U Mf{,@s|dZddlmZddlmZddlmZdZdZdddZ d d Z dd l m Z ee dd Zdd dZddZddZdS)zHFunctions to create and test prime numbers. :undocumented: __package__ )Random)Integer) iter_rangeNc Cs,t|tst|}|dkrtS|r*tStd}t|d}|dkrPtj}t|}d}|rv|dL}|d7}q\t|D]}d}|||fkrtj d|d|d}d|kr|dksnt qt |||} | ||fkrq~td|D]2} t | d|} | |krq~| |krtSqtSq~tS)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 rrNrr)Z min_inclusiveZ max_inclusiverandfunc) isinstancerPROBABLY_PRIMEis_even COMPOSITErnewreadrZ random_rangeAssertionErrorpow) candidateZ iterationsr ZoneZ minus_onemaibasezjr=/tmp/pip-unpacked-wheel-l_0d1exj/Cryptodome/Math/Primality.pymiller_rabin_test-sD            rc Cst|tst|}|dkrtS|s.|r2tSdd}|D]<}||| fkrTq@t||}|dkrptS|dkr@q~q@|d}|d}td}td}td}td} t|dddD]} | |||9}||;}| || |9} | |9} | ||| r| |7} | dL} | |;} | | r| ||| 7}| rX||7}|dL}||;}| | | ||| r||7}|dL}||;}q| || | q|dkrtStS)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 rcss0d}|V|dkr|d7}n|d8}| }qdS)Nr rrr)valuerrr alternates  zlucas_test..alternaterr) r rr r Zis_perfect_squarerZ jacobi_symbol size_in_bitsrsetZmultiply_accumulateZis_oddZget_bit) rrDZjsKrZU_iZV_iZU_tempZV_temprrrr lucas_testwsf                  r%) sieve_basedcs|dkrtj}t|ts$t|}t|tkr4tSzt|j tWnt k r\t YSXd}| z"t tfdd|dd}Wntk rd}YnXt|||dt krt St|t krt StS)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. N) ))i)i)i )il)i)izr )i)ir)itrcs |dkS)NrrxZbit_sizerr z%test_probable_prime..rrr )rrrr rint _sieve_baser mapZfail_if_divisible_by ValueErrorrr listfilter IndexErrorrr%)rr Z mr_rangesZ mr_iterationsrr2rtest_probable_primes>      r=cKs|dd}|dd}|ddd}|r p > 2^(exact_bits-1). .. __: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf exact_bitsNr prime_filtercSsdS)NTrr0rrrr3<r4z)generate_probable_prime..Unknown parameters: zMissing exact_bits parameterzPrime number is not big enough.r>r r) popr9keysrrrrrrandomr=)kwargsr>r r?resultrrrrgenerate_probable_primes,"    rHcKs|dd}|dd}|r,td||dkr>tj}t}|tkrt|d|d}|dd}||krtqBt ||d}qB|S) 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). r>Nr r@rrBrr5) rCr9rDrrrrrHr r=)rFr>r rGqrrrrgenerate_probable_safe_primeRs     rJ)N)N)__doc__Z CryptodomerZCryptodome.Math.NumbersrZCryptodome.Util.py3compatrrr rr%ZCryptodome.Util.numberr&Z_sieve_base_larger!r7r=rHrJrrrrs    Ja  ::