def _share_secret_int(num_players, reconstruction_threshold, max_secret_length, secret):
'''
Args:
num_players, the number of shares to be distributed
reconstruction_threshold, the number of shares needed for reconstruction
any collection of fewer shares will reveal no information about the secret
max_secret_length, the maximum length of the secret represented as a bytestring (ie, len(secret))
secret, an integer to be Shamir secret shared
Returns:
a list of tuples of (x, f(x)) values
Raises:
ValueError, the input parameters are invalid
'''
bitlength = max(num_players.bit_length(), max_secret_length * 8)
prime = primes.get_prime_by_bitlength(bitlength)
if not _verify_parameters(num_players, reconstruction_threshold, secret, prime):
raise ValueError("invalid secret sharing parameters")
# fix n distinct points, alpha_1,...,alpha_n in Z_ps (public)
alphas = [i for i in xrange(1, num_players + 1)]
# choose at random t points, a_1,...,a_t in Z_ps (private)
# we will use the a_i values as our coefficients to define the polynomial f(x) = (a_t x^t) + ... + (a_1 x) + s
coefficients = [secret] + random.get_distinct_positive_random_ints_in_field(reconstruction_threshold - 1, prime)
# for values of i from 1 to n, calculate f(alpha_i)
return polynomials.evaluate(coefficients, alphas, prime)
def get_large_prime(max_length):
'''
Generate a large prime that accommodates the max message length or defaults to a large prime
Args:
integer value of maximum digit-length for a message
Returns:
a sufficiently large prime to be used in the check vector authentication scheme
'''
bitlength = max(PRIME_EXP, max_length * 8)
return primes.get_prime_by_bitlength(bitlength)
def _reconstruct_secret_int(num_players, max_secret_length, shares):
'''
Args:
num_players, the total number of players (can be greater than or equal to the number of shares)
max_secret_length, the maximum length of the secret represented as a bytestring (ie, len(secret))
shares, a list of tuples representing (x, f(x)) values
Returns:
the integer that was shared by _share_secret_int if all shares are valid
otherwise, no guarantees are made about the value of the integer returned
'''
bitlength = max(num_players.bit_length(), max_secret_length * 8)
prime = primes.get_prime_by_bitlength(bitlength)
return polynomials.interpolate(shares, prime)(0)
def test_get_prime_by_bitlength_prime():
secret_size = 17
assert primes.get_prime_by_bitlength(secret_size) == 2**19 - 1
def test_get_prime_by_bitlength_negative():
secret_size = -7
with pytest.raises(ValueError):
primes.get_prime_by_bitlength(secret_size)
def test_get_prime_by_bitlength_standard():
secret_size = 61
assert primes.get_prime_by_bitlength(secret_size) == 2**89 - 1
def test_get_prime_by_bitlength_too_large():
secret_size = 4444
with pytest.raises(ValueError):
primes.get_prime_by_bitlength(secret_size)
def test_get_prime_by_bitlength_very_large():
secret_size = 4400
assert primes.get_prime_by_bitlength(secret_size) == 2**4423 - 1
def test_get_prime_by_batch_equal_prime():
secret_size = 521
assert primes.get_prime_by_bitlength(secret_size) == 2**607 - 1
def test_get_prime_by_bitlength_zero():
secret_size = 0
assert primes.get_prime_by_bitlength(secret_size) == 2**2 - 1
