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-rw-r--r--vector/vector_format.py10
-rw-r--r--vector/vector_util.py104
2 files changed, 87 insertions, 27 deletions
diff --git a/vector/vector_format.py b/vector/vector_format.py
index accf691..67a50f0 100644
--- a/vector/vector_format.py
+++ b/vector/vector_format.py
@@ -40,7 +40,8 @@ SCRIPT_USAGE = "USAGE: vector_format.py [openssl_binary]"
KEY_LENGTH = 1024
-RNG_SEED = 0
+RNG_SEED_MESSAGE = 1
+RNG_SEED_BLINDING = 2
if __name__ == "__main__":
@@ -49,10 +50,11 @@ if __name__ == "__main__":
if len(OPENSSL_BINARY) > 0:
- MESSAGE = vector_util.random_message(RNG_SEED, KEY_LENGTH)
- VECTOR = vector_util.load_vector(OPENSSL_BINARY, KEY_LENGTH)
+ MESSAGE = vector_util.random_message(RNG_SEED_MESSAGE, KEY_LENGTH)
+ BLINDING = vector_util.random_blinding(RNG_SEED_BLINDING, KEY_LENGTH)
+ VECTOR = vector_util.load_vector(OPENSSL_BINARY, KEY_LENGTH)
- vector_ok = VECTOR.selfcheck(MESSAGE)
+ vector_ok = VECTOR.selfcheck(MESSAGE, BLINDING)
if vector_ok:
vector_util.save_vector(VECTOR)
print("Test vector formatted.")
diff --git a/vector/vector_util.py b/vector/vector_util.py
index 413cb61..37e4fb6 100644
--- a/vector/vector_util.py
+++ b/vector/vector_util.py
@@ -42,18 +42,21 @@ from enum import Enum, auto
class VectorPiece(Enum):
- VectorPieceX = auto()
- VectorPieceN = auto()
- VectorPieceD = auto()
- VectorPieceP = auto()
- VectorPieceQ = auto()
- VectorPieceDP = auto()
- VectorPieceDQ = auto()
- VectorPieceQINV = auto()
+ VectorPieceOther = auto()
+ VectorPieceN = auto()
+ VectorPieceD = auto()
+ VectorPieceP = auto()
+ VectorPieceQ = auto()
+ VectorPieceDP = auto()
+ VectorPieceDQ = auto()
+ VectorPieceQINV = auto()
class Vector:
+ # public exponent
+ _f4 = 0x10001
+
def __init__(self, length):
self._bits = length
self._n = ""
@@ -101,7 +104,25 @@ class Vector:
return r
- def selfcheck(self, message):
+ def _calc_blind_y(self, x, modulus):
+ x_inv = self._modinv(x, modulus)
+ return pow(x_inv, self._f4, modulus)
+
+ def _egcd(self, a, b):
+ if a == 0:
+ return (b, 0, 1)
+ else:
+ g, y, x = self._egcd(b % a, a)
+ return (g, x - (b // a) * y, y)
+
+ def _modinv(self, a, m):
+ g, x, y = self._egcd(a, m)
+ if g != 1:
+ raise Exception("_modinv() failed!")
+ else:
+ return x % m
+
+ def selfcheck(self, message, blinding):
self.m = message # message (padded)
self.n = int(self._n, 16) # modulus
@@ -112,6 +133,9 @@ class Vector:
self.dq = int(self._dq, 16) # smaller exponent
self.qinv = int(self._qinv, 16) # helper coefficient
+ self.x = blinding
+ self.y = self._calc_blind_y(self.x, self.n)
+
# check modulus
if self.n == 0:
print("ERROR: n == 0")
@@ -130,22 +154,40 @@ class Vector:
print("ERROR: dq != (d % (q-1))")
return False
- # sign
- s = pow(message, self.d, self.n)
+ # sign to obtain known good value
+ s_reference = pow(message, self.d, self.n)
+
+ # blind message
+ message_blinded = (message * self.y) % self.n
+
+ # sign blinded message
+ s_blinded = pow(message_blinded, self.d, self.n)
+
+ # unblind signature
+ s_unblinded = (s_blinded * self.x) % self.n
+
+ # check, that x and y actually work
+ if s_unblinded != s_reference:
+ print("ERROR: s_unblinded != s_reference!")
+ return False
+
+ # try to do crt with the blinded message
+ sp_blinded = pow(message_blinded, self.dp, self.p)
+ sq_blinded = pow(message_blinded, self.dq, self.q)
- # try to do crt
- sp = pow(message, self.dp, self.p)
- sq = pow(message, self.dq, self.q)
+ # recover full blinded signature
+ sr_blinded = sp_blinded - sq_blinded
+ if sr_blinded < 0: sr_blinded += self.p
- sr = sp - sq
- if sr < 0: sr += self.p
+ sr_qinv_blinded = (sr_blinded * self.qinv) % self.p
- srqinv = (sr * self.qinv) % self.p
+ s_crt_blinded = sq_blinded + self.q * sr_qinv_blinded
- s_crt = sq + self.q * srqinv
+ # unblind crt signature
+ s_crt_unblinded = (s_crt_blinded * self.x) % self.n
- if s_crt != s:
- print("ERROR: s_crt != s!")
+ if s_crt_unblinded != s_reference:
+ print("ERROR: s_crt_unblinded != s_reference!")
return False
self.n_factor = self._calc_mont_factor(self._bits + 16, self.n)
@@ -204,19 +246,33 @@ def random_message(seed, length):
return message
+def random_blinding(seed, length):
+
+ blinding = 0
+ num_bytes = length // 8 - 1
+
+ random.seed(seed)
+
+ for i in range(num_bytes):
+ blinding <<= 8
+ blinding += random.getrandbits(8)
+
+ return blinding
+
+
def load_vector(binary, length):
vector = Vector(length)
- piece_type = VectorPiece.VectorPieceX
+ piece_type = VectorPiece.VectorPieceOther
filename = str(length) + "_randomized.key"
openssl_command = [binary, "rsa", "-in", filename, "-noout", "-text"]
openssl_stdout = subprocess.check_output(openssl_command).decode("utf-8").splitlines()
for line in openssl_stdout:
- if line.startswith("RSA Private-Key:"): piece_type = VectorPiece.VectorPieceX
+ if line.startswith("RSA Private-Key:"): piece_type = VectorPiece.VectorPieceOther
elif line.startswith("modulus:"): piece_type = VectorPiece.VectorPieceN
- elif line.startswith("publicExponent:"): piece_type = VectorPiece.VectorPieceX
+ elif line.startswith("publicExponent:"): piece_type = VectorPiece.VectorPieceOther
elif line.startswith("privateExponent:"): piece_type = VectorPiece.VectorPieceD
elif line.startswith("prime1:"): piece_type = VectorPiece.VectorPieceP
elif line.startswith("prime2:"): piece_type = VectorPiece.VectorPieceQ
@@ -252,6 +308,8 @@ def save_vector(vector):
f.write(" n_coeff = 0x%x\n" % vector.n_coeff)
f.write(" p_coeff = 0x%x\n" % vector.p_coeff)
f.write(" q_coeff = 0x%x\n" % vector.q_coeff)
+ f.write(" x = 0x%x\n" % vector.x)
+ f.write(" y = 0x%x\n" % vector.y)
f.close()