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Filename :
prime.cpython-310.pyc
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o ��a� � @ s� d Z ddlZddlZddgZdededefdd �Zd edefd d �Zd ededefdd�Z d edefdd�Z dedefdd�Z dededefdd�Z e dkr{ed� ddlZed�D ]Ze�� \ZZerf ned dkrterted e � qZed � dS dS ) z�Numerical functions related to primes. Implementation based on the book Algorithm Design by Michael T. Goodrich and Roberto Tamassia, 2002. � N�getprime�are_relatively_prime�p�q�returnc C s" |dkr|| | } }|dks| S )zPReturns the greatest common divisor of p and q >>> gcd(48, 180) 12 r � )r r r r �+/usr/lib/python3/dist-packages/rsa/prime.py�gcd s �r �numberc C s4 t j�| �}|dkr dS |dkrdS |dkrdS dS )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 i � i � i � � )�rsa�common�bit_size)r �bitsizer r r � get_primality_testing_rounds' s r �n�kc C s� | dk rdS | d }d}|d@ s |d7 }|dL }|d@ rt |�D ]?}tj�| d �d }t||| �}|dks<|| d kr=q t |d �D ]}t|d| �}|dkrS dS || d kr[ nqC dS q dS )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 � F� r r T)�ranger �randnum�randint�pow)r r �d�r�_�a�xr r r � miller_rabin_primality_testingA s. � ��r! c C s2 | dk r| dv S | d@ sdS t | �}t| |d �S )z�Returns True if the number is prime, and False otherwise. >>> is_prime(2) True >>> is_prime(42) False >>> is_prime(41) True r > r r � r r F)r r! )r r r r r �is_primev s r# �nbitsc C s( | dksJ � t j�| �}t|�r|S q)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 r )r r �read_random_odd_intr# )r$ �integerr r r r � s �r �bc C s t | |�}|dkS )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 r )r )r r' r r r r r � s �__main__z'Running doctests 1000x or until failurei� �d z%i timesz Doctests done)�__doc__� rsa.commonr � rsa.randnum�__all__�intr r �boolr! r# r r �__name__�print�doctestr �count�testmod�failures�testsr r r r �<module> s, 5 � �