def main():
parser = argparse.ArgumentParser()
parser.add_argument('-m', type=int, default=1)
args = parser.parse_args(sys.argv[1:])
with open('file_to_signature.txt') as f:
file = json.load(f)
m = open(file['file'], 'rb').read()
if args.m == 1: # публичные параметры
len_p = read_param('len_p.j', 'l')
p, q, g = get_public_params(len_p)
save_param('p.json', 'p', p)
save_param('q.json', 'q', q)
save_param('g.json', 'g', g)
elif args.m == 2: # частные парметры
p = read_param('p.json', 'p')
q = read_param('q.json', 'q')
g = read_param('g.json', 'g')
x, y = get_private_params(p, q, g)
save_param('x.json', 'x', x)
save_param('y.json', 'y', y)
elif args.m == 3: # Алиса генерит k < q
q = read_param('q.json', 'q')
k = utils.get_big_prime(2, q)
save_param('k.json', 'k', k)
# elif args.m == 4: # Алиса подписывает
g = read_param('g.json', 'g')
k = read_param('k.json', 'k')
p = read_param('p.json', 'p')
q = read_param('q.json', 'q')
x = read_param('x.json', 'x')
r = pow(g, k, p) % q
s = (utils.inverse(k, q) * (get_hash(m) + x * r)) % q
save_param('signature.json', 'r', r)
save_param('signature.json', 's', s)
elif args.m == 4: # боб проверяет
s = read_param('signature.json', 's')
r = read_param('signature.json', 'r')
q = read_param('q.json', 'q')
p = read_param('p.json', 'p')
g = read_param('g.json', 'g')
y = read_param('y.json', 'y')
w = utils.inverse(s, q)
u1 = get_hash(m) * w % q
u2 = r * w % q
v = ((pow(g, u1, p) * pow(y, u2, p)) % p) % q
save_param('v.json', 'v', v)
if v == r:
print("Подпись верна")
input()
else:
print("Подпись не верна")
# 2.3
else:
write_log('Bad args')
def get_private_params_Bob(p, g):
while True:
y = utils.get_big_digit() % p
if gcd(y, p - 1) == 1 and utils.inverse(y, p - 1) >= 0:
break
d = pow(g, y, p)
z = utils.inverse(y, p - 1)
with open('log.log', 'a') as f:
f.write("Бобом вычислен закрытый параметр y: {}\n".format(y))
f.write(
"Бобом вычислен параметр z (обратный элемент к y): {}\n".format(z))
f.write("Бобом сгенерирован открытый параметр d: {}\n".format(d))
return y, d, z
def sum(P, Q, a, p):
if EllipticPoint.iszero(P):
return Q
elif EllipticPoint.iszero(Q):
return P
if EllipticPoint.equal_inv(P, Q, p):
return EllipticPoint(p, -1, -1)
if not EllipticPoint.equal(P, Q):
m = ((P.y - Q.y) % p) * inverse((P.x - Q.x) % p, p) % p
else:
m = (3 * P.x * P.x + a) * inverse((2 * P.y) % p, p) % p
r = EllipticPoint(p)
r.x = (m * m - P.x - Q.x) % p
r.y = (-P.y + m * (P.x - r.x)) % p
return r
def gauss(n, SOLE, m, changable):
for i in range(n):
if i < n:
if SOLE[i][i] == 0:
change_matrix(SOLE, changable, i, i)
else:
changable.remove(i)
elem = SOLE[i][i]
if elem != 1:
obr_elem = utils.inverse(elem, m)
for j in range(len(SOLE[i])):
SOLE[i][j] *= obr_elem
SOLE[i][j] %= m
for k in range(i + 1, n):
mult = SOLE[k][i]
mult = -mult
for a in range(len(SOLE[i])):
SOLE[k][a] += mult * SOLE[i][a]
SOLE[k][a] %= m
if i != 0:
for k in range(0, i):
mult = SOLE[k][i]
mult = -mult
for a in range(len(SOLE[i])):
SOLE[k][a] += mult * SOLE[i][a]
SOLE[k][a] %= m
for j in range(n):
c = collections.Counter(SOLE[j])
if c[0] == len(SOLE[j]):
SOLE.remove(SOLE[j])
n -= 1
not_solved(SOLE)
return SOLE
def gprod_verify_outer(current_hash, crs, A, len_gprod, gprod, gprod_proof, n, logn):
[crs_g, u, crs_se1, crs_se2] = crs[:]
[B, blinder] = gprod_proof[:]
current_hash = hash_integers([current_hash, gprod, blinder, int(B[0]), int(B[1]), int(B[2])])
x = current_hash % curve_order; inv_x =inverse(x);
C = crs_g[0]
for i in range(1,len_gprod):
C = add( C, crs_g[i])
C = multiply(C, curve_order - inv_x)
C = add(C, A)
vec_crs_h_exp = [1]*n; pow_inv_x = inv_x
for i in range(1,len_gprod):
vec_crs_h_exp[i] = pow_inv_x
pow_inv_x = pow_inv_x * inv_x % curve_order
vec_crs_h_exp[0] = pow_inv_x
pow_inv_x = pow_inv_x * inv_x % curve_order
for i in range(len_gprod, n):
vec_crs_h_exp[i] = pow_inv_x
inner_prod = (blinder * (x ** (len_gprod+1)) + gprod * (x ** len_gprod) - 1) % curve_order
# [current_hash, b] = gprod_verify_inner(current_hash, crs[:], vec_crs_h_exp[:], C, inner_prod, inner_proof[:],
# len_gprod, n, logn)
inner_prod_info = [vec_crs_h_exp[:], B, C, inner_prod, len_gprod]
return [current_hash, inner_prod_info[:]]
def gprod_verify_inner(current_hash, crs, vec_crs_h_exp, C, inner_prod, inner_proof, len_gprod, n, logn):
[crs_g, crs_h, u] = crs[:]
### Adding in zero knowledge
[R, blinder_2,proof, last_b, last_c] = inner_proof[:]
current_hash = hash_integers([current_hash,int(R[0]),int(R[1]), int(R[2]), blinder_2])
x = current_hash % curve_order
inner_prod = (inner_prod + blinder_2 * x ) % curve_order
C = add(C, multiply(R,x))
### Putting inner_prod into exponent.
current_hash = hash_integers([current_hash,inner_prod])
x = current_hash % curve_order;
u = multiply(u, x)
C = add(C, multiply(u,inner_prod))
vec_crs_g_exp = [1] * n;
vec_crs_h_shifted = [1] * n;
n_var = n
for j in range(logn):
n_var = n_var // 2
[CL, CR] = proof[j]
current_hash = hash_integers([current_hash,int(CL[0]),int(CL[1]), int(CL[2]),
int(CR[0]), int(CR[1]), int(CR[2])])
x = current_hash % curve_order; inv_x =inverse(x)
for i in range(n):
bin_i = int_to_binaryintarray(i,logn)
if bin_i[logn - j - 1] == 1:
vec_crs_g_exp[i] = (vec_crs_g_exp[i] * inv_x) % curve_order
vec_crs_h_shifted[i] = (vec_crs_h_shifted[i] * x) % curve_order
C = add(add(multiply(CR, inv_x), C), multiply(CL, x))
vec_crs_h_exp[0] = (vec_crs_h_exp[0] * vec_crs_h_shifted[len_gprod - 1]) % curve_order
for i in range(1,len_gprod):
vec_crs_h_exp[i] = (vec_crs_h_exp[i] * vec_crs_h_shifted[i-1]) % curve_order
for i in range(len_gprod,n):
vec_crs_h_exp[i] = (vec_crs_h_exp[i] * vec_crs_h_shifted[i]) % curve_order
inner_prod = last_b * last_c % curve_order
final_g = compute_multiexp(crs_g[:], vec_crs_g_exp[:])
final_h = compute_multiexp(crs_h[:], vec_crs_h_exp[:])
expected_outcome = multiply(final_g, curve_order - last_b)
expected_outcome = add(expected_outcome, multiply(final_h, curve_order - last_c))
expected_outcome = add(expected_outcome, multiply(u, curve_order - inner_prod))
if add( expected_outcome, C) != (1,1,0):
print("ERROR: final exponent is incorrect")
return [current_hash, 0]
return [current_hash, 1]
def attitude_control(self, quad, Ts, config):
# Current thrust orientation e_z and desired thrust orientation e_z_d
e_z = quad.dcm[:, 2]
e_z_d = -utils.vectNormalize(self.thrust_sp)
if (config.orient == "ENU"):
e_z_d = -e_z_d
# Quaternion error between the 2 vectors
qe_red = np.zeros(4)
qe_red[0] = np.dot(e_z, e_z_d) + sqrt(norm(e_z)**2 * norm(e_z_d)**2)
qe_red[1:4] = np.cross(e_z, e_z_d)
qe_red = utils.vectNormalize(qe_red)
# Reduced desired quaternion (reduced because it doesn't consider the desired Yaw angle)
self.qd_red = utils.quatMultiply(qe_red, quad.quat)
# Mixed desired quaternion (between reduced and full) and resulting desired quaternion qd
q_mix = utils.quatMultiply(utils.inverse(self.qd_red), self.qd_full)
q_mix = q_mix * np.sign(q_mix[0])
q_mix[0] = np.clip(q_mix[0], -1.0, 1.0)
q_mix[3] = np.clip(q_mix[3], -1.0, 1.0)
self.qd = utils.quatMultiply(
self.qd_red,
np.array([
cos(self.yaw_w * np.arccos(q_mix[0])), 0, 0,
sin(self.yaw_w * np.arcsin(q_mix[3]))
]))
# Resulting error quaternion
self.qe = utils.quatMultiply(utils.inverse(quad.quat), self.qd)
# Create rate setpoint from quaternion error
#@ self.rate_sp = (2.0*np.sign(self.qe[0])*self.qe[1:4])*att_P_gain
self.rate_sp = (2.0 * np.sign(self.qe[0]) *
self.qe[1:4]) * self.cTune_att_P_gain * att_P_gain
# Limit yawFF
self.yawFF = np.clip(self.yawFF, -rateMax[2], rateMax[2])
# Add Yaw rate feed-forward
self.rate_sp += utils.quat2Dcm(utils.inverse(
quad.quat))[:, 2] * self.yawFF
# Limit rate setpoint
self.rate_sp = np.clip(self.rate_sp, -rateMax, rateMax)
def shanks(m, g, h):
# Step 1
r = square_root(m) + 1
pairs = {pow(g, a, m): a for a in range(r)}
# Step 2
g1 = pow(utils.inverse(g, m), r, m)
for b in range(r): # r-1 ?
value = (pow(g1, b, m) * h) % m
if value in pairs:
return pairs[value] + r * b
def get_private_params_Alice(p, g):
while True:
x = utils.get_big_digit() % p
if gcd(x, p - 1) == 1 and utils.inverse(x, p - 1) >= 0:
break
k = pow(g, x, p)
with open('log.log', 'a') as f:
f.write("Алисой вычислен закрытый параметр x: {}\n".format(x))
f.write("Алисой сгенерирован открытый параметр k: {}\n".format(k))
return x, k
def generateSignature(p, q, g, x, message):
H = int(hexlify(CryptoBox.generateHash(message, 1)), 16)
k = number.getRandomRange(1, q)
r = utils.mod_exp(g, k, p) % q
k_inv = utils.inverse(k, q)
s = (k_inv * (H + x * r)) % q
if (r == 0 or s == 0):
# since it is very unlikely to make a recursive call, function will terminate eventually
return generateSignature(p, q, g, x, message)
return r, s
def setup(self, nbits=512):
p = get_rand_prime(nbits)
q = get_rand_prime(nbits)
while p == q:
q = get_rand_prime(nbits)
n = p * q
phi = (p-1) * (q-1)
e = randrange(2**16, 2**17)
d = inverse(e, phi)
while d == -1:
e = randrange(2**16, 2**17)
d = inverse(e, phi)
return {
"p": p,
"q": q,
"n": n,
"phi": phi,
"e": e,
"d": d
}
def gprod_prove_inner(current_hash, crs, vec_b, vec_c,inner_prod, n, logn):
[crs_g, crs_h, u] = crs[:]
proof = []
### Adding in zero knowledge
vec_r = [0]*n;
for i in range(n):
vec_r[i] = randbelow(curve_order)
R = compute_multiexp(crs_h[:], vec_r[:])
blinder_2 = compute_innerprod(vec_b[:], vec_r[:])
current_hash = hash_integers([current_hash,int(R[0]),int(R[1]), int(R[2]), blinder_2])
x = current_hash % curve_order
inner_prod = (inner_prod + blinder_2 * x ) % curve_order
for i in range(n):
vec_c[i] = (vec_c[i] + vec_r[i] * x) % curve_order
### Inserting inner_prod into exponent.
current_hash = hash_integers([current_hash,inner_prod])
x = current_hash % curve_order;
u = multiply(u, x)
for j in range(logn):
n = n // 2
zL = compute_innerprod(vec_b[n:], vec_c[:n])
zR = compute_innerprod(vec_b[:n], vec_c[n:])
CL = add(compute_multiexp(crs_g[:n], vec_b[n:]), compute_multiexp(crs_h[n:],vec_c[:n]))
CL = add(CL, multiply(u, zL))
CR = add(compute_multiexp(crs_g[n:], vec_b[:n]), compute_multiexp(crs_h[:n],vec_c[n:]))
CR = add(CR, multiply(u, zR))
proof.append([CL, CR])
current_hash = hash_integers([current_hash,int(CL[0]),int(CL[1]), int(CL[2]),
int(CR[0]), int(CR[1]), int(CR[2])])
x = current_hash % curve_order; inv_x =inverse(x);
for i in range(n):
crs_g[i] = add(multiply(crs_g[n + i],inv_x), crs_g[i] )
crs_h[i] = add(multiply(crs_h[n + i],x), crs_h[i] )
vec_b[i] = (vec_b[i] + x * vec_b[n + i] ) % curve_order
vec_c[i] = (vec_c[i] + inv_x * vec_c[n + i] ) % curve_order
crs_g = crs_g[:n]; crs_h = crs_h[:n]
vec_b = vec_b[:n]; vec_c = vec_c[:n]
return [current_hash, [R, blinder_2, proof[:], vec_b[0], vec_c[0]]]
def verifySignature(p, q, g, y, r, s, message):
if r <= 0 or r >= q or s <= 0 or s >= q:
print "Rejected!"
return
H = int(hexlify(CryptoBox.generateHash(message, 1)), 16)
w = utils.inverse(s, q)
u1 = (H * w) % q
u2 = (r * w) % q
v = ((utils.mod_exp(g, u1, p) * utils.mod_exp(y, u2, p)) % p) % q
return True if v == r else False
def generateSignature(p, q, g, x, message):
H = int(hexlify(CryptoBox.generateHash(message, 1)), 16)
k = number.getRandomRange(1, q)
r = utils.mod_exp(g, k, p) % q
k_inv = utils.inverse(k, q)
s = (k_inv * (H + x * r)) % q
if (r == 0 or s == 0):
# since it is very unlikely to make a recursive call, function will terminate eventually
return generateSignature(p, q, g, x, message)
return r, s
def verifySignature(p, q, g, y, r, s, message):
if r <= 0 or r >= q or s <= 0 or s >= q:
print "Rejected!"
return
H = int(hexlify(CryptoBox.generateHash(message, 1)), 16)
w = utils.inverse(s, q)
u1 = (H * w) % q
u2 = (r * w) % q
v = ((utils.mod_exp(g, u1, p) * utils.mod_exp(y, u2, p)) % p) % q
return True if v == r else False
def ifft(b, m, n, k):
w = utils.inverse(primitive_root(m, n), m) % m
r = {(0, k): b}
for s in range(k - 1, -1, -1):
t = 0
while t < n - 1:
b_new = [r[(t, s + 1)][j] for j in range(pow(2, s + 1))]
e = int(bin(t // pow(2, s))[2:].zfill(k)[::-1], 2)
r[(t, s)] = [(b_new[j] + pow(w, e) * b_new[j + pow(2, s)]) % m
for j in range(pow(2, s))]
r[(t + pow(2, s), s)] = [
(b_new[j] + pow(w, e + n // 2) * b_new[j + pow(2, s)]) % m
for j in range(pow(2, s))
]
t += pow(2, s + 1)
a = [0] * n
for i in range(n):
# print(int(bin(i)[2:].zfill(k)[::-1], 2))
# print(utils.inverse(m, n % m))
a[int(bin(i)[2:].zfill(k)[::-1],
2)] = (utils.inverse(n % m, m) * r[(i, 0)][0]) % m
print('Вектор a = {}'.format(str(a)))
def signature(M, G, a, n, p, x):
r, k, R = 0, None, None
while r == 0:
k = random.randint(1, n - 1)
R = ep.mul(G, k, a, p)
r = R.x % p
e = hsh(M, n)
assert 0 <= e < n
s = (e + r*x) * inverse(k, n) % n
print('Данные подписаны')
print('R={}, s={}'.format(R, s))
return R, s
def create_keys(cnt, l):
result = []
t = []
n = sympy.randprime(2 ** (l - 1), 2 ** l)
for i in range(cnt):
e = random.randint(2, n - 1)
while sympy.gcd(e, n - 1) != 1 and e not in t:
e = random.randint(2, n - 1)
t.append(e)
d = utils.inverse(e, n - 1)
result.append([[e, n], [d, n]])
return result
def gprod_prove_outer(current_hash, crs, vec_a, len_gprod, gprod, n, logn):
[crs_g, u, crs_se1, crs_se2] = crs[:]
vec_b = [0] * n
vec_b[0] = 1
for i in range(1,len_gprod):
vec_b[i] = vec_a[i] * vec_b[i-1] % curve_order
for i in range(len_gprod,n):
vec_b[i] = randbelow(curve_order)
B = compute_multiexp(crs_g[:], vec_b[:])
blinder = compute_innerprod(vec_a[len_gprod:],vec_b[len_gprod:])
current_hash = hash_integers([current_hash, gprod, blinder, int(B[0]), int(B[1]), int(B[2])])
x = current_hash % curve_order; inv_x =inverse(x);
vec_c = [0] * n;
pow_x = x;
pow_x2 = 1
for i in range(len_gprod-1):
vec_c[i] = ( vec_a[i+1] * pow_x - pow_x2) % curve_order
pow_x = pow_x * x % curve_order
pow_x2 = pow_x2 * x % curve_order
vec_c[len_gprod-1] = (vec_a[0] * pow_x - pow_x2) % curve_order
pow_x = pow_x * x % curve_order
for i in range(len_gprod, n):
vec_c[i] = (vec_a[i] * pow_x) % curve_order
crs_h = [0]*n; pow_inv_x = inv_x
for i in range(len_gprod - 1):
crs_h[i] = multiply(crs_g[i+1], pow_inv_x)
pow_inv_x = pow_inv_x * inv_x % curve_order
crs_h[len_gprod-1] = multiply(crs_g[0], pow_inv_x)
pow_inv_x = pow_inv_x * inv_x % curve_order
for i in range(len_gprod, n):
crs_h[i] = multiply(crs_g[i], pow_inv_x)
inner_prod = (blinder * (x ** (len_gprod+1)) + gprod * (x ** len_gprod) - 1) % curve_order
crs = [crs_g[:],crs_h[:],u]
# [current_hash, inner_proof] = gprod_prove_inner(current_hash, crs[:], vec_b[:], vec_c[:], inner_prod, n, logn)
inner_prod_info = [crs_h[:], vec_b[:], vec_c[:], inner_prod]
return [current_hash, [B, blinder], inner_prod_info[:]]
def garner(r, m):
n = len(m)
c = [0] * n
for i in range(1, n):
c[i] = 1
for j in range(0, i):
u = utils.inverse(m[j], m[i])
c[i] = u * c[i] % m[i]
u = r[0]
x = u
for i in range(1, n):
u = (r[i] - x) * c[i] % m[i]
x = x + u * functools.reduce(mul, (m[idx] for idx in range(i)), 1)
return x
def generator_elliptic_curve(l, m):
while True:
while True:
p = get_prime(l)
if p % 4 == 1:
break
a, b = complex_decomposition(1, p)
assert a * a + b * b == p
T = [-2 * a, -2 * b, 2 * a, 2 * b]
for t in T:
N = p + 1 + t
if isprime(N // 2):
r = N // 2
break
if isprime(N // 4):
r = N // 4
break
else:
continue
good = True
for i in range(1, m):
if (p**i) % r == 1:
good = False
if p == r or not good:
continue
while True:
e = EllipticPoint(p)
A = ((e.y**2 - e.x**3) * inverse(e.x, p)) % p
good = False
if N == r * 2:
if legendre_symbol(-A, p) == -1:
good = True
if N == r * 4:
if legendre_symbol(-A, p) == 1:
good = True
if not good:
continue
m = EllipticPoint.mul(e, N, A, p)
if m == EllipticPoint(p, -1, -1):
break
Q = EllipticPoint.mul(e, N // r, A, p)
return p, A, Q, r
def generateKeys(security_level=1):
bit_count = None
if security_level == 1:
bit_count = 1024 / 2
elif security_level == 2:
bit_count = 2048 / 2
elif security_level == 3:
bit_count = 3072 / 2
p, q = number.getPrime(bit_count), number.getPrime(bit_count)
#p = utils.gen_random(bit_count)
#count = 3 # test primality thrice
#while utils.rm_primality(p) == False or (utils.rm_primality(p) == True and count != 0):
# p = utils.gen_random(bit_count)
# if utils.rm_primality(p) == True:
# count -= 1
#q = utils.gen_random(bit_count)
#count = 3 # test primality thrice
#while utils.rm_primality(q) == False or (utils.rm_primality(q) == True and count != 0):
# q = utils.gen_random(bit_count)
# if utils.rm_primality(q) == True:
# count -= 1
N = p * q
phi_N = (p - 1) * (q - 1)
e = randint(1, phi_N - 1)
while gcd(e, phi_N) != 1:
e = randint(1, phi_N - 1)
d = utils.inverse(e, phi_N)
return e, N, d, p, q
def generateKeys(security_level = 1):
bit_count = None
if security_level == 1:
bit_count = 1024 / 2
elif security_level == 2:
bit_count = 2048 / 2
elif security_level == 3:
bit_count = 3072 / 2
p, q = number.getPrime(bit_count), number.getPrime(bit_count)
#p = utils.gen_random(bit_count)
#count = 3 # test primality thrice
#while utils.rm_primality(p) == False or (utils.rm_primality(p) == True and count != 0):
# p = utils.gen_random(bit_count)
# if utils.rm_primality(p) == True:
# count -= 1
#q = utils.gen_random(bit_count)
#count = 3 # test primality thrice
#while utils.rm_primality(q) == False or (utils.rm_primality(q) == True and count != 0):
# q = utils.gen_random(bit_count)
# if utils.rm_primality(q) == True:
# count -= 1
N = p * q
phi_N = (p-1) * (q-1)
e = randint(1, phi_N - 1)
while gcd(e, phi_N) != 1:
e = randint(1, phi_N - 1)
d = utils.inverse(e, phi_N)
return e, N, d, p, q
def __init__(self, terminals, query):
self.variables = [Variable("S"), Variable("C")]
self.terminals = terminals[:]
self.productions = [
CFGRule(
Variable("S"),
[Variable("C"), Terminal(query),
Variable("C")]),
CFGRule(Variable("C"),
[Variable("C"), Variable("C")]),
CFGRule(Variable("C"), [])
]
for terminal in self.terminals:
self.productions.append(
CFGRule(Variable("C"), [
Terminal(terminal),
Variable("C"),
Terminal(inverse(terminal))
]))
self.start = Variable("S")
self.__empty = None
def generate_all_states_rec(bs, functions, n_added=0):
if bs.total_length() >= max_size or len(
functions) == 0 or n_added >= 2:
res.append(bs)
return
cp_temp = bs.get_constraint_path()
function = functions[0]
f_l = function.to_list()
f_str = " ".join(f_l)
if starts_with(f_str, cp) and\
starts_with(f_str, cp_temp):
generate_all_states_rec(
BackwardState(bs.backward_paths[:] +
[BackwardPath(f_str, "f")]), functions[1:],
n_added + 1)
f_str = " ".join(function.get_inverse_function())
if starts_with(f_str, cp) and \
starts_with(f_str, cp_temp):
generate_all_states_rec(
BackwardState(bs.backward_paths[:] +
[BackwardPath(function, "b")]), functions[1:],
n_added + 1)
# kinks
for i in range(1, len(f_l)):
f_left = f_l[:i]
f_right = f_l[i:]
f_str_right = " ".join(f_right)
f_left_inv = " ".join(map(lambda x: inverse(x, "-"), f_left[::-1]))
if starts_with(f_str_right, cp) and \
starts_with(f_str_right, cp_temp) and \
starts_with(f_left_inv, cp) and \
starts_with(f_left_inv, cp_temp) and \
starts_with(f_str_right, f_left_inv):
generate_all_states_rec(
BackwardState(bs.backward_paths[:] + [
BackwardPath(f_left[::-1], "b"),
BackwardPath(f_right, "f")
]), functions, n_added)
generate_all_states_rec(bs, functions[1:], n_added)
def decryption(self, message):
n = self.parameters['p'] * self.parameters['q']
# 1- Convert to CRT domain
yp = message % self.parameters['p']
yq = message % self.parameters['q']
# 2- Do the computations
dp = self.parameters['d'] % (self.parameters['p'] - 1)
dq = self.parameters['d'] % (self.parameters['q'] - 1)
xp = pow(yp, dp, self.parameters['p'])
xq = pow(yq, dq, self.parameters['q'])
# 3- Inverse transform
inv = inverse(self.parameters['p'], self.parameters['q'])
print(inv)
cp = pow(self.parameters['q'], self.parameters['p'] - 2, self.parameters['p'])
cq = pow(self.parameters['p'], self.parameters['q'] - 2, self.parameters['q'])
result = ((self.parameters['q'] * cp * xp) + (self.parameters['p'] * cq * xq)) % n
return result
def verify_multiexp_and_gprod_inner(current_hash, crs, vec_crs_h_exp,
len_gprod, B, C, inner_prod, ciphertexts_1,
ciphertexts_2, commit_exps, multiexp_1,
multiexp_2, inner_proof, n, logn):
[crs_g, u, crs_se1, crs_se2] = crs[:]
### Adding in zero knowledge
[zkinfo, proof, final_values] = inner_proof[:]
[Rgp, Sgp, Rme, blgp1, blgp2, Bl1me, Bl2me] = zkinfo[:]
current_hash = hash_integers([
current_hash,
int(Rgp[0]),
int(Rgp[1]),
int(Rgp[2]),
int(Sgp[0]),
int(Sgp[1]),
int(Sgp[2]), blgp1, blgp2,
int(Rme[0]),
int(Rme[1]),
int(Rme[2]),
int(Bl1me[0]),
int(Bl1me[1]),
int(Bl1me[2]),
int(Bl2me[0]),
int(Bl2me[1]),
int(Bl2me[2])
])
x = current_hash % curve_order
inner_prod = (inner_prod + blgp1 * x + blgp2 * x**2) % curve_order
B = add(B, multiply(Rgp, x))
C = add(C, multiply(Sgp, x))
commit_exps = add(commit_exps, multiply(Rme, x))
multiexp_1 = add(multiexp_1, multiply(Bl1me, x))
multiexp_2 = add(multiexp_2, multiply(Bl2me, x))
### Putting inner_prod into exponent.
current_hash = hash_integers([current_hash, inner_prod])
x = current_hash % curve_order
u = multiply(u, x)
B = add(B, multiply(u, inner_prod))
[final_b, final_c, final_exp] = final_values[:]
vec_crs_g_exp = [final_b] * n
vec_crs_h_shifted = [1] * n
n_var = n
for j in range(logn):
n_var = n_var // 2
[CLgp_b, CLgp_c, CRgp_b, CRgp_c, zLme, zRme, CLme, CRme] = proof[j]
current_hash = hash_integers([
current_hash,
int(CLgp_b[0]),
int(CLgp_b[1]),
int(CLgp_b[2]),
int(CLgp_c[0]),
int(CLgp_c[1]),
int(CLgp_c[2]),
int(CRgp_b[0]),
int(CRgp_b[1]),
int(CRgp_b[2]),
int(CRgp_c[0]),
int(CRgp_c[1]),
int(CRgp_c[2]),
int(zLme[0][0]),
int(zLme[0][1]),
int(zLme[0][2]),
int(zRme[0][0]),
int(zRme[0][1]),
int(zRme[0][2]),
int(CLme[0]),
int(CLme[1]),
int(CLme[2]),
int(CRme[0]),
int(CRme[1]),
int(CRme[2])
])
x = current_hash % curve_order
inv_x = inverse(x)
for i in range(n):
bin_i = int_to_binaryintarray(i, logn)
if bin_i[logn - j - 1] == 1:
vec_crs_g_exp[i] = (vec_crs_g_exp[i] * inv_x) % curve_order
vec_crs_h_shifted[i] = (vec_crs_h_shifted[i] * x) % curve_order
B = add(add(multiply(CRgp_b, inv_x), B), multiply(CLgp_b, x))
C = add(add(multiply(CRgp_c, inv_x), C), multiply(CLgp_c, x))
multiexp_1 = add(add(multiply(zLme[0], x), multiexp_1),
multiply(zRme[0], inv_x))
multiexp_2 = add(add(multiply(zLme[1], x), multiexp_2),
multiply(zRme[1], inv_x))
commit_exps = add(add(multiply(CRme, inv_x), commit_exps),
multiply(CLme, x))
ciphertexts_1_final = compute_multiexp(ciphertexts_1[:],
vec_crs_h_shifted[:])
ciphertexts_2_final = compute_multiexp(ciphertexts_2[:],
vec_crs_h_shifted[:])
if add(multiply(ciphertexts_1_final, curve_order - final_exp),
multiexp_1) != (1, 1, 0):
print("ERROR: final ciphertext 1 is incorrect")
return [current_hash, 0]
if add(multiply(ciphertexts_2_final, curve_order - final_exp),
multiexp_2) != (1, 1, 0):
print("ERROR: final ciphertext 2 is incorrect")
return [current_hash, 0]
current_hash = hash_integers([current_hash, final_b, final_c, final_exp])
x = current_hash % curve_order
vec_crs_h_exp[0] = (x**2 * vec_crs_g_exp[0] +
x * vec_crs_h_shifted[0] * final_exp +
vec_crs_h_exp[0] * vec_crs_h_shifted[len_gprod - 1] *
final_c) % curve_order
for i in range(1, len_gprod):
vec_crs_h_exp[i] = (x**2 * vec_crs_g_exp[i] +
x * vec_crs_h_shifted[i] * final_exp +
vec_crs_h_exp[i] * vec_crs_h_shifted[i - 1] *
final_c) % curve_order
for i in range(len_gprod, n):
vec_crs_h_exp[i] = (
x**2 * vec_crs_g_exp[i] + x * vec_crs_h_shifted[i] * final_exp +
vec_crs_h_exp[i] * vec_crs_h_shifted[i] * final_c) % curve_order
inner_prod = final_b * final_c % curve_order
expected_outcome = compute_multiexp(crs_g[:], vec_crs_h_exp[:])
expected_outcome = add(expected_outcome,
multiply(u, (inner_prod * x**2) % curve_order))
expected_outcome = add(expected_outcome,
multiply(commit_exps, curve_order - x))
expected_outcome = add(expected_outcome, multiply(C, curve_order - 1))
expected_outcome = add(expected_outcome, multiply(B,
(-x**2) % curve_order))
if expected_outcome != Z1:
print("ERROR: final exponent is incorrect")
return [current_hash, 0]
return [current_hash, 1]
def prove_multiexp_and_gprod_inner(current_hash, crs, vec_b, vec_c, inner_prod,
ciphertexts_1, ciphertexts_2, vec_exp, n,
logn):
[crs_g, crs_h_scaled, u] = crs[:]
crs_h = crs_g[:]
proof = []
### Adding in zero knowledge
vec_rgp = [0] * n
vec_sgp = [0] * n
vec_rme = [0] * n
for i in range(n):
vec_rgp[i] = randbelow(curve_order)
vec_sgp[i] = randbelow(curve_order)
vec_rme[i] = randbelow(curve_order)
Rgp = compute_multiexp(crs_g[:], vec_rgp[:])
Sgp = compute_multiexp(crs_h_scaled[:], vec_sgp[:])
blgp1 = (compute_innerprod(vec_b[:], vec_sgp[:]) +
compute_innerprod(vec_c[:], vec_rgp[:])) % curve_order
blgp2 = compute_innerprod(vec_rgp[:], vec_sgp[:])
Rme = compute_multiexp(crs_h[:], vec_rme[:])
Bl1me = compute_multiexp(ciphertexts_1[:], vec_rme[:])
Bl2me = compute_multiexp(ciphertexts_2[:], vec_rme[:])
zkinfo = [Rgp, Sgp, Rme, blgp1, blgp2, Bl1me, Bl2me]
current_hash = hash_integers([
current_hash,
int(Rgp[0]),
int(Rgp[1]),
int(Rgp[2]),
int(Sgp[0]),
int(Sgp[1]),
int(Sgp[2]), blgp1, blgp2,
int(Rme[0]),
int(Rme[1]),
int(Rme[2]),
int(Bl1me[0]),
int(Bl1me[1]),
int(Bl1me[2]),
int(Bl2me[0]),
int(Bl2me[1]),
int(Bl2me[2])
])
x = current_hash % curve_order
inner_prod = (inner_prod + blgp1 * x + blgp2 * x**2) % curve_order
for i in range(n):
vec_b[i] = (vec_b[i] + vec_rgp[i] * x) % curve_order
vec_c[i] = (vec_c[i] + vec_sgp[i] * x) % curve_order
vec_exp[i] = (vec_exp[i] + vec_rme[i] * x) % curve_order
### Inserting inner_prod into exponent.
current_hash = hash_integers([current_hash, inner_prod])
x = current_hash % curve_order
u = multiply(u, x)
for j in range(logn):
n = n // 2
zLgp = compute_innerprod(vec_b[n:], vec_c[:n])
zRgp = compute_innerprod(vec_b[:n], vec_c[n:])
zLme = [
compute_multiexp(ciphertexts_1[n:], vec_exp[:n]),
compute_multiexp(ciphertexts_2[n:], vec_exp[:n])
]
zRme = [
compute_multiexp(ciphertexts_1[:n], vec_exp[n:]),
compute_multiexp(ciphertexts_2[:n], vec_exp[n:])
]
CLgp_b = add(compute_multiexp(crs_g[:n], vec_b[n:]), multiply(u, zLgp))
CLgp_c = compute_multiexp(crs_h_scaled[n:], vec_c[:n])
CRgp_b = add(compute_multiexp(crs_g[n:], vec_b[:n]), multiply(u, zRgp))
CRgp_c = compute_multiexp(crs_h_scaled[:n], vec_c[n:])
CLme = compute_multiexp(crs_h[n:], vec_exp[:n])
CRme = compute_multiexp(crs_h[:n], vec_exp[n:])
proof.append([CLgp_b, CLgp_c, CRgp_b, CRgp_c, zLme, zRme, CLme, CRme])
current_hash = hash_integers([
current_hash,
int(CLgp_b[0]),
int(CLgp_b[1]),
int(CLgp_b[2]),
int(CLgp_c[0]),
int(CLgp_c[1]),
int(CLgp_c[2]),
int(CRgp_b[0]),
int(CRgp_b[1]),
int(CRgp_b[2]),
int(CRgp_c[0]),
int(CRgp_c[1]),
int(CRgp_c[2]),
int(zLme[0][0]),
int(zLme[0][1]),
int(zLme[0][2]),
int(zRme[0][0]),
int(zRme[0][1]),
int(zRme[0][2]),
int(CLme[0]),
int(CLme[1]),
int(CLme[2]),
int(CRme[0]),
int(CRme[1]),
int(CRme[2])
])
x = current_hash % curve_order
inv_x = inverse(x)
for i in range(n):
crs_g[i] = add(multiply(crs_g[n + i], inv_x), crs_g[i])
crs_h_scaled[i] = add(multiply(crs_h_scaled[n + i], x),
crs_h_scaled[i])
vec_b[i] = (vec_b[i] + x * vec_b[n + i]) % curve_order
vec_c[i] = (vec_c[i] + inv_x * vec_c[n + i]) % curve_order
crs_h[i] = add(multiply(crs_h[n + i], x), crs_h[i])
ciphertexts_1[i] = add(multiply(ciphertexts_1[n + i], x),
ciphertexts_1[i])
ciphertexts_2[i] = add(multiply(ciphertexts_2[n + i], x),
ciphertexts_2[i])
vec_exp[i] = (vec_exp[n + i] * inv_x + vec_exp[i]) % curve_order
crs_g = crs_g[:n]
crs_h_scaled = crs_h_scaled[:n]
vec_b = vec_b[:n]
vec_c = vec_c[:n]
crs_h = crs_h[:n]
ciphertexts_1 = ciphertexts_1[:n]
ciphertexts_2 = ciphertexts_2[:n]
vec_exp = vec_exp[:n]
final_values = [vec_b[0], vec_c[0], vec_exp[0]]
current_hash = hash_integers(
[current_hash, vec_b[0], vec_c[0], vec_exp[0]])
return [current_hash, [zkinfo[:], proof[:], final_values[:]]]
from utils import pgcd, bezout, inverse, theoreme_chinois, elements_inversibles, rabin_miller, generer_cle_RSA, signature_RSA_CRT_faute, RSA_CRT_Bellcore if __name__ == '__main__': print "Hello world!" print "pgcd(6, 9) should be equal 3 :", pgcd(6, 9) print "pgcd(3, 1) should be equal 1 :", pgcd(3, 1) print "bezout(57, 33) should be equal (3, -4, 7) :", bezout(57, 33) print "bezout(2, -4) should be equal (2, -1, -1) :", bezout(2, -4) print "inverse(2,7) should be equal 4 :", inverse(2, 7) print "inverse(-2,7) should be equal 3 :", inverse(-2, 7) print "inverse(-9,7) should be equal 3 :", inverse(-9, 7) print "theoreme_chinois([3, 4, 5], [17, 11, 6]) should return 785 :", theoreme_chinois([3, 4, 5], [17, 11, 6]) print "len(elements_inversibles(60)) should return 16 :", len(elements_inversibles(60)) print "rabin_miller(13, 10) should return True :", rabin_miller(13, 10) print "rabin_miller(60, 10) should return False :", rabin_miller(60, 10) K = generer_cle_RSA(1024) s = signature_RSA_CRT_faute(42, K) (p, q, N, e, d) = K (p_, q_) = RSA_CRT_Bellcore(42, K) print (p == p_) and (q == q_)
def received_message(self, message):
message = json.loads(message.data)
message_type = inverse(MESSAGES, head(message))
method = getattr(self, message_type.lower(),
self.raise_not_implemented)
method(*tail(message))
def chinese_theorem(a, e):
m = functools.reduce(mul, e)
u = 0
for idx in range(len(a)):
u += a[idx] * (m // e[idx]) * utils.inverse(m // e[idx], e[idx])
return u % m
#!/usr/bin/env python # coding: utf-8 from utils import multiplication_entiere, produit, affiche_table_multiplicative, exp, inverse, subgroup, generateurs if __name__ == '__main__': print "Hello world!" print "multiplication_entiere(2, 5) =", multiplication_entiere(2, 5) n = 8 poly = (0b1 << 8) ^ (0b1 << 4) ^ (0b1 << 3) ^ (0b1 << 1) ^ 0b1 print produit(n, poly, 45, 72) affiche_table_multiplicative(3, poly & 0b1111) alpha = 0b10 for i in xrange(1, 2**3): print "alpha **", i, ":", exp(3, poly & 0b1111, alpha, i) print inverse(3, poly & 0b1111, 1) print inverse(3, poly & 0b1111, 0b10) print inverse(3, poly & 0b1111, 0b11) print inverse(3, poly & 0b1111, 0b100) print subgroup(3, poly & 0b1111, 0b10) print generateurs(3, poly & 0b1111) print generateurs(8, poly)
def received_message(self, message):
message = json.loads(message.data)
message_type = inverse(MESSAGES, head(message))
method = getattr(self, message_type.lower(),
self.raise_not_implemented)
method(*tail(message))
def decrypt(p, q, x, r, t):
k = utils.inverse(utils.mod_exp(r, x, p), p)
message = (t * k) % p
return message