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Update sample_ans.md

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Pavlos Papadopoulos
2022-02-18 12:29:37 +00:00
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unit04_public_key/lab/sample_ans.md
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@@ -423,6 +423,77 @@ For the prime number we have 65 bytes + 1 bit (521 bits).
# ECC Encryption
## D.1
**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))
```
<pre>
Private key value: 100412371531109186445752967835007606723422767215817529341655177594081088564056. Number of bits 256
D1.py:19: CryptographyDeprecationWarning: encode_point has been deprecated on EllipticCurvePublicNumbers and will be removed in a future version. Please use EllipticCurvePublicKey.public_bytes to obtain both compressed and uncompressed point encoding.
enc_point=binascii.b2a_hex(vals.encode_point()).decode()
Public key encoded point: 048987ec7866a5d1e3116f08a3a8b8d53b7c84ec273956519cbe332e0a66c4c910babe551d3a2081b32746fb9f576c12b25a6a1bc6adc87b4e1c391805cfbbd01b
x=8987ec7866a5d1e3116f08a3a8b8d53b7c84ec273956519cbe332e0a66c4c910
y=babe551d3a2081b32746fb9f576c12b25a6a1bc6adc87b4e1c391805cfbbd01b
Private key (PEM):
-----BEGIN PRIVATE KEY-----
MIGEAgEAMBAGByqGSM49AgEGBSuBBAAKBG0wawIBAQQg3f9jZOIMwueRirpNJc9/
WefKlG5mLuIZNEPDFuJ661ihRANCAASJh+x4ZqXR4xFvCKOouNU7fITsJzlWUZy+
My4KZsTJELq+VR06IIGzJ0b7n1dsErJaahvGrch7Thw5GAXPu9Ab
-----END PRIVATE KEY-----
Private key (DER):
b'308184020100301006072a8648ce3d020106052b8104000a046d306b0201010420ddff6364e20cc2e7918aba4d25cf7f59e7ca946e662ee2193443c316e27aeb58a144034200048987ec7866a5d1e3116f08a3a8b8d53b7c84ec273956519cbe332e0a66c4c910babe551d3a2081b32746fb9f576c12b25a6a1bc6adc87b4e1c391805cfbbd01b'
Public key (PEM):
-----BEGIN PUBLIC KEY-----
MFYwEAYHKoZIzj0CAQYFK4EEAAoDQgAEiYfseGal0eMRbwijqLjVO3yE7Cc5VlGc
vjMuCmbEyRC6vlUdOiCBsydG+59XbBKyWmobxq3Ie04cORgFz7vQGw==
-----END PUBLIC KEY-----
Public key (DER):
b'3056301006072a8648ce3d020106052b8104000a034200048987ec7866a5d1e3116f08a3a8b8d53b7c84ec273956519cbe332e0a66c4c910babe551d3a2081b32746fb9f576c12b25a6a1bc6adc87b4e1c391805cfbbd01b'
</pre>
**Python 2.7**:
@@ -475,46 +546,6 @@ 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>