Update sample_ans.md

unit04_public_key/lab/sample_ans.md

@@ -423,6 +423,9 @@ For the prime number we have 65 bytes + 1 bit (521 bits).
 
 # ECC Encryption
 ## D.1
+
+**Python 2.7**:
+	
 ```python
 import OpenSSL
 import pyelliptic
@@ -471,6 +474,47 @@ Decrypt: Test123
 
 Bob verified: True
 </pre>
+	
+**Python 3.8**:
+
+```
+from cryptography.hazmat.primitives.asymmetric import ec
+from cryptography.hazmat.primitives import serialization
+import binascii
+import sys
+
+private_key = ec.generate_private_key(ec.SECP256K1())
+
+
+vals = private_key.private_numbers()
+no_bits=vals.private_value.bit_length()
+print (f"Private key value: {vals.private_value}. Number of bits {no_bits}")
+
+public_key = private_key.public_key()
+vals=public_key.public_numbers()
+
+enc_point=binascii.b2a_hex(vals.encode_point()).decode()
+
+print (f"\nPublic key encoded point: {enc_point} \nx={enc_point[2:(len(enc_point)-2)//2+2]} \ny={enc_point[(len(enc_point)-2)//2+2:]}")
+
+
+pem = private_key.private_bytes(encoding=serialization.Encoding.PEM,format=serialization.PrivateFormat.PKCS8,encryption_algorithm=serialization.NoEncryption())
+
+der = private_key.private_bytes(encoding=serialization.Encoding.DER,format=serialization.PrivateFormat.PKCS8,encryption_algorithm=serialization.NoEncryption())
+
+
+
+print ("\nPrivate key (PEM):\n",pem.decode())
+print ("Private key (DER):\n",binascii.b2a_hex(der))
+
+pem = public_key.public_bytes(encoding=serialization.Encoding.PEM,format=serialization.PublicFormat.SubjectPublicKeyInfo)
+
+der = public_key.public_bytes(encoding=serialization.Encoding.DER,format=serialization.PublicFormat.SubjectPublicKeyInfo)
+
+print ("\nPublic key (PEM):\n",pem.decode())
+print ("Public key (DER):\n",binascii.b2a_hex(der))	
+```
+	
 ## D.2
 y<sup>2</sup> = x<sup>3 + 7 (mod 89)
 <pre>