asymmetric cryptography

asymm_crypt. 0.1 | 2307

• Agama_bitcoin | home
• Entropy_matrix
• Assymetric cryptography
• Elliptic-curve cryptography
• Mnemonic code BIP/SLIP39
• :.:

~ entropy machine
~ tab_calc | bin hex bech32
~ cbc_xor | symetric crypto

• template test
• test_123
~ .:.:.

Very simple Deffie-Hellman "MATH"

generate_public_key pK 
pK = G ** sk % m
-> gen (pk) from secret/private key (sk)


A = G**a % m
 a ---> A 

B = G**b % m
 b ---> B 

generate_shared_secret S
->
Alice: 
A: H_b^a = (G^b)^a = G^ba = S

 =  + 
Bob: 
B: H_a^b = (G^a)^b = G^ab = S

 =  +

BTC

                                                   
                                                   
                                                   
                                                   
                                                   
                                                   
                    .--------.                    
                   / .------. \                   
                  / /        \ \                  
                  | |        | |                  
                 _| |________| |_                 
               .' |_|        |_| '.               
               '._____ ____ _____.'               
               |     .'____'.     |               
               '.__.'.'    '.'.__.'               
               '.__  |      |  __.'               
               |   '.'.____.'.'   |               
               '.____'.____.'____.'               
               '.________________.'               
                                                  
                 Ag@ma P0iNt L0CK

...

very simple demonstration of Deffie-Hellman with small numbers

m = 17  # p
G = 2  # G

def dh(sk, g=G): # generate_public_key
    pk = g ** sk % m
    return pk 

print("Alice")
a = 5
A = dh(a) = 2*2*2*2*2 / 17 = 32 (% 17) = 15

print("Bob")
b = 3
B = dh(b) = 2*2*2 % 17 = 8 (% 17) = 8

print("Confirm")
dh(a,B)
8**5 = 32768 (% 17) = 9
15**3 = 3375 (% 17) = 9

~ a*b == b*a

more advanced example with larger numbers

# Alice and Bob choose their private keys: 
a = 555555555555
b = 333333333333 

# Create an instance of the DiffieHellmanKeys class
dh_a = DiffieHellmanKeys()
dh_b = DiffieHellmanKeys()
print(dh_b)

print("--- Alice:")
alice_private_key = a
A = dh_a.generate_public_key(a) ->
A = alice_public_key = dh_a.generate_public_key(alice_private_key)

print("--- Bob:")
bob_private_key = b
B = dh_b.generate_public_key(b) ->
B = bob_public_key = dh_b.generate_public_key(bob_private_key)

shared_secret = dh_a.generate_shared_secret(alice_private_key, bob_public_key)
shared_secret_hex32 = dh_a.get_hex_shared32()

print("\n[  --- SIGN ---  ]")
cbc_iv = bytes.fromhex("0c1e24e5917779d297e14d45f14e1a1a") # andreas
cbc_key = bytes.fromhex(shared_secret_hex32) 


cbc = CBC_XOR(cbc_key, cbc_iv)

hash_message = sha256(message_plaintext_bytes).digest() 

print("Encryption ->")
ciphertext = cbc.encrypt(hash_message)
print(f'Ciphertext: {ciphertext.hex()}')

print("\n[ --- VERIFY --- ]")
decrypted_hash = cbc.decrypt(ciphertext)

# Bob computes the hash of the original message
bob_computed_hash = sha256(message_plaintext_bytes).digest()

# Verification
if decrypted_hash == bob_computed_hash:
    print("Verification successful: The decrypted hash matches the original hash.")
 
  
"""
[ --- KEY GENERATION --- ]
DiffieHellmanKeys/parameters
(g = 3, p = 170141183460469231731687303715884105727) # Mersenne prime M127=2**127-1 

--- Alice:
Private key: 555555555555 | 0x8159b108e3
Public key: 0x236d61d241c8deec988b449371ef59fb :. 38
--- Bob:
Private key: 333333333333 | 0x4d9c370555
Public key: 0x20119b431bf77946dab17b2056cacf56 :. 38
6d299f5dae62c2e9c9f2806ae9ab66cc  (32)

[  --- SIGN ---  ]
message_plaintext_bytes: b'a short text for signing and subsequent verification | Agama 123'
cbc_key:  6d299f5dae62c2e9c9f2806ae9ab66cc  :..  32
cbc_iv_:  0c1e24e5917779d297e14d45f14e1a1a
cbc_block_size: 16

Encryption ->
Ciphertext: 85f4c1e6017c5ae53accb79a97379a2e094668dff975431b7a777be4d1a1c200747fe792470791e2a395eb9e281ab4dc

[ --- VERIFY --- ]
Verification successful: The decrypted hash matches the original hash.
Hash: e4c37a5e3e69e1de64df7ab58fd2e6f8e19b3664566bdb1789494c14af3d3ee2 :. 64
"""

simple_dh_keys.py |