GIF89a=( õ' 7IAXKgNgYvYx\%wh…hŽth%ˆs%—x¨}9®Œ©€&©‰%¶†(¹–.¹5·œD¹&Çš)ÇŸ5ǘ;Í£*È¡&Õ²)ׯ7×µ<Ñ»4ï°3ø‘HÖ§KͯT÷¨Yÿšqÿ»qÿÔFØ !ù ' !ÿ NETSCAPE2.0 , =( þÀ“pH,È¤rÉl:ŸÐ¨tJ­Z¯Ø¬vËíz¿à°xL.›Ïè´zÍn»ßð¸|N¯Ûïø¼~Ïïûÿ€‚ƒ„…†‡ˆ‰Š‹ŒŽ‘’“”•–—˜™š›œžŸ ¡¢£¤¥¦§gª«ªE¯°¨¬ª±²Œ¹º¹E¾­”´ÂB¶¯ §Åȸ»ÑD¾¿Á•ÄÅ®° ÝH¾ÒLÀÆDÙ«D¶BÝïðÀ¾DÑÑÔTÌÍíH òGö¨A RÎڐ |¥ ٭&ºìE8œ¹kGÔAÞpx­a¶­ã R2XB®åE8I€Õ6Xî:vT)äžþÀq¦è³¥ì仕F~%xñ  4#ZÔ‰O|-4Bs‘X:= QÉ œš lºÒyXJŠGȦ|s hÏíK–3l7·B|¥$'7Jީܪ‰‡àá”Dæn=Pƒ ¤Òëí‰`䌨ljóá¯Éüv>á–Á¼5 ½.69ûϸd«­ºÀûnlv©‹ªîf{¬ÜãPbŸ  l5‘Ž¯pß ´ ˜3aÅùäI«O’ý·‘áÞ‡˜¾Æ‚ÙÏiÇÿ‹Àƒ #öó)pâš Þ½ ‘Ý{ó)vmÞü%D~ 6f s}ŃƒDØW Eþ`‡þ À…L8xá†ç˜{)x`X/> Ì}mø‚–RØ‘*|`D=‚Ø_ ^ð5 !_…'aä“OÚ—7âcð`D”Cx`ÝÂ¥ä‹éY¹—F¼¤¥Š?¡Õ™ n@`} lď’ÄÉ@4>ñd œ à‘vÒxNÃ×™@žd=ˆgsžG±æ ´²æud &p8Qñ)ˆ«lXD©øÜéAžHìySun jª×k*D¤LH] †¦§C™Jä–´Xb~ʪwStŽ6K,°£qÁœ:9ت:¨þªl¨@¡`‚ûÚ ».Û¬¯t‹ÆSÉ[:°=Š‹„‘Nåû”Ìî{¿ÂA ‡Rà›ÀÙ6úë°Ÿð0Ä_ ½;ÃϱîÉì^ÇÛÇ#Ëë¼ôº!±Ä˜íUîÅÇ;0L1óÁµö«p% AÀºU̬ݵ¼á%霼€‡¯Á~`ÏG¯»À× ­²± =4ªnpð3¾¤³¯­ü¾¦îuÙuµÙ®|%2ÊIÿür¦#0·ÔJ``8È@S@5ê¢ ö×Þ^`8EÜ]ý.뜃Âç 7 ú ȉÞj œ½Dç zý¸iþœÑÙûÄë!ˆÞÀl§Ïw‹*DçI€nEX¯¬¼ &A¬Go¼QföõFç°¯;é¦÷îŽêJ°îúôF5¡ÌQ|îúöXªæ»TÁÏyñêï]ê² o óÎC=öõ›ÒÓPB@ D×½œä(>èCÂxŽ`±«Ÿ–JЀ»Û á¤±p+eE0`ëŽ`A Ú/NE€Ø†À9‚@¤à H½7”à‡%B‰`Àl*ƒó‘–‡8 2ñ%¸ —€:Ù1Á‰E¸àux%nP1ð!‘ðC)¾P81lÑɸF#ˆ€{´âé°ÈB„0>±û °b¡Š´±O‚3È–Ù()yRpbµ¨E.Z‘D8ÊH@% òŒx+%Ù˜Æcü »¸˜fõ¬b·d`Fê™8èXH"ÉÈ-±|1Ô6iI, 2““¬$+](A*jÐ QTÂo‰.ÛU슬Œã„Ž`¯SN¡–¶Äåyše¯ª’­¬‚´b¦Éož œ)åyâ@Ì®3 ÎtT̉°&Ø+žLÀf"Ø-|žçÔ>‡Ðv¦Ðžì\‚ Q1)Ž@Žh#aP72”ˆ™¨$‚ !ù " , =( …7IAXG]KgNgYvYxR"k\%w]'}hŽth%ˆg+ˆs%—r.—m3šx3˜x¨}9®€&©€+¨‡7§‰%¶†(¹–.¹œD¹&ǘ;Í•&ײ)×»4ïÌ6ò§KÍ þ@‘pH,È¤rÉl:ŸÐ¨tJ­Z¯Ø¬vËíz¿à°xL.›Ïè´zÍn»ßð¸|N¯Ûïø¼~Ïïûÿ€‚ƒ„…†‡ˆ‰Š‹ŒŽ‘’“”•–—˜™š›œžŸ ¡¢£¤¥¦§g «¬ E ±± ¨­¶°ººE Á´”·®C¬²§Ç¶Œ»ÓDÃÕƷ¯Ê±H½ºM×ÁGÚ¬D¶BËÁ½î½DÓôTÏÛßîG»ôõC×CÌ l&âž:'òtU³6ɹ#·Ø)€'Ü.6±&ëÍÈ» K(8p0N?!æ2"ÛˆNIJX>R¼ÐO‚M '¡¨2¸*Ÿþ>#n↠å@‚<[:¡Iïf’ ¤TÚ˘CdbÜÙ“[«ŽEú5MBo¤×@€`@„€Êt W-3 ¶Ÿ¡BíêäjIÝ…Eò9[T…$íêﯧ„…•s»Óȳ¹€ÅÚdc®UUρ#±Ùïldj?´í¼²`\ŽÁðÞu|3'ÖŒ]ë6 ¶S#²‡˜FKLÈ *N E´‘áäŠ$˜›eÄYD„ºq«.è촁ƒs \-ÔjA 9²õ÷å- üúM[Âx(ís÷ì®x€|í¡Ù’p¦‚ ŽkÛTÇDpE@WÜ ²Ç]kŠ1¨ þ€·Yb ÓÁ‰l°*n0 ç™—žzBdОu¾7ĉBl€â‰-ºx~|UåU‰  h*Hœ|e"#"?vpÄiŠe6^ˆ„+qâŠm8 #VÇá ‘å–ÄV„œ|Šè•m"сœn|@›U¶ÆΞ—Špb¥G¨ED”€±Úê2FÌIç? >Éxå Œ± ¡¤„%‘žjŸ‘ꄯ<Ìaà9ijÐ2˜D¦È&›†Z`‚å]wþ¼Â:ç6àB¤7eFJ|õÒ§Õ,¨äàFÇ®cS·Ê¶+B°,‘Þ˜ºNûãØ>PADÌHD¹æž«ÄÀnÌ¥}­#Ë’ë QÀÉSÌÂÇ2ÌXÀ{æk²lQÁ2«ÊðÀ¯w|2Í h‹ÄÂG€,m¾¶ë3ÐÙ6-´ÅE¬L°ÆIij*K½ÀÇqï`DwVÍQXœÚÔpeœ±¬Ñ q˜§Tœ½µƒ°Œìu Â<¶aØ*At¯lmEØ ü ôÛN[P1ÔÛ¦­±$ÜÆ@`ùåDpy¶yXvCAyåB`ŽD¶ 0QwG#¯ æš[^Äþ $ÀÓÝǦ{„L™[±úKÄgÌ;ï£S~¹ìGX.ôgoT.»åˆ°ùŸûù¡?1zö¦Ÿž:ÅgÁ|ìL¹ „®£œŠ‚à0œ]PÁ^p F<"•ç?!,ñ‡N4—…PÄ Á„ö¨Û:Tè@hÀ‹%táÿ:ø-žI<`þ‹p I….)^ 40D#p@ƒj4–؀:²‰1Øâr˜¼F2oW¼#Z†;$Q q” ‘ ÂK¦ñNl#29 !’F@¥Bh·ᏀL!—XFóLH‘Kh¤.«hE&JòG¨¥<™WN!€ÑÙÚˆY„@†>Œž19J" 2,/ &.GXB%ÌRÈ9B6¹W]’î×ÔW¥’IÎ$ ñ‹ÓŒE8YÆ ¼³™ñA5“à®Q.aŸB€&Ø©³ JÁ—! ¦t)K%tœ-¦JF bòNMxLôþ)ÐR¸Ð™‘ èÝ6‘O!THÌ„HÛ ‰ !ù ) , =( …AXKgNgYvYxR"k\%wh…hŽh%ˆg+ˆs%—r.—x3˜x¨}9®€&©€+¨Œ,©‡7§‰%¶†(¹–.¹5·&Çš)ǘ;Í•&×£*Ȳ)ׯ7×»4ï°3øÌ6ò‘HÖ§KÍ»Hó¯T÷¨Yÿ»qÿÇhÿ þÀ”pH,È¤rÉl:ŸÐ¨tJ­Z¯Ø¬vËíz¿à°xL.›Ïè´zÍn»ßð¸|N¯Ûïø¼~Ïïûÿ€‚ƒ„…†‡ˆ‰Š‹ŒŽ‘’“”•–—˜™š›œžŸ ¡¢£¤¥¦§g ª« E$±²¨ª­ · °²½$E$ÂÕ««D· Í ¿¦Ç¶¸ÌŒ¾³CÃÅÆ E ééH½MÛÂGâªD­ çBêêϾD²ÒaÀà€Š1r­ðÓ¤ ÔožzU!L˜C'¾yW½UGtäÇïÙllê0×àÂuGþ)AÀs[þ·xì ÁxO%ƒûX2ó—  P£n›R/¡ÑšHše+êDm?# —‘Ç£6¡8íJ¡ŸâDiäªM¥Ö„ôj“¬¹£5oQ7°- <‡ *´lãÓŒ2r/a!l)dÈ A™ÈE¢ôÔ͆…ð ;Ö˜c ¡%ß‚’Ùˆâ¸b½—pe~C"BíëÚHïeF2§æŠ8qb t_`urŠeü wÅu3êæPv§h•"ß`íÍxçLĹÜÖ3á  ~Öº“®›¸ÏMDfJÙ °„ÛµáWõ%§œ‚à©–‚X Ó؁)@®Ñ›Eþ´wëuÅSxb8y\mÖzœ¥§ZbºE—ÂLªÌw!y(>¡™wú=Ç|ÅÝs¢d €CÁW)HÜcC$€L Ä7„r.á\{)@ð` @ äXÈ$PD” `šaG:§æˆOˆ72EÐamn]ù"ŒcÊxÑŒ° &dR8`g«iÙŸLR!¦P …d’ä¡“¦ðÎTƒ¦ià|À _ ¥ Qi#¦Šg›Æ ›noMµ ›V ã£)p ç£ÎW…š=Âeªk§†j„ ´®1ß²sÉxéW«jšl|0¯B0Û, \jÛ´›6±¬¶C ÛíWþï|ëÙ‹¸ñzĸV {ì;Ýñn¼òVˆm³I¼³.Ðã¤PN¥ ²µ¼„µCã+¹ÍByî£Ñ¾HŸ›ëê 7ìYÆFTk¨SaoaY$Dµœìï¿Ã29RÈkt Çïfñ ÇÒ:ÀÐSp¹3ÇI¨â¥DZÄ ü9Ïýögñ½­uÔ*3)O‘˜Ö[_hv ,àî×Et Ÿé¶BH€ Õ[ü±64M@ÔSÌM7dÐl5-ÄÙU܍´©zߌ3Ô€3ž„ „ ¶ÛPô½5×g› êÚ˜kN„Ý…0Îj4€Ìë°“#{þÕ3S2çKÜ'ợlø¼Ú2K{° {Û¶?žm𸧠ËI¼nEò='êüóºè^üæÃ_Û=°óž‚ì#Oý¿Í'¡½áo..ÏYìnüñCœO±Áa¿¢Kô½o,üÄËbö²çºíï{ËC Ú— "”Ï{ËK ÍÒw„õ±Oz dÕ¨à:$ ƒô—«v»] A#ð «€¿šéz)Rx׿ˆ¥‚d``èw-îyÏf×K!ð€þ­Ð|ìPľ„=Ì`ý(f” 'Pa ¥ÐBJa%Ðâf§„%Š¡}FàáÝ×6>ÉäŠG"éŽè=ø!oŠ°^FP¼Ø©Q„ÀCÙÁ`(Ž\ÄÝ® ©Â$<n@dÄ E#ììUÒI! ‚#lù‹`k¦ÐÇ'Rró’ZýNBÈMF Í[¤+‹ðɈ-áwj¨¥þ8¾rá ,VÂh„"|½œ=×G_¦Ñ™EØ 0i*%̲˜Æda0mV‚k¾)›;„&6 p>ÓjK “¦Ç# âDÂ:ûc?:R Ó¬fÞéI-Ì“•Ã<ä=™Ï7˜3œ¨˜c2ŒW ,ˆ”8(T™P‰F¡Jhç"‚ ; 403WebShell
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Current File : /opt/imunify360/venv/lib/python3.11/site-packages/Crypto/Math/_IntegerBase.py
# ===================================================================
#
# Copyright (c) 2018, Helder Eijs <[email protected]>
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions
# are met:
#
# 1. Redistributions of source code must retain the above copyright
#    notice, this list of conditions and the following disclaimer.
# 2. Redistributions in binary form must reproduce the above copyright
#    notice, this list of conditions and the following disclaimer in
#    the documentation and/or other materials provided with the
#    distribution.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
# COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
# LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
# ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
# POSSIBILITY OF SUCH DAMAGE.
# ===================================================================

import abc

from Crypto.Util.py3compat import iter_range, bord, bchr, ABC

from Crypto import Random


class IntegerBase(ABC):

    # Conversions
    @abc.abstractmethod
    def __int__(self):
        pass

    @abc.abstractmethod
    def __str__(self):
        pass

    @abc.abstractmethod
    def __repr__(self):
        pass

    @abc.abstractmethod
    def to_bytes(self, block_size=0, byteorder='big'):
        pass

    @staticmethod
    @abc.abstractmethod
    def from_bytes(byte_string, byteorder='big'):
        pass

    # Relations
    @abc.abstractmethod
    def __eq__(self, term):
        pass

    @abc.abstractmethod
    def __ne__(self, term):
        pass

    @abc.abstractmethod
    def __lt__(self, term):
        pass

    @abc.abstractmethod
    def __le__(self, term):
        pass

    @abc.abstractmethod
    def __gt__(self, term):
        pass

    @abc.abstractmethod
    def __ge__(self, term):
        pass

    @abc.abstractmethod
    def __nonzero__(self):
        pass
    __bool__ = __nonzero__

    @abc.abstractmethod
    def is_negative(self):
        pass

    # Arithmetic operations
    @abc.abstractmethod
    def __add__(self, term):
        pass

    @abc.abstractmethod
    def __sub__(self, term):
        pass

    @abc.abstractmethod
    def __mul__(self, factor):
        pass

    @abc.abstractmethod
    def __floordiv__(self, divisor):
        pass

    @abc.abstractmethod
    def __mod__(self, divisor):
        pass

    @abc.abstractmethod
    def inplace_pow(self, exponent, modulus=None):
        pass

    @abc.abstractmethod
    def __pow__(self, exponent, modulus=None):
        pass

    @abc.abstractmethod
    def __abs__(self):
        pass

    @abc.abstractmethod
    def sqrt(self, modulus=None):
        pass

    @abc.abstractmethod
    def __iadd__(self, term):
        pass

    @abc.abstractmethod
    def __isub__(self, term):
        pass

    @abc.abstractmethod
    def __imul__(self, term):
        pass

    @abc.abstractmethod
    def __imod__(self, term):
        pass

    # Boolean/bit operations
    @abc.abstractmethod
    def __and__(self, term):
        pass

    @abc.abstractmethod
    def __or__(self, term):
        pass

    @abc.abstractmethod
    def __rshift__(self, pos):
        pass

    @abc.abstractmethod
    def __irshift__(self, pos):
        pass

    @abc.abstractmethod
    def __lshift__(self, pos):
        pass

    @abc.abstractmethod
    def __ilshift__(self, pos):
        pass

    @abc.abstractmethod
    def get_bit(self, n):
        pass

    # Extra
    @abc.abstractmethod
    def is_odd(self):
        pass

    @abc.abstractmethod
    def is_even(self):
        pass

    @abc.abstractmethod
    def size_in_bits(self):
        pass

    @abc.abstractmethod
    def size_in_bytes(self):
        pass

    @abc.abstractmethod
    def is_perfect_square(self):
        pass

    @abc.abstractmethod
    def fail_if_divisible_by(self, small_prime):
        pass

    @abc.abstractmethod
    def multiply_accumulate(self, a, b):
        pass

    @abc.abstractmethod
    def set(self, source):
        pass

    @abc.abstractmethod
    def inplace_inverse(self, modulus):
        pass

    @abc.abstractmethod
    def inverse(self, modulus):
        pass

    @abc.abstractmethod
    def gcd(self, term):
        pass

    @abc.abstractmethod
    def lcm(self, term):
        pass

    @staticmethod
    @abc.abstractmethod
    def jacobi_symbol(a, n):
        pass

    @staticmethod
    def _tonelli_shanks(n, p):
        """Tonelli-shanks algorithm for computing the square root
        of n modulo a prime p.

        n must be in the range [0..p-1].
        p must be at least even.

        The return value r is the square root of modulo p. If non-zero,
        another solution will also exist (p-r).

        Note we cannot assume that p is really a prime: if it's not,
        we can either raise an exception or return the correct value.
        """

        # See https://rosettacode.org/wiki/Tonelli-Shanks_algorithm

        if n in (0, 1):
            return n

        if p % 4 == 3:
            root = pow(n, (p + 1) // 4, p)
            if pow(root, 2, p) != n:
                raise ValueError("Cannot compute square root")
            return root

        s = 1
        q = (p - 1) // 2
        while not (q & 1):
            s += 1
            q >>= 1

        z = n.__class__(2)
        while True:
            euler = pow(z, (p - 1) // 2, p)
            if euler == 1:
                z += 1
                continue
            if euler == p - 1:
                break
            # Most probably p is not a prime
            raise ValueError("Cannot compute square root")

        m = s
        c = pow(z, q, p)
        t = pow(n, q, p)
        r = pow(n, (q + 1) // 2, p)

        while t != 1:
            for i in iter_range(0, m):
                if pow(t, 2**i, p) == 1:
                    break
            if i == m:
                raise ValueError("Cannot compute square root of %d mod %d" % (n, p))
            b = pow(c, 2**(m - i - 1), p)
            m = i
            c = b**2 % p
            t = (t * b**2) % p
            r = (r * b) % p

        if pow(r, 2, p) != n:
            raise ValueError("Cannot compute square root")

        return r

    @classmethod
    def random(cls, **kwargs):
        """Generate a random natural integer of a certain size.

        :Keywords:
          exact_bits : positive integer
            The length in bits of the resulting random Integer number.
            The number is guaranteed to fulfil the relation:

                2^bits > result >= 2^(bits - 1)

          max_bits : positive integer
            The maximum length in bits of the resulting random Integer number.
            The number is guaranteed to fulfil the relation:

                2^bits > result >=0

          randfunc : callable
            A function that returns a random byte string. The length of the
            byte string is passed as parameter. Optional.
            If not provided (or ``None``), randomness is read from the system RNG.

        :Return: a Integer object
        """

        exact_bits = kwargs.pop("exact_bits", None)
        max_bits = kwargs.pop("max_bits", None)
        randfunc = kwargs.pop("randfunc", None)

        if randfunc is None:
            randfunc = Random.new().read

        if exact_bits is None and max_bits is None:
            raise ValueError("Either 'exact_bits' or 'max_bits' must be specified")

        if exact_bits is not None and max_bits is not None:
            raise ValueError("'exact_bits' and 'max_bits' are mutually exclusive")

        bits = exact_bits or max_bits
        bytes_needed = ((bits - 1) // 8) + 1
        significant_bits_msb = 8 - (bytes_needed * 8 - bits)
        msb = bord(randfunc(1)[0])
        if exact_bits is not None:
            msb |= 1 << (significant_bits_msb - 1)
        msb &= (1 << significant_bits_msb) - 1

        return cls.from_bytes(bchr(msb) + randfunc(bytes_needed - 1))

    @classmethod
    def random_range(cls, **kwargs):
        """Generate a random integer within a given internal.

        :Keywords:
          min_inclusive : integer
            The lower end of the interval (inclusive).
          max_inclusive : integer
            The higher end of the interval (inclusive).
          max_exclusive : integer
            The higher end of the interval (exclusive).
          randfunc : callable
            A function that returns a random byte string. The length of the
            byte string is passed as parameter. Optional.
            If not provided (or ``None``), randomness is read from the system RNG.
        :Returns:
            An Integer randomly taken in the given interval.
        """

        min_inclusive = kwargs.pop("min_inclusive", None)
        max_inclusive = kwargs.pop("max_inclusive", None)
        max_exclusive = kwargs.pop("max_exclusive", None)
        randfunc = kwargs.pop("randfunc", None)

        if kwargs:
            raise ValueError("Unknown keywords: " + str(kwargs.keys))
        if None not in (max_inclusive, max_exclusive):
            raise ValueError("max_inclusive and max_exclusive cannot be both"
                         " specified")
        if max_exclusive is not None:
            max_inclusive = max_exclusive - 1
        if None in (min_inclusive, max_inclusive):
            raise ValueError("Missing keyword to identify the interval")

        if randfunc is None:
            randfunc = Random.new().read

        norm_maximum = max_inclusive - min_inclusive
        bits_needed = cls(norm_maximum).size_in_bits()

        norm_candidate = -1
        while not 0 <= norm_candidate <= norm_maximum:
            norm_candidate = cls.random(
                                    max_bits=bits_needed,
                                    randfunc=randfunc
                                    )
        return norm_candidate + min_inclusive

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