5ik,|SrSSKJr SSKJr SSKJr SrSrSSjr Sr SS K J r \"\ SS 5rSS jrS rS rg)zHFunctions to create and test prime numbers. :undocumented: __package__ )Random)Integer) iter_rangeNc[U[5(d [U5nUS;a[$UR5(a[$[S5n[US- 5nUc[ R "5Rn[U5nSnUR5(a!US-nUS- nUR5(aM![U5HnSnXU4;a7[R"SUS- US9nSUs=::a US- ::de eXU4;aM7[XU5n XU4;aMX[SU5H'n [U SU5n X:Xa M|X:XdM[s s $ [s $ [$)aPerform 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 c/var/www/html/BTCUSD/btcusdt_trading_app/venv/lib/python3.13/site-packages/Crypto/Math/Primality.pymiller_rabin_testr"-sr( i ) )I& L  !*C A &I::<$$  A A ))++ a Q ))++ #I&&''a"+a-%'D- A - .- .- I&&  # i Aq!AAq)$A~x  " /$4 c\[U[5(d [U5nUS;a[$UR5(dUR 5(a[ $SnU"5H9nXU*4;aM [R "X 5nUS:Xa[ s $US:XdM9 O US-nUR5S- n[S5n[S5n[S5n[S5n [US- SS5GHn URU5 X-nX-nU RU5 X-n U W-n U RXw5 U R5(aX- n U S-n X-n URU 5(a}URU5 Xi- nUR5(aX`- nUS-nX`-nURU 5 URX5 UR5(aXp- nUS-nXp-nMURU5 URU 5 GM" US:Xa[$[ $)a?Perform a Lucas primality test on an integer. The test is specified in Section C.3.3 of `FIPS PUB 186-4`__. :Parameters: candidate : integer The number to test for primality. :Returns: ``Primality.COMPOSITE`` or ``Primality.PROBABLY_PRIME``. .. __: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf rc3D# SnUv US:aUS- nOUS-nU*nM7f)Nr rr )values r! alternatelucas_test..alternates7Kqy  FE s rr) rrrris_perfect_squarer jacobi_symbol size_in_bitsrsetmultiply_accumulateis_oddget_bit) rr(DjsKrU_iV_iU_tempV_temprs r! lucas_testr:ws i ) )I& L i99;;[ QB    " "1 0 7  8  A A 1A !*C !*C QZF QZF Ar2 &  3  3 ! ""3, ==??  F1  99Q<< GGFO MCzz||  AIC  C GGFO  # #F .zz||  AIC  C GGFO GGFOC'F ax r#) sieve_basedc^Uc[R"5Rn[U[5(d [ U5n[ U5[ ;a[$[UR[ 5 SnUR5m[[U4SjU55SSn[!XUS9[:Xa[$[#U5[:Xa[$[$![a [s$f=f![a SnN[f=f)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>TUS:$)Nrr&)xbit_sizes r!%test_probable_prime.. s h1or#rrr)rrrrrint _sieve_basermapfail_if_divisible_by ValueErrorrr-listfilter IndexErrorr"r:)rr mr_ranges mr_iterationsrHs @r!test_probable_primerVs,::<$$ i ) )I&  9~$ I * *K8'I%%'HV$=$-/0013346 "*,/89) ) -   s$C! C7!C43C47 DDc URSS5nURSS5nURSS5nU(a[SUR5-5eUc [S5eUS:a [S 5eUc[R"5R n[ nU[ :Xa>[R"UUS 9S -nU"U5(dM1[XR5nU[ :XaM>W$) aGenerate a random probable prime. The prime will not have any specific properties (e.g. it will not be a *strong* prime). Random numbers are evaluated for primality until one passes all tests, consisting of a certain number of Miller-Rabin tests with random bases followed by a single Lucas test. The number of Miller-Rabin iterations is chosen such that the probability that the output number is a non-prime is less than 1E-30 (roughly 2^{-100}). This approach is compliant to `FIPS PUB 186-4`__. :Keywords: exact_bits : integer The desired size in bits of the probable prime. It must be at least 160. randfunc : callable An RNG function where candidate primes are taken from. prime_filter : callable A function that takes an Integer as parameter and returns True if the number can be passed to further primality tests, False if it should be immediately discarded. :Return: A probable prime in the range 2^exact_bits > p > 2^(exact_bits-1). .. __: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf exact_bitsNr prime_filtercg)NTr&)rGs r!rI)generate_probable_prime..<sr#Unknown parameters: zMissing exact_bits parameterzPrime number is not big enough.rXrr) poprPkeysrrrrrrandomrV)kwargsrXrrYresultrs r!generate_probable_primerdsDL$/Jzz*d+H::nn=L /&++-?@@788C:;;::<$$ F I NNj,4689: I&& $Y9 I  r#c xURSS5nURSS5nU(a[SUR5-5eUc[R"5R n[ nU[ :Xa@[US- US9nUS-S-nUR5U:waM5[XRS9nU[ :XaM@W$) asGenerate 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). rXNrr\rr^r rK) r_rPr`rrrrrdr-rV)rbrXrrcqrs r!generate_probable_safe_primergRs L$/Jzz*d+H /&++-?@@::<$$ F I  #zA~ QEAI  ! ! #z 1 $YB I  r#)N)__doc__CryptorCrypto.Math.NumbersrCrypto.Util.py3compatrrrr"r:Crypto.Util.numberr;_sieve_base_larger.rMrVrdrgr&r#r!rnsW> ', GT^B?#DS)* 7t7tr#