def sim(g, msg, pks, sk, p_id, v_id):
a_list = []
r_list = []
h_list = []
for i in range(len(pks)):
if i == v_id:
a_list.append(None)
r_list.append(None)
h_list.append(None)
else:
a_i = Fr()
a_i.set_by_CSPRNG()
a_list.append(a_i)
r_i = g * a_i
r_list.append(r_i)
h_i = Fr.set_hash_of(f"{msg}{r_i.getStr()}")
h_list.append(h_i)
a = Fr()
a.set_by_CSPRNG()
r = (g * a) + reduce(
operator.add,
[pks[i] * h_list[i].neg() for i in range(len(pks)) if i != v_id])
h = Fr.set_hash_of(f"{msg}{r.getStr()}")
s = reduce(
operator.add,
[a_list[i] + a + (sk * h) for i in range(len(pks)) if i != v_id])
r_list[v_id] = r * sk
return (r_list, s)
def sign(g, msg, pks, sk, p_id, v_id):
a_list = []
r_list = []
h_list = []
for i in range(len(pks)):
if i == p_id:
a_list.append(None)
r_list.append(None)
h_list.append(None)
else:
a_i = Fr()
a_i.set_by_CSPRNG()
a_list.append(a_i)
r_i = g * a_i
r_list.append(r_i)
h_i = Fr.set_hash_of(f"{msg}{r_i.getStr()}")
h_list.append(h_i)
a = Fr()
a.set_by_CSPRNG()
r_list[p_id] = (g * a) + reduce(
operator.add,
[pks[i] * h_list[i].neg() for i in range(len(pks)) if i != p_id])
h = Fr.set_hash_of(f"{msg}{r_list[p_id].getStr()}")
s = reduce(
operator.add,
[a_list[i] + a + (sk * h) for i in range(len(pks)) if i != p_id])
r_list[v_id] = pks[v_id] * a_list[v_id]
g_hat = G2.hashAndMapToG2(f'{msg}{r_list}{pks}')
S = g_hat * s
return (r_list, S)
def verify(g, msg, pks, sk, p_id, v_id, R, S):
g_hat = G2.hashAndMapToG2(f'{msg}{R}{pks}')
R[v_id] = R[v_id] * sk.inv()
h_list = []
for i in range(len(pks)):
h_i = Fr.set_hash_of(f"{msg}{R[i].getStr()}")
h_list.append(h_i)
prod = R[v_id] + (pks[v_id] * h_list[v_id])
for i in range(len(pks)):
if i == v_id:
continue
else:
prod += R[i] + (pks[i] * h_list[i])
assert pairing(g, S) == pairing(prod, g_hat)
def verify(g, msg, pks, sk, p_id, v_id, R, s):
R[v_id] = R[v_id] * sk.inv()
h_list = [Fr.set_hash_of(f"{msg}{R[i].getStr()}") for i in range(len(pks))]
prod = reduce(operator.add,
[R[i] + (pks[i] * h_list[i]) for i in range(len(pks))])
assert g * s == prod