def secret_int_to_points(secret_int, point_threshold, num_points, prime=None):
""" Split a secret (integer) into shares (pair of integers / x,y coords).
Sample the points of a random polynomial with the y intercept equal to
the secret int.
"""
if point_threshold < 2:
raise ValueError("Threshold must be >= 2.")
if point_threshold > num_points:
raise ValueError("Threshold must be < the total number of points.")
if not prime:
prime = get_large_enough_prime([secret_int, num_points])
if not prime:
raise ValueError("Error! Secret is too long for share calculation!")
coefficients = random_polynomial(point_threshold-1, secret_int, prime)
points = get_polynomial_points(coefficients, num_points, prime)
return points
def secret_int_to_points(secret_int, point_threshold, num_points):
""" Split a secret (integer) into shares (pair of integers / x,y coords).
Sample the points of a random polynomial with the y intercept equal to
the secret int.
"""
if point_threshold < 2:
raise ValueError("Threshold must be >= 2.")
if point_threshold > num_points:
raise ValueError("Threshold must be < the total number of points.")
prime = get_large_enough_prime([secret_int, num_points])
if not prime:
raise ValueError("Error! Secret is too long for share calculation!")
print 'Selected Prime Number = ', prime
coefficients = random_polynomial(point_threshold-1, secret_int, prime)
points = get_polynomial_points(coefficients, num_points, prime)
return points
def points_to_secret_int(points):
""" Join int points into a secret int.
Get the intercept of a random polynomial defined by the given points.
"""
if not isinstance(points, list):
raise ValueError("Points must be in list form.")
for point in points:
if not isinstance(point, tuple) and len(point) == 2:
raise ValueError("Each point must be a tuple of two values.")
if not isinstance(point[0], (int, long)) and \
isinstance(point[1], (int, long)):
raise ValueError("Each value in the point must be an int.")
x_values, y_values = zip(*points)
prime = get_large_enough_prime(y_values)
free_coefficient = modular_lagrange_interpolation(0, points, prime)
secret_int = free_coefficient # the secret int is the free coefficient
return secret_int
def points_to_secret_int(points):
""" Join int points into a secret int.
Get the intercept of a random polynomial defined by the given points.
"""
if not isinstance(points, list):
raise ValueError("Points must be in list form.")
for point in points:
if not isinstance(point, tuple) and len(point) == 2:
raise ValueError("Each point must be a tuple of two values.")
if not isinstance(point[0], (int, long)) and \
isinstance(point[1], (int, long)):
raise ValueError("Each value in the point must be an int.")
x_values, y_values = zip(*points)
prime = get_large_enough_prime(y_values)
free_coefficient = modular_lagrange_interpolation(0, points, prime)
secret_int = free_coefficient # the secret int is the free coefficient
return secret_int
print '---' print 'Example: python additions.py 7 3 123 -556 3 -4' print '---' sys.exit() # Get inputs. Just trying this for 2 secrets and 2 coefficients num_points = int(sys.argv[1]) threshold = int(sys.argv[2]) secret1 = int(sys.argv[3]) secret2 = int(sys.argv[4]) coeff1 = int(sys.argv[5]) coeff2 = int(sys.argv[6]) # Determine a large-enough prime number prime = get_large_enough_prime([max(abs(secret1), abs(secret2))*max(abs(coeff1), abs(coeff2)), num_points]) # Compute shares of each secret shares1 = secret_int_to_points_given_prime(secret1, threshold, num_points, prime) print shares1 shares2 = secret_int_to_points_given_prime(secret2, threshold, num_points, prime) print shares2 # Reconstruct the shares of the linear combination of the secret shares3 = [] for i in range(1,num_points+1): shares3.append((i, (coeff1*shares1[i-1][1] + coeff2*shares2[i-1][1]) % prime)) print shares3 recovered_sum = points_to_secret_int(shares3[1:1+threshold])
