{}}$ LNN  i$("  %ei$(&:A > >?BC D!edh*a /48b=!DH, 1T\2r***rcd}|}|jr ||jz}|dkrtS|tkrtS|dksJd|z}t|j|j|j |j}||dz}|}|dkrM|}||zdkr||zdkr||z}||zdkr||zdkr||z}|dz}|dkM|S)Multiply a point by an integer.cB|dksJd}||kr d|z}||k |dzS)Nrrr$)rresults r leftmost_bitz#Point.__mul__..leftmost_bitxs;q5555FA++VA++Q; rrr=r)r+r,r&r(r)r*r4)r r1r?ee3 negative_selfir>s r__mul__z Point.__mul__us     < !DL A 66O 8  O1uuuuUdlDHtxiNN L   !!ee]]__FQ1}}!a%A$Q1}}!a%A-/QA!ee rc ||zS)r;r$r0s r__rmul__zPoint.__rmul__se|rc>|tkrdSd|j|jfzS)Ninfinityz(%d,%d))r,r)r*rs rrz Point.__str__s& 8  :DHdh///rcx|tkrtS|j}|j}d|jz|jz|zt jd|jz|z|z}||zd|jzz |z}||j|z z|jz |z}t|j||S)z)Return a new point that is twice the old.r@r=) r,r(rrr)rr5r*r&)r rrr6r7r8s rr4z Point.doubles 8  O LNN   LNN  $(lTX%)  %a$(lA 6 67:; <!ea$(l"a '48b=!DH, 1T\2r***rc|jSr)r)rs rrzPoint.xrrc|jSr)r*rs rrzPoint.yrrc|jSr)r(rs rr-z Point.curve |rc|jSr)r+rs rr.z Point.orderrNrr)r r!r"r#rr2r9rErGrr4rrr-r.r$rrr&r&Bs99 , , , ,+++4###J 000 +++&rr&ceZdZdZedZedZedZedZ e ddZ d Z d Z d Z d ZddZedZdS) AbstractPointz2Class for common methods of elliptic curve points.ct||ksJ|d|dz}||dzd}t||dzksJt||dzksJt|}t|}||fS)z Decode public point from :term:`raw encoding`. :term:`raw encoding` is the same as the :term:`uncompressed` encoding, but without the 0x04 byte at the beginning. Nr=)lenstring_to_number)dataraw_encoding_lengthxsyscoord_xcoord_ys r_from_raw_encodingz AbstractPoint._from_raw_encodings4yy///// ,'1,, - %*,, -2ww-222222ww-22222"2&&"2&&rc|dddvrtd|dddk}t|dd}|}t|d|||zz|z|z} t j||}n'#t j$r}td|d}~wwxYw|t|dzkr||z }n|}||fS)z-Decode public point from compressed encoding.Nr)z#Malformed compressed point encodingr]r@0Encoding does not correspond to a point on curve) MalformedPointErrorrTrpowrrrsquare_root_mod_primeErrorbool) rUr-is_evenrralphabetarArs r_from_compressedzAbstractPoint._from_compresseds 8- - -%&KLL Lrr(g% T!""X & & GGIIQ1Q/%''));q@ 5eQ??DD!   %BA   d4!8nn $ $DAAA!t sB--C<C  Cc|dddvsJ||dd|\}}|r5|dzr|dddks|dzs|dddkrtd||fS)z)Decode public point from hybrid encoding.Nrrlrkz"Inconsistent hybrid point encoding)r[r`)clsrUrVvalidate_encodingrrs r _from_hybridzAbstractPoint._from_hybridsBQBx-----%%d122h0CDD1  L E LRaRG##E$RaRG##%&JKK K!t rct|}|}t|dzdzdz}t||krt d|ddzdz }|dxxdzcc<t |d}t rt|}||zdz tj | |z|z| z |z|z} tj ||}n'#tj $r} t d | d } ~ wwxYw|d z|kr| |z}||fS) z#Decode a point on an Edwards curve.rz%Point length doesn't match the curve.littler_Nr=) bytearrayr bit_lengthrSr` bytes_to_intGMPYmpzrr5drrbrc) rmr-rUrexp_lenx_0rx2rrAs r _from_edwardszAbstractPoint._from_edwardssc GGIIa==1$q(Q. t99  %&MNN NBx$1$ RH x ( (  AAUQY&uwwyy1}q'857799'DaHH I   22q99AA!   %BA   q5C<<QA!t s1DD+D&&D+TNc^|stgd}td|Dstdt|}t |t r|||St|}dt| z}||krd|vr| ||\}}n||dzkrvd|vsd|vrn|d dd vrd|vr| |||\}}n|d dd kr&d|vr"| |dd |\}}nntd ||dzdzkrd |vr| ||\}}n5tdd|||fS)a Initialise the object from byte encoding of a point. The method does accept and automatically detect the type of point encoding used. It supports the :term:`raw encoding`, :term:`uncompressed`, :term:`compressed`, and :term:`hybrid` encodings. Note: generally you will want to call the ``from_bytes()`` method of either a child class, PointJacobi or Point. :param data: single point encoding of the public key :type data: :term:`bytes-like object` :param curve: the curve on which the public key is expected to lay :type curve: ~ecdsa.ellipticcurve.CurveFp :param validate_encoding: whether to verify that the encoding of the point is self-consistent, defaults to True, has effect only on ``hybrid`` encoding :type validate_encoding: bool :param valid_encodings: list of acceptable point encoding formats, supported ones are: :term:`uncompressed`, :term:`compressed`, :term:`hybrid`, and :term:`raw encoding` (specified with ``raw`` name). All formats by default (specified with ``None``). :type valid_encodings: :term:`set-like object` :raises `~ecdsa.errors.MalformedPointError`: if the public point does not lay on the curve or the encoding is invalid :return: x and y coordinates of the encoded point :rtype: tuple(int, int)  uncompressed compressedhybridrawc38K|]}|tdvVdS)rN)set).0rDs r z+AbstractPoint.from_bytes..NsD   DEE E      rz@Only uncompressed, compressed, hybrid or raw encoding supported.r=rrrrNrjz*Invalid X9.62 encoding of the public pointrz[Length of string does not match lengths of any of the enabled ({0}) encodings of the curve.z, )rall ValueErrornormalise_bytes isinstance CurveEdTwrrSorderlenrr[ror`rhformatjoin) rmr-rUrnvalid_encodingskey_lenrVrYrZs r from_byteszAbstractPoint.from_bytes(sJD !???O  $       t$$ eY ' ' 2$$UD11 1d))(57799"5"55 ) ) )e.F.F"55)   GWW+a/ / /  ' '>_+L+LBQBx---(o2M2M##3-/@$$ bqbW$$?)J)J# #9H1$$ *@ *a/!3 3 3//"33D%@@ GWW% / : :;;  rc|}t||}t||}||zS)z.Convert the point to the :term:`raw encoding`.r-rnumber_to_stringrr)r primex_stry_strs r _raw_encodezAbstractPoint._raw_encode}sQ    511 511u}rc|}t||}|dzrd|zSd|zS)z*Encode the point into the compressed form.rr^r]r)r rrs r_compressed_encodez AbstractPoint._compressed_encodesX    511 6688a< #U? "rcl|}|dzrd|zSd|zS)z&Encode the point into the hybrid form.rrlrk)rr)r raw_encs r_hybrid_encodezAbstractPoint._hybrid_encodes=""$$ 6688a< %W$ $  rcF||||}}}t |dzdzdz}t ||d}|dzr|dxxdzcc<|S)z/Encode the point according to RFC8032 encoding.rrqrrrvr=rsrt)scalerrr-rrx int_to_bytes)r rrrenc_lenrs r_edwards_encodezAbstractPoint._edwards_encodes &&((DFFHHdjjllnn&6&6a1a==1$q(Q.Q22 q5  "III III rrcR|dvsJ|}t|tr|S|dkr|S|dkrd|zS|dkr|S|S)a Convert the point to a byte string. The method by default uses the :term:`raw encoding` (specified by `encoding="raw"`. It can also output points in :term:`uncompressed`, :term:`compressed`, and :term:`hybrid` formats. For points on Edwards curves `encoding` is ignored and only the encoding defined in RFC 8032 is supported. :return: :term:`raw encoding` of a public on the curve :rtype: bytes )rrrrrrrr)r-rrrrrr)r encodingr-s rto_byteszAbstractPoint.to_bytessJJJJJ  eY ' ' -'')) )   ##%% %  ' 'T--/// /  ! !&&(( (**,, ,rcg}|rL|dzr+|dz}|dkr|dz}||||z}n|d|dz}|L|S)z&Calculate non-adjacent form of number.r=r)append)multretnds r_nafzAbstractPoint._nafs{ ax AX77!GB 2  1 QJD  r)TN)r)r r!r"r# staticmethodr[rh classmethodrorrrrrrrrr$rrrQrQs<<  \ (\*[&  [ DBFR R R [R h!!!   ----6  \   rrQceZdZdZd"fd Ze d#fd ZdZdZd Z d Z d Z d Z d Z dZdZdZdZed$dZdZdZdZdZdZdZdZdZdZdZdZdZdZ d Z!d!Z"xZ#S)% PointJacobiu Point on a short Weierstrass elliptic curve. Uses Jacobi coordinates. In Jacobian coordinates, there are three parameters, X, Y and Z. They correspond to affine parameters 'x' and 'y' like so: x = X / Z² y = Y / Z³ NFc@tt|||_trHt |t |t |f|_|ot ||_n|||f|_||_||_g|_ dS)aF Initialise a point that uses Jacobi representation internally. :param CurveFp curve: curve on which the point resides :param int x: the X parameter of Jacobi representation (equal to x when converting from affine coordinates :param int y: the Y parameter of Jacobi representation (equal to y when converting from affine coordinates :param int z: the Z parameter of Jacobi representation (equal to 1 when converting from affine coordinates :param int order: the point order, must be non zero when using generator=True :param bool generator: the point provided is a curve generator, as such, it will be commonly used with scalar multiplication. This will cause to precompute multiplication table generation for it N) superrr_PointJacobi__curverzr{_PointJacobi__coords_PointJacobi__order_PointJacobi__generator_PointJacobi__precompute)r r-rrzr. generator __class__s rrzPointJacobi.__init__s" k4  ))+++  ! VVSVVSVV4DM /SZZDLL1IDM DL$rTctt|||||\}}t|||d||S)aP Initialise the object from byte encoding of a point. The method does accept and automatically detect the type of point encoding used. It supports the :term:`raw encoding`, :term:`uncompressed`, :term:`compressed`, and :term:`hybrid` encodings. :param data: single point encoding of the public key :type data: :term:`bytes-like object` :param curve: the curve on which the public key is expected to lay :type curve: ~ecdsa.ellipticcurve.CurveFp :param validate_encoding: whether to verify that the encoding of the point is self-consistent, defaults to True, has effect only on ``hybrid`` encoding :type validate_encoding: bool :param valid_encodings: list of acceptable point encoding formats, supported ones are: :term:`uncompressed`, :term:`compressed`, :term:`hybrid`, and :term:`raw encoding` (specified with ``raw`` name). All formats by default (specified with ``None``). :type valid_encodings: :term:`set-like object` :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 generation for it :raises `~ecdsa.errors.MalformedPointError`: if the public point does not lay on the curve or the encoding is invalid :return: Point on curve :rtype: PointJacobi r)rrr) rmr-rUrnrr.rrYrZrs rrzPointJacobi.from_bytessNT!c22== 4*O  5'7AuiHHHrc|jr|jrdS|j}|sJg}d}|dz}|j\}}}t |j||||}|dz}|||f||krl|dz}| }|||f||kl||_dS)Nrr=) rrrrrrrrrr4r)r r. precomputerDrYrZcoord_zdoublers r_maybe_precomputezPointJacobi._maybe_precompute!s  4#4  F     $(M!'dlGWguMM  799;; 4555%ii FAnn&&,,..G   wyy{{GIIKK8 9 9 9%ii 'rc8|j}|Sr)__dict__copyr states r __getstate__zPointJacobi.__getstate__;s  ""$$ rc:|j|dSr)rupdaters r __setstate__zPointJacobi.__setstate__Cs U#####rc|j\}}}|tur| St|tr+||d}}}n(t|t r |j\}}}ntS|j| krdS|j }||z|z} ||z|z} || z|| zz |zdko|| z|z|| z|zz |zdkS)z}Compare for equality two points with each-other. Note: only points that lay on the same curve can be equal. rFr) rr,rr&rrrNotImplementedrr-r) r r1x1y1z1ry2z2rzz1zz2s rr2zPointJacobi.__eq__Fs ] B H  6M eU # # "EGGIIqBBB { + + "JBBB! ! <5;;== ( (5 LNN  2gk2gk S28#q(A- HrMBHrM ) 33 rc||k S)z2Compare for inequality two points with each-other.r$r0s r__ne__zPointJacobi.__ne__bs5=  rc|jS)zIReturn the order of the point. None if it is undefined. )rrs rr.zPointJacobi.orderfs |rc|jS)z-Return curve over which the point is defined.)rrs rr-zPointJacobi.curvems |rc|j\}}}|dkr|S|j}tj||}||dzz|zS)aC 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. rr=rrrrr5)r r_rrs rrz PointJacobi.xqT-1a 66H LNN    $Q * *1a4x!|rc|j\}}}|dkr|S|j}tj||}||dzz|zS)aC 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. rr@r)r rrrrs rrz PointJacobi.yrrc|j\}}}|dkr|S|j}tj||}||z|z}||z|z}||z|z|z}||df|_|S)ze Return point scaled so that z == 1. Modifies point in place, returns self. rr)r rrrrz_invzz_invs rrzPointJacobi.scales -1a 66K LNN  (A.." JN J  "Aq   rc|j\}}}|j}||zstS||j\}}}|dksJt |j|||jS)zReturn point in affine form.r)rrrr,rr&r)r rrrrrs r to_affinezPointJacobi.to_affinesp-1a LNN  A O -1aAvvvvT\1a666rct|||d||S)a 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. r)rr-rrr.)pointrs r from_affinezPointJacobi.from_affinesC KKMM57799eggiiEKKMM9   rc||z|z||z|z}}|sdS||z|z}d||zdz|z |z z|z}d|z|z} | | zd|zz |z} | || z zd|zz |z} d|z|z} | | | fS)z"Add a point to itself with z == 1.rrrr=r@rrr$) r X1Y1rrXXYYYYYYSMTY3Z3s r_double_with_z_1zPointJacobi._double_with_z_1sb1b2gkB 7Bw{ "r'a"$t+ ,q 0 FQJ UQU]a 1q5kAH$ ) VaZ"byrcB|dkr|||||S|sdS||z|z||z|z}}|sdS||z|z}||z|z} d||zdz|z |z z|z} d|z|| z| zz|z} | | zd| zz |z} | | | z zd|zz |z} ||zdz|z | z |z}| | |fS)z#Add a point to itself, arbitrary z.rrr=r@rr)r)r rrZ1rrrrrZZrrrrrs r_doublezPointJacobi._doubles  77((RA66 6 7b1b2gkB 7Bw{ "Wq[ "r'a"$t+ ,q 0 Va"frk !Q & UQU]a 1q5kAH$ )Bw1nr!B&! +"byrc|j\}}}|stS|j|j}}||||||\}}}|stSt |j||||jS)zAdd a point to itself.)rr,rrrrrr) r rrrrrX3rrs rr4zPointJacobi.doubles] B O|~~!1!11\\"b"a33 B O4<RT\BBBrc||z }||z}d|z|z}||z} d||z z} |s1| s/|||||jS||z} | dz| z d| zz |z} | | | z zd|z| zz |z} d|z|z}| | |fS)z&add points when both Z1 and Z2 equal 1rr=rrr)r rrX2Y2rHHHIJrVrrrs r _add_with_z_1zPointJacobi._add_with_z_1s G U FQJ E bM F F((RDLNN4D4DEE E FdQhQ! #1r6lQVaZ'1 , UQY2rzrc||z dz|z}||z|z}||z} ||z dz|z} |s2| s0||||||jS| |z | z |z} ||z || z z|| |z zz |z} |||z z|z} | | | fS)zadd points when Z1 == Z2r=rrr)r rrrrrrABCDrrrs r_add_with_z_eqzPointJacobi._add_with_z_eq s"WNQ  FQJ F "WNQ  A A<<BAt|~~/?/?@@ @!eai1_Bw1r6"R1q5\1Q 6 27^a 2rzrcn||z|z}||z|z||z|z|z} }||z |z} | | z|z} d| z|z} | | z} d| |z z|z}|s1| s/|||||jS|| z}||z| z d|zz |z}|||z zd|z| zz |z}|| zdz|z | z |z}|||fS)zadd points when Z2 == 1rr=r)r rrrrrrZ1Z1U2S2rrrrrrrrrs r_add_with_z2_1zPointJacobi._add_with_z2_1sBw{dQR$ 2B "WM UQY FQJ E bMA  F F((RDLNN4D4DEE E F!eai!a%1 $1r6lQVaZ'1 ,Av!md"R'1 ,2rzrc||z|z}||z|z} || z|z} ||z|z} ||z| z|z} ||z|z|z} | | z }d|z|z|z}||z|z}d| | z z|z}|s2|s0||||||jS| |z}||z|z d|zz |z}|||z zd| z|zz |z}||zdz|z | z |z|z}|||fS)zadd points with arbitrary zrr=r)r rrrrrZ2rrZ2Z2U1rS1rrrrrrrrrs r_add_with_z_nezPointJacobi._add_with_z_ne/s<Bw{Bw{ $Y] $Y] "Wt^a  "Wt^a  G EAIM EAI bMA  A A<<BAt|~~/?/?@@ @ F!eai!a%1 $1r6lQVaZ'1 ,Bw1nt#d*a /! 32rzrc ||zS)zAdd other to self.r$r0s r__radd__zPointJacobi.__radd__F e|rc v|s||z||z||zfS|s||z||z||zfS||kr9|dkr||||||S|||||||S|dkr|||||||S|dkr|||||||S||||||||S)z&add two points, select fastest method.r)rr rr)r rrrrrrrs r_addzPointJacobi._addJs *62626) ) *62626) ) 88Qww))"b"b!<<<&&r2r2r1== = 77&&r2r2r1== = 77&&r2r2r1== =""2r2r2r1===rc |tkr|S|tkr|St|trt|}|j|jkrt d|j}|j\}}}|j\}}}| |||||||\} } } | stSt|j| | | |j S)z!Add two points on elliptic curve.z%The other point is on different curve) r,rr&rrrrrrrr) r r1rrrrrrrrrrs rr9zPointJacobi.__add__Zs 8  L H  K eU # # 3++E22E <5= ( (DEE E LNN  ] B^ BYYr2r2r2q99 B O4<RT\BBBrc ||zS)Multiply point by an integer.r$r0s rrGzPointJacobi.__rmul__orrc Zddd|jf\}}}}|j}|jD]U\}}|dzrF|dzdkr|dzdz}|||||| d|\}}}2|dz dz}||||||d|\}}}P|dz}V|stSt |j||||jS)z4Multiply point by integer with precomputation table.rr=rr)rrrrr,rr) r r1rrrrrrrs r_mul_precomputezPointJacobi._mul_precomputess1a!1!11 BAy'  FBqy 19>>"QY1,E!%b"b"rc1a!@!@JBBB"QY1,E!%b"b"b!Q!?!?JBBB!  O4<RT\BBBrc |jdr|stS|dkr|S|jr ||jdzz}||jr||S|}|j\}}}d\}}}|j|j } }|j } |j } t| |D]M} | ||||| \}}}| dkr| ||||| d|\}}}2| dkr| |||||d|\}}}N|stSt|j||||jS)r rr=rr)rr,rrrr"rrrrrrreversedrr) r r1rrrrrrrrrrrDs rrEzPointJacobi.__mul__s}Q u O A::K < /T\A-.E      /''.. .zz||M B B|~~!1!11,y$))E**++ < > ) )sc)nns8}}<=HHH ]]S^^ + +s8}}s9~~=>JI),, M MDAq RQ22JBBAvv66UU!%b"b"rc2q!A!AJBBBq5555!%b"b"b"a!@!@JBBBQ66!%b"b"rc2q!A!AJBBBUU!%b"b&&&!!L!LJBBBq5555!%b"b&&&!!L!LJBBB1uuuu66!%b"b"b"a!@!@JBBBUU!%b"b&&&!!L!LJBBBq5555!%b"b&&&!!L!LJBBB O4<RT\BBBrcT|j\}}}t|j|| ||jS)zReturn negated point.)rrrr)r rrrs r__neg__zPointJacobi.__neg__ s+-1a4<QB4<@@@r)NF)TNNF)F)$r r!r"r#rrrrrrr2rr.r-rrrrrrrrr4rr rrrrr9rGr"rEr9r; __classcell__)rs@rrrsG8 ,I,I,I,I,I[,I\'''4$$$8!!!  ( 7 7 7    \  , , C C C"   &.>>> CCC*CCC&CCCB`C`C`CDAAAAAAArrN) __future__rrobjectrr&rQrr,r$rrr@sF LLLLLfLLL4FBEEEEEFEEEPA AA AA AA AA A-A AA AA AH 5tT " "r