initial commit

core/b_dhke.py

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+"""
+Implementation of https://gist.github.com/RubenSomsen/be7a4760dd4596d06963d67baf140406
+
+Alice:
+A = a*G
+return A
+
+Bob:
+Y = hash_to_curve(secret_message)
+r = random blinding factor
+B'= Y + r*G
+return B'
+
+Alice:
+C' = a*B'
+  (= a*Y + a*r*G)
+return C'
+
+Bob:
+C = C' - r*A
+ (= C' - a*r*G)
+ (= a*Y)
+return C, secret_message
+
+Alice:
+Y = hash_to_curve(secret_message)
+C == a*Y
+
+If true, C must have originated from Alice
+"""
+
+import hashlib
+from ecc.curve import secp256k1, Point
+from ecc.key import gen_keypair
+
+
+G = secp256k1.G
+
+
+def hash_to_curve(secret_msg):
+    """Generates x coordinate from the message hash and checks if the point lies on the curve.
+    If it does not, it tries computing again a new x coordinate from the hash of the coordinate."""
+    point = None
+    msg = secret_msg
+    while point is None:
+        x_coord = int(hashlib.sha256(msg).hexdigest().encode("utf-8"), 16)
+        y_coord = secp256k1.compute_y(x_coord)
+        try:
+            # Fails if the point is not on the curve
+            point = Point(x_coord, y_coord, secp256k1)
+        except:
+            msg = str(x_coord).encode("utf-8")
+
+    return point
+
+
+def step1_bob(secret_msg):
+    secret_msg = secret_msg.encode("utf-8")
+    Y = hash_to_curve(secret_msg)
+    r, _ = gen_keypair(secp256k1)
+    B_ = Y + r * G
+    return B_, r
+
+
+def step2_alice(B_, a):
+    C_ = a * B_
+    return C_
+
+
+def step3_bob(C_, r, A):
+    C = C_ - r * A
+    return C
+
+
+def verify(a, C, secret_msg):
+    Y = hash_to_curve(secret_msg.encode("utf-8"))
+    return C == a * Y
+
+
+### Below is a test of a simple positive and negative case
+
+# # Alice private key
+# a, A = gen_keypair(secp256k1)
+# secret_msg = "test"
+# B_, r = step1_bob(secret_msg)
+# C_ = step2_alice(B_, a)
+# C = step3_bob(C_, r, A)
+# print("C:{}, secret_msg:{}".format(C, secret_msg))
+
+# assert verify(a, C, secret_msg)
+# assert verify(a, C + 1*G, secret_msg) == False  # adding 1*G shouldn't pass