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a c�hH, � @ s| d Z ddlmZ ddlmZ ddlmZ dZdZddd�Z d d � Z dd l m Z ee dd � �Zdd d�Zdd� Zdd� ZdS )zHFunctions to create and test prime numbers. :undocumented: __package__ � )�Random)�Integer)� iter_range� Nc C s* t | t�st| �} | dv r tS | �� r*tS td�}t| d �}|du rPt�� j}t|�}d}|�� rv|dL }|d7 }q\t|�D ]�}d}|||fv r�tj d| d d�}d| kr�| d ks�n J �q�t ||| �} | ||fv r�q~td|�D ]2} t | d| �} | |k�r q~| |kr�t S q�t S q~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 �r � � � r Nr r )Z min_inclusiveZ max_inclusive) � isinstancer �PROBABLY_PRIME�is_even� COMPOSITEr �new�readr Z random_range�pow) � candidateZ iterations�randfunc�oneZ minus_one�m�a�i�base�z�j� r ��/root/rpmbuild/BUILDROOT/imh-python39-modules-3.9.7-92.el8.x86_64/opt/imh-python/lib/python3.9/site-packages/Crypto/Math/Primality.py�miller_rabin_test- sB � r c C s� t | t�st| �} | dv r tS | �� s.| �� r2tS dd� }|� D ]<}| || fv rTq@t�|| �}|dkrpt S |dkr@ q~q@| d }|�� d }td�}td�}td�}td�} t|d dd�D ]�} |� |� ||9 }|| ; }| � |� | |9 } | |9 } | � ||� | � � �r| | 7 } | dL } | | ; } |� | ��r�|� |� || 7 }|� � �rX|| 7 }|dL }|| ; }|� | � |� ||� |� � �r�|| 7 }|dL }|| ; }q�|� |� |� | � q�|dk�r�tS tS )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 r c s s0 d} | V | dkr | d7 } n| d8 } | } qd S )Nr r r r )�valuer r r � alternate� s z lucas_test.<locals>.alternater ���r ) r r r r Zis_perfect_squarer Z jacobi_symbol� size_in_bitsr �setZmultiply_accumulateZis_oddZget_bit) r r �D�js�K�rZU_iZV_iZU_tempZV_tempr r r r � lucas_testv sf r& )� sieve_base�d c s� |du rt �� j}t| t�s$t| �} t| �tv r4tS zt| j t� W n t yZ t Y S 0 d}| � � � z"t t� fdd�|��d d }W n ty� d}Y n0 t| ||d�t kr�t S t| �t kr�t S tS )a� Test 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� � )iz r )i� � )i� r )it r c s � | d k S )Nr r ��x�Zbit_sizer r �<lambda> � z%test_probable_prime.<locals>.<lambda>r r �r )r r r r r �int� _sieve_baser �mapZfail_if_divisible_by� ValueErrorr r �list�filter� IndexErrorr r& )r r Z mr_rangesZ mr_iterationsr r3 r �test_probable_prime� s> ��� �� r> c K s� | � dd�}| � dd�}| � ddd� �}| r<td| �� ��|du rLtd��|d k r\td ��|du rnt�� j}t}|tkr�tj||d �d B }||�s�qrt ||�}qr|S ) ax Generate 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_filterc S s dS )NTr r1 r r r r4 ; r5 z)generate_probable_prime.<locals>.<lambda>�Unknown parameters: z Missing exact_bits parameter� z Prime number is not big enough.�r? r r ) �popr: �keysr r r r r �randomr> )�kwargsr? r r@ �resultr r r r �generate_probable_prime s, " �� rI c K s� | � dd�}| � dd�}| r,td| �� ��|du r>t�� j}t}|tkr�t|d |d�}|d d }|�� |krtqBt ||d�}qB|S ) a� Generate 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 rA r rC r r6 ) rD r: rE r r r r rI r r> )rG r? r rH �qr r r r � generate_probable_safe_primeQ s rK )N)N)�__doc__ZCryptor ZCrypto.Math.Numbersr ZCrypto.Util.py3compatr r r r r& ZCrypto.Util.numberr' Z_sieve_base_larger! r8 r> rI rK r r r r �<module> s Ia ::
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