def test_evaluate_pos_point_pos_coef():
polynomial = [9, 7, 4, 2]
xlist = [5, 11]
p = 71
# 9 + 7 * 5 + 4 * 5^2 + 2 * 5^3 = 394
# 9 + 7 * 11 + 4 * 11^2 + 2 * 11^3 = 3,232
assert polynomials.evaluate(polynomial, xlist, p) == [(5, 39), (11, 37)]
def test_evaluate_pos_result_below_p():
polynomial = [7, 88, -5, 33]
xlist = [4, 3]
p = 3643
# 7 + 88 * 4 + -5 * 4^2 + 33 * 4^3 = 2,391
# 7 + 88 * 3 + -5 * 3^2 + 33 * 3^3 = 1,117
assert polynomials.evaluate(polynomial, xlist, p) == [(4, 2391), (3, 1117)]
def test_evaluate_pos_result_above_p():
polynomial = [7, 88, -5, 33]
xlist = [4, 5]
p = 1013
# 7 + 88 * 4 + -5 * 4^2 + 33 * 4^3 = 2,391
# 7 + 88 * 5 + -5 * 5^2 + 33 * 5^3 = 4,447
assert polynomials.evaluate(polynomial, xlist, p) == [(4, 365), (5, 395)]
def test_evaluate_neg_result_above_p():
polynomial = [-36, 88, -5, -33]
xlist = [10, 11]
p = 1013
# -36 + 88 * 10 + -5 * 10^2 + -33 * 10^3 = -32,656
# -36 + 88 * 11 + -5 * 11^2 + -33 * 11^3 = -43,596
assert polynomials.evaluate(polynomial, xlist, p) == [(10, 773), (11, 976)]
def test_evaluate_pos_secret_above_p():
polynomial = [88, -5, 33]
xlist = [5, 8]
p = 71
# 88 - 5 * 5 + 33 * 5^2 = 888
# 88 - 5 * 8 + 33 * 8^2 = 2,160
assert polynomials.evaluate(polynomial, xlist, p) == [(5, 36), (8, 30)]
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 test_evaluate_neg_result_below_p():
polynomial = [-3, 8, -5, -6]
xlist = [10, -7, 3]
p = 11443
# -3 + 8 * 10 + -5 * 10^2 + -6 * 10^3 = -6,423
# -3 + 8 * (-7) + -5 * (-7)^2 + -6 * (-7)^3 = 1,754
# -3 + 8 * 3 + -5 * 3^2 + -6 * 3^3 = -186
assert polynomials.evaluate(polynomial, xlist, p) == [(10, 5020), (-7, 1754), (3, 11257)]
def test_evaluate_neg_secret_below_p():
polynomial = [-7, 88, -5, 33]
xlist = [4, -3, 7]
p = 71
# -7 + 88 * 4 + -5 * 4^2 + 33 * 4^3 = 2,377
# -7 + 88 * (-3) + -5 * (-3)^2 + 33 * (-3)^3 = -1,207
# -7 + 88 * 7 + -5 * 7^2 + 33 * 7^3 = 11,683
assert polynomials.evaluate(polynomial, xlist, p) == [(4, 34), (-3, 0), (7, 39)]
def test_evaluate_pos_secret_below_p():
polynomial = [15, -5, 33]
xlist = [2, 5, 8]
p = 71
# 15 + (-10) + 33 * 4 = 137
# 15 + (-25) + 33 * 25 = 815
# 15 + (-40) + 33 * 8^2 = 2,087
assert polynomials.evaluate(polynomial, xlist, p) == [(2, 66), (5, 34), (8, 28)]
def test_evaluate_neg_point_pos_coef():
polynomial = [9, 7, 4, 2]
xlist = [-6, -7, -2]
p = 71
# 9 + 7 * (-6) + 4 * (-6)^2 + 2 * (-6)^3 = -321
# 9 + 7 * (-7) + 4 * (-7)^2 + 2 * (-7)^3 = -530
# 9 + 7 * (-2) + 4 * (-2)^2 + 2 * (-2)^3 = -5
assert polynomials.evaluate(polynomial, xlist, p) == [(-6, 34), (-7, 38), (-2, 66)]
def test_evaluate_pos_point_neg_coef():
polynomial = [-2, 5, -3, 0, 7]
xlist = [12, 5, 11]
p = 991
# -2 + 5 * 12 + -3 * 12^2 + 0 + 7 * 12^4 = 144,778
# -2 + 5 * 5 + -3 * 5^2 + 0 + 7 * 5^4 = 4,323
# -2 + 5 * 11 + -3 * 11^2 + 0 + 7 * 11^4 = 102,177
assert polynomials.evaluate(polynomial, xlist, p) == [(12, 92), (5, 359), (11, 104)]
def test_evaluate_neg_point_neg_coef():
polynomial = [-2, 5, -3, 7, 0]
xlist = [-12, -5, -11]
p = 991
# -2 + 5 * -12 + -3 * (-12)^2 + 7 * (-12)^3 + 0 = -12,590
# -2 + 5 * -5 + -3 * (-5)^2 + 7 * (-5)^3 + 0 = -977
# -2 + 5 * -11 + -3 * (-11)^2 + 7 * (-11)^3 + 0 = -9,737
assert polynomials.evaluate(polynomial, xlist, p) == [(-12, 293), (-5, 14), (-11, 173)]
def test_interpolate_result_prime_above():
coefficients = [43, 10, 5]
prime = 71
xlist = [-2, 4, 5]
points = polynomials.evaluate(coefficients, xlist, prime)
f = polynomials.interpolate(points, prime)
assert f(10) == 643 % prime
def test_interpolate_result_prime_below():
coefficients = [1, 2, 2]
prime = 71
xlist = [-2, 4, 5]
points = polynomials.evaluate(coefficients, xlist, prime)
f = polynomials.interpolate(points, prime)
assert f(5) == 61
def test_evaluate_neg_secret_above_p():
polynomial = [-3643, 88, -5, 33]
xlist = [4, -3, 7]
p = 1013
# -3643 + 88 * 4 + -5 * 4^2 + 33 * 4^3 = -1,259
# -3643 + 88 * (-3) + -5 * (-3)^2 + 33 * (-3)^3 = -4,843
# -3643 + 88 * 7 + -5 * 7^2 + 33 * 7^3 = 8,047
assert polynomials.evaluate(polynomial, xlist, p) == [(4, 767), (-3, 222), (7, 956)]
def test_interpolate_eval_neg():
coefficients = [-22, 7, -5]
prime = 71
xlist = [-2, 4, 5]
points = polynomials.evaluate(coefficients, xlist, prime)
f = polynomials.interpolate(points, prime)
assert f(2) == -28 % prime and f(-2) == -56 % prime
def test_interpolate_eval_pos_below_p():
coefficients = [22, -7, 5]
prime = 71
xlist = [-2, 4, 5]
points = polynomials.evaluate(coefficients, xlist, prime)
f = polynomials.interpolate(points, prime)
assert f(2) == 28 % prime and f(-2) == 56 % prime
def test_interpolate_pos_point_pos_coef_pos_eval():
# polynomial: 9 * x^3 + 4 * x^2 + 3 * x + 11
coefficients = [11, 3, 4, 9]
prime = 71
xlist = [2, 4, 5, 9, 11]
points = polynomials.evaluate(coefficients, xlist, prime)
f = polynomials.interpolate(points, prime)
assert f(3) == 299 % prime and f(8) == 4899 % prime
def test_interpolate_pos_point_neg_coef_pos_eval():
# polynomial: -9 * x^3 + -4 * x^2 + -3 * x + -11
coefficients = [-11, -3, -4, -9]
prime = 71
xlist = [2, 4, 5, 9, 11]
points = polynomials.evaluate(coefficients, xlist, prime)
f = polynomials.interpolate(points, prime)
assert f(3) == -299 % prime and f(8) == -4899 % prime
def test_interpolate_neg_point_pos_coef_neg_eval():
# polynomial: 9 * x^3 + 4 * x^2 + 3 * x + 11
coefficients = [11, 3, 4, 9]
prime = 71
xlist = [-2, -4, -5, -9, -11]
points = polynomials.evaluate(coefficients, xlist, prime)
f = polynomials.interpolate(points, prime)
assert f(-3) == -205 % prime and f(-8) == -4365 % prime
def test_interpolate_neg_point_neg_coef_neg_eval():
# polynomial: -9 * x^3 + -4 * x^2 + -3 * x + -11
coefficients = [-11, -3, -4, -9]
prime = 71
xlist = [-2, -4, -5, -9, -11]
points = polynomials.evaluate(coefficients, xlist, prime)
f = polynomials.interpolate(points, prime)
assert f(-3) == 205 % prime and f(-8) == 4365 % prime
def test_evaluate_no_points():
polynomial = [9, 7, 4, 2]
xlist = []
p = 3
assert polynomials.evaluate(polynomial, xlist, p) == []
def test_evaluate_empty_coef():
polynomial = []
xlist = [12]
p = 71
with pytest.raises(ValueError):
polynomials.evaluate(polynomial, xlist, p)