File: //lib/python3/dist-packages/rsa/__pycache__/prime.cpython-312.pyc
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dk( rQ ed� ddlZ ed� D ]1 Z ej$ � \ ZZer nedz dk( s�$es�' edez � �3 ed� yy)z�Numerical functions related to primes.
Implementation based on the book Algorithm Design by Michael T. Goodrich and
Roberto Tamassia, 2002.
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|| |z }} |dk7 r�
| S )zPReturns the greatest common divisor of p and q
>>> gcd(48, 180)
12
r � )r r s �+/usr/lib/python3/dist-packages/rsa/prime.py�gcdr s& � � �q�&��Q��U�A�� �q�&� �H� �numberc �f � t j j | � }|dk\ ry|dk\ ry|dk\ ryy)a� Returns minimum number of rounds for Miller-Rabing primality testing,
based on number bitsize.
According to NIST FIPS 186-4, Appendix C, Table C.3, minimum number of
rounds of M-R testing, using an error probability of 2 ** (-100), for
different p, q bitsizes are:
* p, q bitsize: 512; rounds: 7
* p, q bitsize: 1024; rounds: 4
* p, q bitsize: 1536; rounds: 3
See: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf
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k( s�! �t y y)a. Calculates whether n is composite (which is always correct) or prime
(which theoretically is incorrect with error probability 4**-k), by
applying Miller-Rabin primality testing.
For reference and implementation example, see:
https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test
:param n: Integer to be tested for primality.
:type n: int
:param k: Number of rounds (witnesses) of Miller-Rabin testing.
:type k: int
:return: False if the number is composite, True if it's probably prime.
:rtype: bool
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� �%�( r c �T � | dk r| dv S | dz syt | � }t | |dz � S )z�Returns True if the number is prime, and False otherwise.
>>> is_prime(2)
True
>>> is_prime(42)
False
>>> is_prime(41)
True
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�is_primer) v sA � � ��{�� �%�%�
�Q�J�� %�V�,�A� *�&�!�a�%� 8�8r �nbitsc �l � | dkD sJ � t j j | � }t |� r|S �-)a Returns a prime number that can be stored in 'nbits' bits.
>>> p = getprime(128)
>>> is_prime(p-1)
False
>>> is_prime(p)
True
>>> is_prime(p+1)
False
>>> from rsa import common
>>> common.bit_size(p) == 128
True
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��+�+�1�1�%�8�� �G� ��N� r r$ �bc �$ � t | |� }|dk( S )z�Returns True if a and b are relatively prime, and False if they
are not.
>>> are_relatively_prime(2, 3)
True
>>> are_relatively_prime(2, 4)
False
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