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The return value r is the square root of modulo p. If non-zero, another solution will also exist (p-r). Note we cannot assume that p is really a prime: if it's not, we can either raise an exception or return the correct value. )rrOzCannot compute square rootTrz'Cannot compute square root of %d mod %d)pow ValueError __class__r) r=prootsqzZeulermctrirFr r r _tonelli_shankssT         zIntegerBase._tonelli_shanksc Ks|dd}|dd}|dd}|durtj}|dur'|dur'td|dur3|dur3td|p6|}|ddd}d|d|}t|dd }|dur[|d|d>O}|d|>dM}|t|||dS) a!Generate a random natural integer of a certain size. :Keywords: exact_bits : positive integer The length in bits of the resulting random Integer number. The number is guaranteed to fulfil the relation: 2^bits > result >= 2^(bits - 1) max_bits : positive integer The maximum length in bits of the resulting random Integer number. The number is guaranteed to fulfil the relation: 2^bits > result >=0 randfunc : callable A function that returns a random byte string. The length of the byte string is passed as parameter. Optional. If not provided (or ``None``), randomness is read from the system RNG. :Return: a Integer object exact_bitsNmax_bitsrandfuncz3Either 'exact_bits' or 'max_bits' must be specifiedz2'exact_bits' and 'max_bits' are mutually exclusiverOr)poprnewreadrTrrr) clskwargsrarbrcbitsZ bytes_neededZsignificant_bits_msbZmsbr r r random)s"    zIntegerBase.randomc Ks|dd}|dd}|dd}|dd}|r#tdt|jd||fvr-td|dur5|d}d||fvr?td |durHtj}||}||}d }d |kr^|ksun|j||d }d |krs|kr_||Sq_||S) aGenerate a random integer within a given internal. :Keywords: min_inclusive : integer The lower end of the interval (inclusive). max_inclusive : integer The higher end of the interval (inclusive). max_exclusive : integer The higher end of the interval (exclusive). randfunc : callable A function that returns a random byte string. The length of the byte string is passed as parameter. Optional. If not provided (or ``None``), randomness is read from the system RNG. :Returns: An Integer randomly taken in the given interval. min_inclusiveN max_inclusive max_exclusiverczUnknown keywords: z8max_inclusive and max_exclusive cannot be both specifiedrOz(Missing keyword to identify the intervalr)rbrc) rerTstrkeysrrfrgrArk) rhrirlrmrnrcZ norm_maximumZ bits_neededZnorm_candidater r r random_rangeYs4        zIntegerBase.random_range)rr)rr )9__name__ __module__ __qualname__abcabstractmethodrrrr staticmethodrrrrrrrr __bool__r!r"r#r%r'r(r,r-r.r0r1r2r3r4r5r6r9r:r;r<r>r?r@rArBrCrDrGrIrJrKrLrMrNr` classmethodrkrrr r r r r&s                                              @ /r) rvZCrypto.Util.py3compatrrrrZCryptorrr r r r s