def ECP_SpDSA(S, F):
FS = curve.EFS
G = generator()
m = hashlib.new(curve.SHA)
m.update(F)
H = m.digest()
HS = m.digest_size
if HS >= FS:
B = H[0:FS]
else:
B = bytearray(FS)
for i in range(0, HS):
B[i + FS - HS] = H[i]
C = bytearray(FS)
D = bytearray(FS)
r = curve.r
s = big.from_bytes(S)
f = big.from_bytes(B)
c = 0
d = 0
while d == 0:
u = big.rand(curve.r)
w = big.rand(curve.r) # masking
V = G.copy()
V = u * V
vx = V.getx()
c = vx % r
if c == 0:
continue
u = big.modmul(u, w, r)
u = big.invmodp(u, r)
d = big.modmul(s, c, r)
d += f
d = big.modmul(d, w, r)
d = big.modmul(d, u, r)
C = big.to_bytes(c)
D = big.to_bytes(d)
return C, D
def ECP_SpDSA(S, F):
FS = curve.EFS
G = generator()
m = hashlib.new(curve.SHA)
m.update(F)
H = m.digest()
HS = m.digest_size
if HS >= FS:
B = H[0:FS]
else:
B = bytearray(FS)
for i in range(0, HS):
B[i + FS - HS] = H[i]
C = bytearray(FS)
D = bytearray(FS)
r = curve.r
s = big.from_bytes(S)
f = big.from_bytes(B)
c = 0
d = 0
while d == 0:
u = big.rand(curve.r)
w = big.rand(curve.r) # masking
V = G.copy()
V = u * V
vx = V.getx()
c = vx % r
if c == 0:
continue
u = big.modmul(u, w, r)
u = big.invmodp(u, r)
d = big.modmul(s, c, r)
d += f
d = big.modmul(d, w, r)
d = big.modmul(d, u, r)
C = big.to_bytes(c)
D = big.to_bytes(d)
return C, D
def ECP_SvDSA(P, F, C, D):
FS = curve.EFS
G = generator()
m = hashlib.new(curve.SHA)
m.update(F)
H = m.digest()
HS = m.digest_size
if HS >= FS:
B = H[0:FS]
else:
B = bytearray(FS)
for i in range(0, HS):
B[i + FS - HS] = H[i]
c = big.from_bytes(C)
d = big.from_bytes(D)
f = big.from_bytes(B)
r = curve.r
if c == 0 or c >= r or d == 0 or d >= r:
return False
d = big.invmodp(d, r)
f = big.modmul(f, d, r)
h2 = big.modmul(c, d, r)
WP = ECp()
if not WP.fromBytes(P):
return False
P = ECp.mul(WP, h2, G, f)
if P.isinf():
return False
d = P.getx() % r
if c != d:
return False
return True
def ECP_SvDSA(P, F, C, D):
FS = curve.EFS
G = generator()
m = hashlib.new(curve.SHA)
m.update(F)
H = m.digest()
HS = m.digest_size
if HS >= FS:
B = H[0:FS]
else:
B = bytearray(FS)
for i in range(0, HS):
B[i + FS - HS] = H[i]
c = big.from_bytes(C)
d = big.from_bytes(D)
f = big.from_bytes(B)
r = curve.r
if c == 0 or c >= r or d == 0 or d >= r:
return False
d = big.invmodp(d, r)
f = big.modmul(f, d, r)
h2 = big.modmul(c, d, r)
WP = ECp()
if not WP.fromBytes(P):
return False
P = ECp.mul(WP, h2, G, f)
if P.isinf():
return False
d = P.getx() % r
if c != d:
return False
return True
def inverse(self):
return Fp(big.invmodp(self.x, Fp.p))
def inverse(self):
return Fp(big.invmodp(self.x, Fp.p))