(gk,xdZddlmZddlmZddlmZdZdZddZ dZ dd l m Z ee dd Zdd Zd Zd Zy)zHFunctions to create and test prime numbers. :undocumented: __package__ )Random)Integer) iter_rangeNct|ts t|}|dvrtS|jrtStd}t|dz }|t j j}t|}d}|jr|dz}|dz }|jrt|D]}d}|||fvr5tjd|dz |}d|cxkr |dz ksJJ|||fvr5t|||} | ||fvrTtd|D]%} t| d|} | |k(rw| |k(stccStcStS)a:Perform a Miller-Rabin primality test on an integer. The test is specified in Section C.3.1 of `FIPS PUB 186-4`__. :Parameters: candidate : integer The number to test for primality. iterations : integer The maximum number of iterations to perform before declaring a candidate a probable prime. randfunc : callable An RNG function where bases are taken from. :Returns: ``Primality.COMPOSITE`` or ``Primality.PROBABLY_PRIME``. .. __: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf rrrr ) min_inclusive max_inclusiverandfunc) isinstancerPROBABLY_PRIMEis_even COMPOSITErnewreadr random_rangepow) candidate iterationsrone minus_onemaibasezjs S/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/Crypto/Math/Primality.pymiller_rabin_testr"-s~( i )I& L  !*C A &I::<$$  A A ))+ a Q ))+ #sI&&''a"+a-%'D- A - .- .- sI&& a # i Aq! AAq)$AI~Cx    /4 ct|ts t|}|dvrtS|js|j rt Sd}|D]4}||| fvr tj ||}|dk(rt cS|dk(s4n|dz}|jdz }td}td}td}td} t|dz ddD]} |j|||z}||z}| j|| |z} | z} | j||| jr| |z } | dz} | |z} |j| rx|j||| z }|jr||z }|dz}||z}|j| |j|||jr||z }|dz}||z}|j||j| |dk(rtSt S)a_Perform a Lucas primality test on an integer. The test is specified in Section C.3.3 of `FIPS PUB 186-4`__. :Parameters: candidate : integer The number to test for primality. :Returns: ``Primality.COMPOSITE`` or ``Primality.PROBABLY_PRIME``. .. __: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf rc3@Kd} ||dkDr|dz }n|dz}| }w)Nr rr )values r! alternatezlucas_test..alternates8Kqy  FE srr) rrrris_perfect_squarer jacobi_symbol size_in_bitsrsetmultiply_accumulateis_oddget_bit) rr(DjsKrU_iV_iU_tempV_temprs r! lucas_testr9ws i )I& L i99;[ QB    " "1i 0 7  8  A A 1A !*C !*C QZF QZF Ar2 &!  3# ) 3# ! ""3, ==? i F1 ) 99Q< GGFO 6MCzz|y  AIC 9 C GGFO  # #FA .zz|y  AIC 9 C GGFO GGFOC!F ax r#) sieve_basedc|tjj}t|ts t |}t |t vrtS t|jt d}|j ttfd|dd}t!|||tk(rtSt#|tk(rtStS#t$r tcYSwxYw#t$rd}Y[wxYw)aTest if a number is prime. A number is qualified as prime if it passes a certain number of Miller-Rabin tests (dependent on the size of the number, but such that probability of a false positive is less than 10^-30) and a single Lucas test. For instance, a 1024-bit candidate will need to pass 4 Miller-Rabin tests. :Parameters: candidate : integer The number to test for primality. randfunc : callable The routine to draw random bytes from to select Miller-Rabin bases. :Returns: ``PROBABLE_PRIME`` if the number if prime with very high probability. ``COMPOSITE`` if the number is a composite. For efficiency reasons, ``COMPOSITE`` is also returned for small primes. ) ))i)i)i )il)i)izr )i)ir )itr c|dkS)Nrr&)xbit_sizes r!z%test_probable_prime.. sh1or#rrr)rrrrrint _sieve_basermapfail_if_divisible_by ValueErrorrr,listfilter IndexErrorr"r9)rr mr_ranges mr_iterationsrGs @r!test_probable_primerTs,::<$$ i )I&  9~$ I * *K8'I%%'HV$=$-/0013346 M"*,/89) ) -   s$CC.C+*C+. C<;C<c |jdd}|jdd}|jdd}|rtd|jz| td|dkr td |tjj }t }|t k(r9tj|| d z}||s,t||}|t k(r9S) axGenerate a random probable prime. The prime will not have any specific properties (e.g. it will not be a *strong* prime). Random numbers are evaluated for primality until one passes all tests, consisting of a certain number of Miller-Rabin tests with random bases followed by a single Lucas test. The number of Miller-Rabin iterations is chosen such that the probability that the output number is a non-prime is less than 1E-30 (roughly 2^{-100}). This approach is compliant to `FIPS PUB 186-4`__. :Keywords: exact_bits : integer The desired size in bits of the probable prime. It must be at least 160. randfunc : callable An RNG function where candidate primes are taken from. prime_filter : callable A function that takes an Integer as parameter and returns True if the number can be passed to further primality tests, False if it should be immediately discarded. :Return: A probable prime in the range 2^exact_bits > p > 2^(exact_bits-1). .. __: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf exact_bitsNr prime_filtercy)NTr&)rFs r!rHz)generate_probable_prime..<sr#Unknown parameters: zMissing exact_bits parameterzPrime number is not big enough.rVrr) poprNkeysrrrrrrandomrT)kwargsrVrrWresultrs r!generate_probable_primerasDL$/Jzz*d+H::nn=L /&++-?@@788C:;;::<$$ F I NNj,4689: I& $Y9 I  r#c n|jdd}|jdd}|rtd|jz|tjj }t }|t k(rCt|dz |}|dzdz}|j|k7r5t||}|t k(rCS) aGenerate a random, probable safe prime. Note this operation is much slower than generating a simple prime. :Keywords: exact_bits : integer The desired size in bits of the probable safe prime. randfunc : callable An RNG function where candidate primes are taken from. :Return: A probable safe prime in the range 2^exact_bits > p > 2^(exact_bits-1). rVNrrYrr[r rI) r\rNr]rrrrrar,rT)r_rVrr`qrs r!generate_probable_safe_primerdRs L$/Jzz*d+H /&++-?@@::<$$ F I  #zA~ QEAI  ! ! #z 1 $YB I  r#)N)__doc__CryptorCrypto.Math.NumbersrCrypto.Util.py3compatrrrr"r9Crypto.Util.numberr:_sieve_base_larger-rKrTrardr&r#r!rksW> ', GT^B?#DS)* 7t7tr#