8tc(NddlZddlmZmZmZmZddlmZGddeZdS)N) iter_rangebordbchrABC)Randomc<eZdZejdZejdZejdZejd4dZe ejdZ ejdZ ejdZ ejd Z ejd Zejd Zejd Zejd ZeZejdZejdZejdZejdZejdZejdZejd5dZejd5dZejdZejd5dZejdZejdZejdZejdZ ejdZ!ejdZ"ejdZ#ejd Z$ejd!Z%ejd"Z&ejd#Z'ejd$Z(ejd%Z)ejd&Z*ejd'Z+ejd(Z,ejd)Z-ejd*Z.ejd+Z/ejd,Z0ejd-Z1ejd.Z2ejd/Z3e ejd0Z4e d1Z5e6d2Z7e6d3Z8dS)6 IntegerBasecdSNselfs >/usr/lib/python3/dist-packages/Cryptodome/Math/_IntegerBase.py__int__zIntegerBase.__int__) cdSr r r s r__str__zIntegerBase.__str__-rrcdSr r r s r__repr__zIntegerBase.__repr__1rrrcdSr r )r block_sizes rto_byteszIntegerBase.to_bytes5rrcdSr r ) byte_strings r from_byteszIntegerBase.from_bytes9  rcdSr r rterms r__eq__zIntegerBase.__eq__?rrcdSr r rs r__ne__zIntegerBase.__ne__CrrcdSr r rs r__lt__zIntegerBase.__lt__GrrcdSr r rs r__le__zIntegerBase.__le__KrrcdSr r rs r__gt__zIntegerBase.__gt__OrrcdSr r rs r__ge__zIntegerBase.__ge__SrrcdSr r r s r __nonzero__zIntegerBase.__nonzero__WrrcdSr r r s r is_negativezIntegerBase.is_negative\rrcdSr r rs r__add__zIntegerBase.__add__arrcdSr r rs r__sub__zIntegerBase.__sub__errcdSr r )rfactors r__mul__zIntegerBase.__mul__irrcdSr r rdivisors r __floordiv__zIntegerBase.__floordiv__mrrcdSr r r8s r__mod__zIntegerBase.__mod__qrrNcdSr r rexponentmoduluss r inplace_powzIntegerBase.inplace_powurrcdSr r r>s r__pow__zIntegerBase.__pow__yrrcdSr r r s r__abs__zIntegerBase.__abs__}rrcdSr r rr@s rsqrtzIntegerBase.sqrtrrcdSr r rs r__iadd__zIntegerBase.__iadd__rrcdSr r rs r__isub__zIntegerBase.__isub__rrcdSr r rs r__imul__zIntegerBase.__imul__rrcdSr r rs r__imod__zIntegerBase.__imod__rrcdSr r rs r__and__zIntegerBase.__and__rrcdSr r rs r__or__zIntegerBase.__or__rrcdSr r rposs r __rshift__zIntegerBase.__rshift__rrcdSr r rVs r __irshift__zIntegerBase.__irshift__rrcdSr r rVs r __lshift__zIntegerBase.__lshift__rrcdSr r rVs r __ilshift__zIntegerBase.__ilshift__rrcdSr r )rns rget_bitzIntegerBase.get_bitrrcdSr r r s ris_oddzIntegerBase.is_oddrrcdSr r r s ris_evenzIntegerBase.is_evenrrcdSr r r s r size_in_bitszIntegerBase.size_in_bitsrrcdSr r r s r size_in_byteszIntegerBase.size_in_bytesrrcdSr r r s ris_perfect_squarezIntegerBase.is_perfect_squarerrcdSr r )r small_primes rfail_if_divisible_byz IntegerBase.fail_if_divisible_byrrcdSr r )rabs rmultiply_accumulatezIntegerBase.multiply_accumulaterrcdSr r )rsources rsetzIntegerBase.setrrcdSr r rGs rinplace_inversezIntegerBase.inplace_inverserrcdSr r rGs rinversezIntegerBase.inverserrcdSr r rs rgcdzIntegerBase.gcdrrcdSr r rs rlcmzIntegerBase.lcmrrcdSr r )rpr`s r jacobi_symbolzIntegerBase.jacobi_symbolrrcP|dvr|S|dzdkr=t||dzdz|}t|d||krtd|Sd}|dz dz}|dzs|dz }|dz}|dz|d} t||dz dz|}|dkr|dz }$||dz krntd|}t|||}t|||} t||dzdz|} | dkrtd|D]} t| d| z|dkrn| |krtd ||fzt|d|| z dz z|} | }| dz|z}| | dzz|z} | | z|z} | dkt| d||krtd| S) aTonelli-shanks algorithm for computing the square root of n modulo a prime p. n must be in the range [0..p-1]. p must be at least even. The return value r is the square root of modulo p. If non-zero, another solution will also exist (p-r). Note we cannot assume that p is really a prime: if it's not, we can either raise an exception or return the correct value. )rrzCannot compute square rootTrz'Cannot compute square root of %d mod %d)pow ValueError __class__r) r`prootsqzeulermctrirqs r_tonelli_shankszIntegerBase._tonelli_shankss(" ;;H q5A::q1q5Q,**D4A!## !=>>>K  UqLq5  FA !GAq5  KKNN ;AEa<++EzzQA~~9:: :  1aLL 1aLL AEa< # #1ff1%%  q!Q$??a''E(Avv !JaQRV!STTTAq1q519~q))AA1qAQTQAQ! A1ff q!Q<<1  9:: :rc |dd}|dd}|dd}|tjj}||t d||t d|p|}|dz dzdz}d|dz|z z }t |dd }| |d|dz zz}|d|zdz z}|t|||dz zS) a!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_bitsNmax_bitsrandfuncz3Either 'exact_bits' or 'max_bits' must be specifiedz2'exact_bits' and 'max_bits' are mutually exclusiverr)poprnewreadrrrr) clskwargsrrrbits bytes_neededsignificant_bits_msbmsbs rrandomzIntegerBase.random)s+2ZZ d33 ::j$//::j$//  z||(H  ("2RSS S  !h&:QRR R%Xa1,  L1$4t$;<88A;;q>""  ! 1-12 2C ))Q..~~d3ii((>\>@-F-F[-F^-.-.[-.-.-.rr ) rCryptodome.Util.py3compatrrrr Cryptodomerr r rrrs> AAAAAAAAAAAAa.a.a.a.a.#a.a.a.a.a.r