diff --git a/cashu/core/b_dhke.py b/cashu/core/b_dhke.py
index 5e9d2e5..5c83ddc 100644
--- a/cashu/core/b_dhke.py
+++ b/cashu/core/b_dhke.py
@@ -44,9 +44,12 @@ def hash_to_curve(message: bytes):
     return point
 
 
-def step1_alice(secret_msg: str):
+def step1_alice(secret_msg: str, blinding_factor: bytes = None):
     Y = hash_to_curve(secret_msg.encode("utf-8"))
-    r = PrivateKey()
+    if blinding_factor:
+        r = PrivateKey(privkey=blinding_factor, raw=True)
+    else:
+        r = PrivateKey()
     B_ = Y + r.pubkey
     return B_, r
 
diff --git a/tests/test_crypto.py b/tests/test_crypto.py
index 947dc2a..e10f340 100644
--- a/tests/test_crypto.py
+++ b/tests/test_crypto.py
@@ -1,6 +1,6 @@
 import pytest
-
-from cashu.core.b_dhke import hash_to_curve
+from cashu.core.secp import PublicKey, PrivateKey
+from cashu.core.b_dhke import hash_to_curve, step1_alice, step2_bob, step3_alice
 
 
 def test_hash_to_curve():
@@ -26,6 +26,7 @@ def test_hash_to_curve():
 
 
 def test_hash_to_curve_iteration():
+    """This input causes multiple rounds of the hash_to_curve algorithm."""
     result = hash_to_curve(
         bytes.fromhex(
             "0000000000000000000000000000000000000000000000000000000000000002"
@@ -35,3 +36,65 @@ def test_hash_to_curve_iteration():
         result.serialize().hex()
         == "02076c988b353fcbb748178ecb286bc9d0b4acf474d4ba31ba62334e46c97c416a"
     )
+
+
+def test_step1():
+    """"""
+    B_, blinding_factor = step1_alice(
+        "test_message", blinding_factor=b"00000000000000000000000000000001"  # 32 bytes
+    )
+
+    assert (
+        B_.serialize().hex()
+        == "0243379106c73dfc635cd1422f406e83fbfa25be83bb3620aefc08f2b89d02d777"
+    )
+    assert blinding_factor.private_key == b"00000000000000000000000000000001"
+
+
+def test_step2():
+    B_, _ = step1_alice(
+        "test_message",
+        blinding_factor=bytes.fromhex(
+            "0000000000000000000000000000000000000000000000000000000000000001"
+        ),  # 32 bytes
+    )
+    a = PrivateKey(
+        privkey=bytes.fromhex(
+            "0000000000000000000000000000000000000000000000000000000000000001"
+        ),
+        raw=True,
+    )
+    C_ = B_.mult(a)
+    assert (
+        C_.serialize().hex()
+        == "02a9acc1e48c25eeeb9289b5031cc57da9fe72f3fe2861d264bdc074209b107ba2"
+    )
+
+
+def test_step3():
+    # C = C_ - A.mult(r)
+    C_ = PublicKey(
+        bytes.fromhex(
+            "02b15f14ae9259c101cdbc437e8877b1ca5d4af3a0c0684866b38d8c8d0b6f6374"
+        ),
+        raw=True,
+    )
+    r = PrivateKey(
+        privkey=bytes.fromhex(
+            "0000000000000000000000000000000000000000000000000000000000000001"
+        )
+    )
+
+    A = PublicKey(
+        pubkey=b"\x02"
+        + bytes.fromhex(
+            "0000000000000000000000000000000000000000000000000000000000000001",
+        ),
+        raw=True,
+    )
+    C = step3_alice(C_, r, A)
+
+    assert (
+        C.serialize().hex()
+        == "03398f7153b381ce54d57962a5e03ce0a4f3b79755e882c972b788e8488e59b0c9"
+    )