o 6Î h§Eã @s8ddlmZddlZddlmZmZddlmZzeWn e y'e ZYnwzddl m Z m Z dZdZWn!eyWdZz ddlm Z dZWn eyTdZYnwYnwes\ergeeee d ƒƒfƒZddlZddlZddlZd d lmZGd d „d eƒZGd d„deƒZGdd„deƒZGdd„deƒZdd„Zdd„Zdd„Z dd„Z!dd„Z"dd„Z#er¸dd „Z$ner¿d!d „Z$nej%d"krÉd#d „Z$nd$d „Z$zej&Z'Wn e(yßd%d&„Z'Ynwd'd(„Z&d)d*„Z)d+d,„Z*d-d.„Z+d/d0„Z,d1d2„Z-d3d4„Z.d5d6„Z/d7d8„Z0d9d:„Z1d;d<„Z2d=d>„Z3d?d@„Z4gdA¢Z5da6dS)Bé)ÚdivisionN)Ú integer_typesÚPY2)Úreduce)ÚpowmodÚmpzTF©ré)Ú bit_lengthc@seZdZdZdS)ÚErrorz)Base class for exceptions in this module.N)Ú__name__Ú __module__Ú __qualname__Ú__doc__©rrúf/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/ecdsa/numbertheory.pyr /sr c@ó eZdZdS)Ú JacobiErrorN©r r rrrrrr5órc@r)ÚSquareRootErrorNrrrrrr9rrc@r)ÚNegativeExponentErrorNrrrrrr=rrcCs,t dt¡|dkrtd|ƒ‚t|||ƒS)z+Raise base to exponent, reducing by moduluszRFunction is unused in library code. If you use this code, change to pow() builtin.rz#Negative exponents (%d) not allowed)ÚwarningsÚwarnÚDeprecationWarningrÚpow)ÚbaseÚexponentÚmodulusrrrÚ modular_expAsýÿ rcCsš|ddksJ‚t|ƒdksJ‚t|ƒt|ƒkrK|ddkr=tdt|ƒdƒD]}|| |d|| ||| <q'|dd…}t|ƒt|ƒks|S)zReduce poly by polymod, integer arithmetic modulo p. Polynomials are represented as lists of coefficients of increasing powers of x.éÿÿÿÿr ré)ÚlenÚxrange)ÚpolyÚpolymodÚpÚirrrÚpolynomial_reduce_modPs  ( ür(cCsrt|ƒt|ƒddg}tt|ƒƒD]}tt|ƒƒD]}|||||||||||<qqt|||ƒS)z—Polynomial multiplication modulo a polynomial over ints mod p. Polynomials are represented as lists of coefficients of increasing powers of x.r r)r"r#r()Úm1Úm2r%r&Úprodr'ÚjrrrÚpolynomial_multiply_modgs  *ÿ r-cCs~||ksJ‚|dkr dgS|}|}|ddkr|}ndg}|dkr=|d}t||||ƒ}|ddkr9t||||ƒ}|dks!|S)z—Polynomial exponentiation modulo a polynomial over ints mod p. Polynomials are represented as lists of coefficients of increasing powers of x.rr r!)r-)rrr%r&ÚGÚkÚsrrrÚpolynomial_exp_mods   ür1cCsâ|dkstdƒ‚|ddkstdƒ‚||}|dkrdS|dkr"dS|d}}|ddkr<|d|d}}|ddks-|ddksN|ddksN|ddkrQd}nd }|dkrY|S|d dkrh|d dkrh| }|t|||ƒS) z Jacobi symbolézn must be larger than 2r!r z n must be oddréér é)rÚjacobi)ÚaÚnÚa1Úer0rrrr6Ÿs*     ÿ$r6cCsvd|kr |ksJ‚J‚d|ksJ‚|dkrdS|dkr |St||ƒ}|dkr1td||fƒ‚|ddkrAt||dd|ƒS|dd kryt||dd|ƒ}|dkr_t||dd|ƒS||dksgJ‚d|td||d d|ƒ|Strtd |ƒ}n|}td|ƒD].}t||d||ƒdkr¶|| df}td |dd||ƒ}|dr°td ƒ‚|dSqˆtd ƒ‚)z)Modular square root of a, mod p, p prime.rr r!r z%d has no square root modulo %dr5r2r3éiÿÿÿ)rr zp is not primez No b found.)r6rrrÚminr#r1Ú RuntimeError)r7r&ÚjacÚdÚ range_topÚbÚfÚffrrrÚsquare_root_mod_prime¿s:    $   ûrDcCó|dkrdSt|d|ƒS©úInverse of a mod m.rr )r©r7ÚmrrrÚ inverse_modòó rJcCs€|dkrdSt|ƒ}t|ƒ}tdƒtdƒ}}|||}}|dkr<||}||||||||f\}}}}|dks"||S)rGrr r©r7rIÚlmÚhmÚlowÚhighÚrrrrrJús$þ)r2r3cCrErF)rrHrrrrJrKcCsf|dkrdSd\}}|||}}|dkr/||}||||||||f\}}}}|dks||S)rGr)r rr rrLrrrrJs$þcCs|r |||}}|s|S)z1Greatest common divisor using Euclid's algorithm.r©r7rArrrÚgcd2*sÿrScGó:t|ƒdkr tt|ƒSt|ddƒrtt|dƒS|dS)zRGreatest common divisor. Usage: gcd([ 2, 4, 6 ]) or: gcd(2, 4, 6) r rÚ__iter__)r"rrSÚhasattr©r7rrrÚgcd1ó  rXcCs||t||ƒS)z&Least common multiple of two integers.)rXrRrrrÚlcm2?srZcGrT)zPLeast common multiple. Usage: lcm([ 3, 4, 5 ]) or: lcm(3, 4, 5) r rrU)r"rrZrVrWrrrÚlcmErYr[cCsNt|tƒsJ‚|dkr gSg}tD]6}||krn/t||ƒ\}}|dkrGd}||kr@|}t||ƒ\}}|dkr8n|d}||ks*| ||f¡q|tdkr¥t|ƒr[| |df¡|Std} |d}t||ƒ\}}||krpn*|dkr™d}|}||kr’t||ƒ\}}|dkrˆn |}|d}||ks|| ||f¡q`|dkr¥| |df¡|S)z2Decompose n into a list of (prime,exponent) pairs.r!rr r )Ú isinstancerÚ smallprimesÚdivmodÚappendÚis_prime)r8Úresultr?ÚqrQÚcountrrrÚ factorizationSsXû€ ìûñrdcCs‚t dt¡t|tƒs J‚|dkrdSd}t|ƒ}|D]#}|d}|dkr6||d|d|dd}q||dd}q|S)z'Return the Euler totient function of n.ú{Function is unused by library code. If you use this code, please open an issue in https://github.com/tlsfuzzer/python-ecdsar2r r)rrrr\rrd)r8rarCrBr:rrrÚphi‹sü"rfcCst dt¡tt|ƒƒS)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. re)rrrÚcarmichael_of_factorizedrd)r8rrrÚ carmichael¥s ü rhcCsRt dt¡t|ƒdkrdSt|dƒ}tdt|ƒƒD] }t|t||ƒƒ}q|S)zlReturn the Carmichael function of a number that is represented as a list of (prime,exponent) pairs. rer r)rrrr"Úcarmichael_of_ppowerr#r[)Úf_listrar'rrrrg¶sü  rgcCsDt dt¡|\}}|dkr|dkrd|dS|d||dS)z:Carmichael function of the given power of the given prime.rer!r )rrr)Úppr&r7rrrriÌsü ricCsZt dt¡|dkr dSt||ƒdksJ‚|}d}|dkr+|||}|d}|dks|S)z8Return the order of x in the multiplicative group mod m.rer r)rrrrX)ÚxrIÚzrarrrÚ order_modÝsü  þrncCsLt dt¡ t||ƒ}|dkr |S|} t||ƒ\}}|dkr"n|}qq)z5Return the largest factor of a relatively prime to b.rer r)rrrrXr^)r7rAr?rbrQrrrÚlargest_factor_relatively_prime÷s"ü úüûrocCst dt¡t|t||ƒƒS)z}Return the order of x in the multiplicative group mod m', where m' is the largest factor of m relatively prime to x. re)rrrrnro)rlrIrrrÚkinda_order_mods ürpc Csdda|tdkr|tvrdSdSt|dƒdkrdSd}dt|ƒ}d|kr,d ks/J‚J‚d D] \}}||kr;n|}q1d}|d}|d dkrX|d}|d }|d dksJt|ƒD]S}t t¡}t|||ƒ} | dkr¯| |dkr¯d} | |dkr¢| |dkr¢t| d |ƒ} | dkr’|dadS| d} | |dkr¢| |dks| |dkr¯|dadSq\dS) a@Return True if x is prime, False otherwise. 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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 é(é i@) )édé)é–é)éÈé)éúé )i,é )i^r3)ir4)iÂé)i&r;)iŠr5)iRr2)ir!r!)Úmiller_rabin_test_countr]rXr r#ÚrandomÚchoicer) r8ÚtÚn_bitsr/Úttr0rQr'r7Úyr,rrrr`sJ     þ    û €r`cCs4|dkrdS|ddB}t|ƒs|d}t|ƒr|S)z9Return the smallest prime larger than the starting value.r!r )r`)Ústarting_valuerarrrÚ next_primels ÿr…)Ér!r2r;r4rré éééééé%é)é+é/é5é;é=éCéGéIéOéSéYéaéeégékéméqééƒé‰é‹é•é—éé£é§é­é³éµé¿éÁéÅéÇéÓéßéãéåéééïéñéûiii iiiii%i3i7i9i=iKiQi[i]iaigioiui{ii…ii‘i™i£i¥i¯i±i·i»iÁiÉiÍiÏiÓißiçiëiói÷iýi i ii#i-i3i9i;iAiKiQiWiYi_ieiiikiwiiƒi‡ii“i•i¡i¥i«i³i½iÅiÏi×iÝiãiçiïiõiùiiiii)i+i5i7i;i=iGiUiYi[i_imiqisiwi‹ii—i¡i©i­i³i¹iÇiËiÑi×ißiåiñiõiûiýii iiii%i'i-i?iCiEiIiOiUi]iciiiii‹i“ii£i©i±i½iÁiÇiÍ)7Ú __future__rÚsysÚsixrrÚ six.movesrr#Ú NameErrorÚrangeÚgmpy2rrÚGMPY2ÚGMPYÚ ImportErrorÚgmpyÚtupleÚtypeÚmathrr~Úutilr Ú Exceptionr rrrrr(r-r1r6rDrJÚ version_inforXrSÚAttributeErrorrZr[rdrfrhrgrirnrorpr`r…r]r}rrrrÚs†   ÿ   ÿ€ú    1       þ 8O M