V.jEbddlmZddlZddlmZmZddlmZ e ddl m Z m Z dZdZesereeee d fzZddlZddlZddlZd d lmZGd d eZGd deZGddeZGddeZdZdZdZ dZ!dZ"dZ#erdZ$nerdZ$nejJdk\rdZ$ndZ$ ejLZ'dZ&d Z)d!Z*d"Z+d#Z,d$Z-d%Z.d&Z/d'Z0d(Z1d)Z2d*Z3d+Z4gd,Z5da6y#e $re ZYwxYw#e$rdZ ddlm Z dZn #e$rdZYnwxYwYwxYw#e($rdZ'YiwxYw)-)divisionN) integer_typesPY2)reduce)powmodmpzTFr) bit_lengthceZdZdZy)Errorz)Base class for exceptions in this module.N)__name__ __module__ __qualname____doc__TC:\xampp\htdocs\tradingbinance\backend\.venv\Lib\site-packages\ecdsa/numbertheory.pyr r /s3rr c eZdZy) JacobiErrorNrrrrrrrr5rrc eZdZy)SquareRootErrorNrrrrrr9rrrc eZdZy)NegativeExponentErrorNrrrrrr=rrrcvtjdt|dkrtd|zt |||S)z+Raise base to exponent, reducing by moduluszRFunction is unused in library code. If you use this code, change to pow() builtin.rz#Negative exponents (%d) not allowed)warningswarnDeprecationWarningrpow)baseexponentmoduluss r modular_expr%AsG MM # !|# 1H <   tXw ''rc |ddk(sJt|dkDsJt|t|k\r\|ddk7r7tdt|dzD]}|| |d|| zz |z|| <|dd}t|t|k\r\|S)zReduce poly by polymod, integer arithmetic modulo p. Polynomials are represented as lists of coefficients of increasing powers of x.r r)lenxrange)polypolymodpis rpolynomial_reduce_modr/Ps 2;!   wd}|}||kr"t||\}}|dk7rn |}|dz}||kr"|j ||f^|dkDr|j |df|S)z2Decompose n into a list of (prime,exponent) pairs.r(rr r') isinstancer smallprimesdivmodappendis_prime)rBresultrJqr\counts r factorizationruSsx a '' '1u F q5 a|1 6Eq&a|16  q& MM1e* %" ;r? A; MM1a& !, M)BAEa|1q56EAq&%a|16! %  q& MM1e*- 1u q!f% Mrctjdtt|tsJ|dkryd}t |}|D]/}|d}|dkDr||d|dz zz|ddz z}%||ddz z}1|S)z'Return the Euler totient function of n.{Function is unused by library code. If you use this code, please open an issue in https://github.com/tlsfuzzer/python-ecdsar<r r)rrr rmrru)rBrrrNrMrDs rphirxs MM 4   a '' '1u F q B  aD q5adq1uo-1:Fqtax(F  Mrc^tjdttt |S)zReturn Carmichael function of n. Carmichael(n) is the smallest integer x such that m**x = 1 mod n for all m relatively prime to n. rw)rrr carmichael_of_factorizedru)rBs r carmichaelr{s, MM 4   $M!$4 55rctjdtt|dkryt |d}t dt|D]}t |t ||}|S)zlReturn the Carmichael function of a number that is represented as a list of (prime,exponent) pairs. rwr r)rrr r)carmichael_of_ppowerr*rk)f_listrrr.s rrzrzsj  MM 4   6{Q !&) ,F As6{ #V1&)<=$ Mrctjdt|\}}|dk(r |dkDrd|dz zS|dz ||dz zzS)z:Carmichael function of the given power of the given prime.rwr(r )rrr )ppr-rAs rr}r}sW MM 4   DAqAv!a%QU|Aq1u%%rctjdt|dkryt||dk(sJ|}d}|dk7r||z|z}|dz}|dk7r|S)z8Return the order of x in the multiplicative group mod m.rwr r)rrr rf)xrTzrrs r order_modrso MM 4   Av q!9>> A F q& UaK! q& Mrctjdt t||}|dkr |S|} t ||\}}|dkDrn|}0)z5Return the largest factor of a relatively prime to b.rwr r)rrr rfro)rArLrJrsr\s rlargest_factor_relatively_primersm MM 4   1I 6  H !Q>rc(da|tdkr |tvryyt|ddk7ryd}dt|z}d|cxkrd ksJJd D]\}}||krn|}d}|dz }|d zdk(r|dz}|d z}|d zdk(rt |D]}t j t}t|||} | dk7s/| |dz k7s8d} | |dz kr7| |dz k7r/t| d |} | dk(r|dzay| dz} | |dz kr | |dz k7r/| |dz k7s|dzayy) a@Return True if x is prime, False otherwise. We use the Miller-Rabin test, as given in Menezes et al. p. 138. This test is not exact: there are composite values n for which it returns True. In testing the odd numbers from 10000001 to 19999999, about 66 composites got past the first test, 5 got past the second test, and none got past the third. Since factors of 2, 3, 5, 7, and 11 were detected during preliminary screening, the number of numbers tested by Miller-Rabin was (19999999 - 10000001)*(2/3)*(4/5)*(6/7) = 4.57 million. rr'TFi r ( i@) )d))) )i, )i^r=)ir>)i)i&rF)ir?)iRr<)ir(r()miller_rabin_test_countrnrfr r*randomchoicer!) rBtn_bitsr8ttr9r\r.rAyr4s rrqrqst& KO  1d|q A A F  5    2 A:  ! ( A AA q5Q, E F q5Q,AY MM+ & 1aL 6a1q5jAq1u*a!e1aL6./!e+ E q1u*a!e AEz*+a%' rcZ|dkry|dzdz}t|s|dz}t|s|S)z9Return the smallest prime larger than the starting value.r(r )rq)starting_valuerrs r next_primerls>q A %Fv!v Mr)r(r<rFr>r %)+/5;=CGIOSYaegkmqiii iiiii%i3i7i9i=iKiQi[i]iaigioiui{iiiiiiiiiiiiiiiiiiiiiii i ii#i-i3i9i;iAiKiQiWiYi_ieiiikiwiiiiiiiiiiiiiiiiiiiiiiiii)i+i5i7i;i=iGiUiYi[i_imiqisiwiiiiiiiiiiiiiiiiiiii iiii%i'i-i?iCiEiIiOiUi]iciiiiiiiiiiiiii)7 __future__rsyssixrr six.movesrr* NameErrorrangegmpy2rrGMPY2GMPY ImportErrorgmpytupletypemathrrutilr Exceptionr rrrr%r/r5r:r@rOrU version_inforfraAttributeErrorrirkrurxr{rzr}rrrrqrrnrrrrrs "  ! E D D-4A