

'''simple docstring'''

from __future__ import annotations

import math




def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_     ):
 UpperCAmelCase	:     str						 =			u
 for i in range(1  ,	UpperCAmelCase_     ):
  UpperCAmelCase	:     Dict						 =			temp * (u - i)
 return temp




def 				UpperCamelCase(					):
 UpperCAmelCase	:     Tuple						 =			int(input('enter the numbers of values: '     )     )
 UpperCAmelCase	:     list[list[float]]						 =			[]
 for _ in range(UpperCAmelCase_     ):
  y.append([]     )
 for i in range(UpperCAmelCase_     ):
  for j in range(UpperCAmelCase_     ):
   y[i].append(UpperCAmelCase_     )
   UpperCAmelCase	:     Optional[Any]						 =			0

 print('enter the values of parameters in a list: '     )
 UpperCAmelCase	:     Optional[int]						 =			list(map(UpperCAmelCase_  ,	input().split()     )     )

 print('enter the values of corresponding parameters: '     )
 for i in range(UpperCAmelCase_     ):
  UpperCAmelCase	:     Optional[int]						 =			float(input()     )

 UpperCAmelCase	:     Dict						 =			int(input('enter the value to interpolate: '     )     )
 UpperCAmelCase	:     int						 =			(value - x[0]) / (x[1] - x[0])

 # for calculating forward difference table

 for i in range(1  ,	UpperCAmelCase_     ):
  for j in range(n - i     ):
   UpperCAmelCase	:     List[str]						 =			y[j + 1][i - 1] - y[j][i - 1]

 UpperCAmelCase	:     Optional[Any]						 =			y[0][0]
 for i in range(1  ,	UpperCAmelCase_     ):
  summ += (ucal(UpperCAmelCase_  ,	UpperCAmelCase_     ) * y[0][i]) / math.factorial(UpperCAmelCase_     )

 print(F"""the value at {value} is {summ}"""     )


if __name__ == "__main__":
 main()







'''simple docstring'''

import os
import random
import sys

from . import cryptomath_module as cryptomath
from . import rabin_miller

lowercase__         =      3




def 				UpperCamelCase(					UpperCAmelCase_     ):
 print('Generating primitive root of p'     )
 while True:
  UpperCAmelCase	:     Union[str, Any]						 =			random.randrange(3  ,	UpperCAmelCase_     )
  if pow(UpperCAmelCase_  ,	2  ,	UpperCAmelCase_     ) == 1:
   continue
  if pow(UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     ) == 1:
   continue
  return g




def 				UpperCamelCase(					UpperCAmelCase_     ):
 print('Generating prime p...'     )
 UpperCAmelCase	:     str						 =			rabin_miller.generate_large_prime(UpperCAmelCase_     )  # select large prime number.
 UpperCAmelCase	:     List[str]						 =			primitive_root(UpperCAmelCase_     )  # one primitive root on modulo p.
 UpperCAmelCase	:     List[Any]						 =			random.randrange(3  ,	UpperCAmelCase_     )  # private_key -> have to be greater than 2 for safety.
 UpperCAmelCase	:     List[Any]						 =			cryptomath.find_mod_inverse(pow(UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     )  ,	UpperCAmelCase_     )

 UpperCAmelCase	:     Tuple						 =			(key_size, e_a, e_a, p)
 UpperCAmelCase	:     Optional[int]						 =			(key_size, d)

 return public_key, private_key




def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_     ):
 if os.path.exists(F"""{name}_pubkey.txt"""     ) or os.path.exists(F"""{name}_privkey.txt"""     ):
  print('\nWARNING:'     )
  print(
      F"""\"{name}_pubkey.txt\" or \"{name}_privkey.txt\" already exists. \n"""
      'Use a different name or delete these files and re-run this program.'     )
  sys.exit()

 UpperCAmelCase ,			UpperCAmelCase	:     Dict						 =			generate_key(UpperCAmelCase_     )
 print(F"""\nWriting public key to file {name}_pubkey.txt..."""     )
 with open(F"""{name}_pubkey.txt"""  ,	'w'     ) as fo:
  fo.write(F"""{public_key[0]},{public_key[1]},{public_key[2]},{public_key[3]}"""     )

 print(F"""Writing private key to file {name}_privkey.txt..."""     )
 with open(F"""{name}_privkey.txt"""  ,	'w'     ) as fo:
  fo.write(F"""{private_key[0]},{private_key[1]}"""     )




def 				UpperCamelCase(					):
 print('Making key files...'     )
 make_key_files('elgamal'  ,	20_48     )
 print('Key files generation successful'     )


if __name__ == "__main__":
 main()




