qtjEddlmZddlZddlmZmZddlmZ en #e $re ZYnwxYw ddl m Z m Z dZdZn$#e$rdZ ddlm Z dZn #e$rdZYnwxYwYnwxYweser!eeee d fzZddlZddlZddlZd d lmZGd d eZGd deZGddeZGddeZdZdZdZ dZ!dZ"dZ#erdZ$nerdZ$nej%dkrdZ$ndZ$ ej&Z'n#e($rdZ'YnwxYwdZ&d Z)d!Z*d"Z+d#Z,d$Z-d%Z.d&Z/d'Z0d(Z1d)Z2d*Z3d+Z4gd,Z5da6dS)-)divisionN) integer_typesPY2)reduce)powmodmpzTFr) bit_lengthceZdZdZdS)Errorz)Base class for exceptions in this module.N)__name__ __module__ __qualname____doc__P/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/ecdsa/numbertheory.pyr r /s33Drr ceZdZdS) JacobiErrorNrrrrrrrr5DrrceZdZdS)SquareRootErrorNrrrrrr9rrrceZdZdS)NegativeExponentErrorNrrrrrr=rrrctjdt|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%AsY M # !||# 1H <    tXw ' ''rc|ddksJt|dksJt|t|kr||ddkrFtdt|dzD]%}|| |d|| zz |z|| <&|dd}t|t|k||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;!     w<>V1&)<<== Mrctjdt|\}}|dkr|dkrd|dz zS|dz ||dz zzS)z:Carmichael function of the given power of the given prime.rwr(r )rrr )ppr-rAs rr}r}sc M 4   DAqAvv!a%%QU|Aq1u%%rctjdt|dkrdSt||dksJ|}d}|dkr||z|z}|dz}|dk|S)z8Return the order of x in the multiplicative group mod m.rwr r)rrr rf)xrTzrrs r order_modrs M 4   Avvq q!99>>>> A F q&& UaK! q&& Mrctjdt t||}|dkrn!|} t ||\}}|dkrn|}8|S)z5Return the largest factor of a relatively prime to b.rwr r)rrr rfro)rArLrJrsr\s rlargest_factor_relatively_primers} M 4    1II 66   !Q< >>rcrda|tdkr |tvrdSdSt|ddkrdSd}dt|z}d|cxkrd ksnJd D]\}}||krn|}d}|dz }|d zdkr|dz}|d z}|d zdkt |D]}t jt}t|||} | dkrd| |dz kr[d} | |dz kr?| |dz kr6t| d |} | dkr|dzadS| dz} | |dz kr | |dz k6| |dz kr|dzadSdS) 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 rrqrqs& KO  45 1d||qu A A F  5  2 A:: E  A AA q5Q,, E F q5Q,,AYY   M+ & & 1aLL 66a1q5jjAq1u**a!e1aLL66./!e+ 55E q1u**a!e AEzz*+a%'uu 4rcl|dkrdS|dzdz}t|s|dz}t||S)z9Return the smallest prime larger than the starting value.r(r )rq)starting_valuerrs r next_primerlsSqq 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  """""""" FF FFF !!!!!!!! E DD E   ;D;E-44A<