Current File : //proc/self/root/opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyc
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integer_typest PY3( t reduce( t powmod( t mpzNt Errorc B s e Z d Z RS( s) Base class for exceptions in this module.( t __name__t
__module__t __doc__( ( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyR $ s t SquareRootErrorc B s e Z RS( ( R R ( ( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyR
) s t NegativeExponentErrorc B s e Z RS( ( R R ( ( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyR - s c C s? t j d t � | d k r/ t d | � � n t | | | � S( s+ Raise base to exponent, reducing by modulussR Function is unused in library code. If you use this code, change to pow() builtin.i s# Negative exponents (%d) not allowed( t warningst warnt DeprecationWarningR t pow( t baset exponentt modulus( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyt modular_exp1 s
c C s� | d d k s t � t | � d k s. t � x� t | � t | � k r� | d d k r� xI t d t | � d � D]+ } | | | d | | | | | <qs Wn | d d !} q1 W| S( s� Reduce poly by polymod, integer arithmetic modulo p.
Polynomials are represented as lists of coefficients
of increasing powers of x.i����i i i ( t AssertionErrort lent xrange( t polyt polymodt pt i( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyt polynomial_reduce_mod< s
,c C s� t | � t | � d d g } xa t t | � � D]M } xD t t | � � D]0 } | | | | | | | | | | | <qM Wq4 Wt | | | � S( s� Polynomial multiplication modulo a polynomial over ints mod p.
Polynomials are represented as lists of coefficients
of increasing powers of x.i i ( R R R ( t m1t m2R R t prodR t j( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyt polynomial_multiply_modS s
!2c C s� | | k s t � | d k r% d g S| } | } | d d k rJ | } n d g } xW | d k r� | d } t | | | | � } | d d k rV t | | | | � } qV qV W| S( s� Polynomial exponentiation modulo a polynomial over ints mod p.
Polynomials are represented as lists of coefficients
of increasing powers of x.i i i ( R R ( R R R R t Gt kt s( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyt polynomial_exp_modk s
c C s | d k s t � | d d k s( t � | | } | d k rB d S| d k rR d S| d } } x) | d d k r� | d | d } } qb W| d d k s� | d d k s� | d d k r� d } n d } | d k r� | S| d d k r| d d k r| } n | t | | | � S( s
Jacobi symboli i i i i i i����i ( R t jacobi( t at nt a1t eR# ( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyR% � s$
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c C s� d | k o | k n s" t � d | k s4 t � | d k rD d S| d k rT | St | | � } | d k r� t d | | f � � n | d d k r� t | | d d | � S| d d k rEt | | d d | � } | d k r� t | | d d | � S| | d k r6d | t d | | d d | � | St d
� � n t rT| } n t d | � } x� t d | � D]r } t | | d | | � d k rs| | d f } t d | d d | | � } | d d k s�t � | d SqsWt d � � d
S( s) Modular square root of a, mod p, p prime.i i i i����s %d has no square root modulo %di i i i s Shouldn't get here.i���s No b found.N( i i ( R R% R
R t RuntimeErrorR t minR R$ ( R& R t jact dt range_topt bt ft ff( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyt square_root_mod_prime� s: " ( ! c C s | d k r d St | d | � S( s Inverse of a mod m.i i����( R ( R& t m( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyt inverse_mod� s c C s� | d k r d St | � } t | � } t d � t d � } } | | | } } xH | d k r� | | } | | | | | | | | f \ } } } } qU W| | S( s Inverse of a mod m.i i ( R ( R& R3 t lmt hmt lowt hight r( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyR4 � s
2c C s� | d k r d Sd \ } } | | | } } xH | d k rw | | } | | | | | | | | f \ } } } } q0 W| | S( s Inverse of a mod m.i i ( i i ( ( R& R3 R5 R6 R7 R8 R9 ( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyR4 � s
2c C s" x | r | | | } } q W| S( s1 Greatest common divisor using Euclid's algorithm.( ( R& R/ ( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyt gcd2 s c G sK t | � d k r t t | � St | d d � rC t t | d � S| d S( sL Greatest common divisor.
Usage: gcd([ 2, 4, 6 ])
or: gcd(2, 4, 6)
i i t __iter__( R R R: t hasattr( R& ( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyt gcd
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c C s | | t | | � S( s& Least common multiple of two integers.( R= ( R& R/ ( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyt lcm2 s c G sK t | � d k r t t | � St | d d � rC t t | d � S| d S( sJ Least common multiple.
Usage: lcm([ 3, 4, 5 ])
or: lcm(3, 4, 5)
i i R; ( R R R> R< ( R& ( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyt lcm s
c C s� t | t � s t � | d k r% g Sg } d } x� t D]� } | | k rN Pn t | | � \ } } | d k r8 d } xE | | k r� | } t | | � \ } } | d k r� Pn | d } qx W| j | | f � q8 q8 W| t d k r�t | � r | j | d f � q�t d } x� | d } t | | � \ } } | | k rEPn | d k rd } | } xE | | k r�t | | � \ } } | d k r�Pn | } | d } q`W| j | | f � qqW| d k r�| j | d f � q�n | S( s2 Decompose n into a list of (prime,exponent) pairs.i i i i����( t
isinstanceR R t smallprimest divmodt appendt is_prime( R' t resultR- t qR9 t count( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyt
factorization, sP
c C s� t j d t � t | t � s% t � | d k r5 d Sd } t | � } x[ | D]S } | d } | d k r� | | d | d | d d } qN | | d d } qN W| S( s' Return the Euler totient function of n.sx Function is unused by library code. If you use this code, please open an issue in https://github.com/warner/python-ecdsai i i ( R R
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%c C s t j d t � t t | � � S( s� Return Carmichael function of n.
Carmichael(n) is the smallest integer x such that
m**x = 1 mod n for all m relatively prime to n.
sx Function is unused by library code. If you use this code, please open an issue in https://github.com/warner/python-ecdsa( R R
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carmichael| s c C ss t j d t � t | � d k r& d St | d � } x6 t d t | � � D] } t | t | | � � } qL W| S( sh Return the Carmichael function of a number that is
represented as a list of (prime,exponent) pairs.
sx Function is unused by library code. If you use this code, please open an issue in https://github.com/warner/python-ecdsai i ( R R
R R t carmichael_of_ppowerR R? ( t f_listRE R ( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyRJ � s c C sX t j d t � | \ } } | d k r@ | d k r@ d | d S| d | | d Sd S( s= Carmichael function of the given power of the given prime.
sx Function is unused by library code. If you use this code, please open an issue in https://github.com/warner/python-ecdsai i N( R R
R ( t ppR R& ( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyRL � s c C sv t j d t � | d k r d St | | � d k s; t � | } d } x( | d k rq | | | } | d } qJ W| S( s; Return the order of x in the multiplicative group mod m.
sx Function is unused by library code. If you use this code, please open an issue in https://github.com/warner/python-ecdsai i ( R R
R R= R ( t xR3 t zRE ( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyt order_mod� s c C sr t j d t � x[ t | | � } | d k r2 Pn | } x/ t | | � \ } } | d k r` Pn | } q; Wq W| S( s8 Return the largest factor of a relatively prime to b.
sx Function is unused by library code. If you use this code, please open an issue in https://github.com/warner/python-ecdsai i ( R R
R R= RB ( R& R/ R- RF R9 ( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyt largest_factor_relatively_prime� s c C s& t j d t � t | t | | � � S( sy Return the order of x in the multiplicative group mod m',
where m' is the largest factor of m relatively prime to x.
sx Function is unused by library code. If you use this code, please open an issue in https://github.com/warner/python-ecdsa( R R
R RQ RR ( RO R3 ( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyt kinda_order_mod� s c
C s� d a | t d k r- | t k r& t St Sn t | d! � d k rF t Sd } d t t j | d � � } xN d" d# d$ d% d& d' d( d) d* d+ d, d- f D]" \ } } | | k r� Pn | } q� Wd } | d } x( | d d k r� | d } | d } q� Wx� t | � D]� } t | } t | | | � } | d k r| | d k rd }
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| d k r�| | d k r�t | d | � } | d k r�| d a t S|
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qHW| | d k r�| d a t SqqWt S(. s* Return True if x is prime, False otherwise.
We use the Miller-Rabin test, as given in Menezes et al. p. 138.
This test is not exact: there are composite values n for which
it returns True.
In testing the odd numbers from 10000001 to 19999999,
about 66 composites got past the first test,
5 got past the second test, and none got past the third.
Since factors of 2, 3, 5, 7, and 11 were detected during
preliminary screening, the number of numbers tested by
Miller-Rabin was (19999999 - 10000001)*(2/3)*(4/5)*(6/7)
= 4.57 million.
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t miller_rabin_test_countRA t Truet FalseR= t intt matht logR R ( R' t tt n_bitsR" t ttR# R9 R R& t yR ( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyRD � sX
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c C s? | d k r d S| d d B} x t | � s: | d } q! W| S( s9 Return the smallest prime larger than the starting value.i i ( RD ( t starting_valueRE ( ( sG /opt/plesk/python/2.7/lib/python2.7/site-packages/ecdsa/numbertheory.pyt
next_prime8 s i i i i i i
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