def step_4_batched(n, gk, g1_d, g1_a, g1_hat_a, crs_sm):
y2 = [gk.q.random() for x in range(n - 1)] + [1]
inf1, _ = prover.get_infs(gk)
g2_beta = crs_sm.g2_beta
g2_beta_hat = crs_sm.g2_betahat
left = gk.e(mexp(y2, g1_d, inf1), gk.g2)
right = (gk.e(mexp(y2, g1_a, inf1), g2_beta) *
gk.e(mexp(y2, g1_hat_a, inf1), g2_beta_hat))
return left == right
def step_5_batched(gk, pk, g1_t, crs_con, g1_a_hat, N, M, MP):
infT = get_infT(gk)
_, inf2 = prover.get_infs(gk)
g1_hat_rho = crs_con.g1rhohat
g1_poly_hats = crs_con.g1_poly_hats
y3 = [gk.q.random(), 1]
q = gk.e(g1_t, mexp(y3, pk, inf2))
right = q * gk.e(g1_hat_rho, mexp(y3, N, inf2)).inv()
left = infT
for ph, mp, a, m in zip(g1_poly_hats, MP, g1_a_hat, M):
left *= gk.e(ph, mexp(y3, mp, inf2)) * gk.e(a, mexp(y3, m, inf2)).inv()
return left == right
def step_3_batched(n, gk, g1_a, g2_b, g1_c, crs_1sp, g2_rho):
y1 = [gk.q.random() for x in range(n - 1)] + [1]
infT = get_infT(gk)
inf1, _ = prover.get_infs(gk)
g1_alpha_poly_zero = crs_1sp.g1_alpha_poly_zero
g2alpha = crs_1sp.g2alpha
pair_alpha = crs_1sp.pair_alpha
right = (gk.e(mexp(y1, g1_c, inf1), g2_rho) *
(pair_alpha**(sum(y1) % gk.q)))
left = infT
for yi, a, b in zip(y1, g1_a, g2_b):
left *= gk.e(yi * (a + g1_alpha_poly_zero), b + g2alpha)
return left == right