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Books / Practical Cryptography for Developers (Unfinished) / Chapter 5
DHKE - Examples
Let’s give a simple code example in Python to demonstrate the classical Diffie–Hellman Key Exchange (DHKE) algorithm.
First, install the Python package PyDHE:
pip install pyDHE
Next, write the code for the DHKE example:
import pyDHE
alice = pyDHE.new()
alicePubKey = alice.getPublicKey()
print("Alice public key:", hex(alicePubKey))
bob = pyDHE.new()
bobPubKey = bob.getPublicKey()
print("Bob public key:", hex(bobPubKey))
print("Now exchange the public keys (e.g. through Internet)")
aliceSharedKey = alice.update(bobPubKey)
print("Alice shared key:", hex(aliceSharedKey))
bobSharedKey = bob.update(alicePubKey)
print("Bob shared key:", hex(bobSharedKey))
print("Equal shared keys:", aliceSharedKey == bobSharedKey)
Run the above code example: https://repl.it/@nakov/Diffie-Hellman-Key-Exchange-in-Python.
When you run the above code, it will generate and print two 2048-bit public keys (for Alice and for Bob). Assume that Allice and Bob have exchanged their public keys (e.g. send them to each other through Internet). Once Alice has received Bob’s public key, she can calculate the shared secret by combining it to her private key. Respectively, once Bob has received Alice’s public key, he can calculate the shared secret by combining it to his private key. The sample output from the above example shows that the shared secret is always the same number (2048-bit integer):
Alice public key: 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
Bob public key: 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
Now exchange the public keys (e.g. through Internet)
Alice shared key: 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
Bob shared key: 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
Equal shared keys: True
Note that your output will be different due to the randomness during the key generation process. The above code uses a 2048-bit public and private keys, as specified in the RFC 3526 (group 14). You can change the DHKE key size (from 1536-bits to 8192-bits) by specifying a different RFC 3526 group (e.g. 18 for 8192-bit keys). For example change these two lines:
alice = pyDHE.new(group=18)
bob = pyDHE.new(group=18)
Run the above code example: https://repl.it/@nakov/DHKE-Example-in-Python.
The above changes will switch to 8192-bit keys and will significantly slow-down the calculations. The output will look like this:
Alice public key: 0x86b2c2bda3982af803084b65d982c08f3462046d154c9ee6fb7c8dcdd4a2922b72487c46e42777ea8bbfad73ca2f340397ddc2b3ddb215891b4811fe014ae176918cc01817e4d9358e6053ed49790e224721bd14abe7cdeac10be211782d0b1a110c5968654873b1eb3e591c6e5acd0197459aac04da06620d424b327124dee4958fe49be3f44100591e8560a0e137abb9c47973e4701b3e127a05482934b3b9fdb4117365c476bb6665d867b2dd58cab72073bcb6632883fba3043b8544a4726fcd013f1676963d612f634675674de1d295e90101d9a0523ae1717eb2ea11a05e4902af572a9bfff0344c3383e8b85fa7db234927b053d098eda9fda0970c92917caa95fe4dc79376f6b8f0ee4a9682c88870c36b345049b3ef89bdcfc0f8751b02afa88b22fd5b94d33a49bcf6d262255ac18e27e96675f311b654f99fa31e060f7e2afbd888099bba072cefaab1e1c40a73845c139e3feaecee76965b71255473b485976e7f7d87e2ff61a62ddadd5f7f02e9353f5d4f091360418eb7935e83d1e6355c82feff3583725017e8b8b6148af839e3e7cfd3d549b679d9878544366676509b61b590ce25abbb440207b23fec9c04daef70590c46d720af273d6dafb34d2e5b68e24499a4b7ac254ee000712dd0e4ae72299fb103098b8d54c2c28a66e74d52db4853bb695cbff9a09f8223c55f1e2fd351d419a091cc643b3abc42a477ef6f3eb9d2913e45bcb3ba76771bccfafa85abe3cf37c42bf1baf59f122785ec47b51b45c4ba0875e6a80230c5035e45c1cf32e8b7b52ee44e2c3b06330c29f047dd5b0983ae8db34d1ca1a127d1da72d4e0244690c63af4ecf3003152a1cfaa5b4139c361cd3cc54fb7e91bdcac9bf81498da90cf249621df90947ccbece28c5befec6bf832d873e18293e7b8e9562596c4b50c61e1aff9b8d13a02df25675c5045aec14d3e83253d210ae7e6f2c62d622c7bcaf87cd6a4bb63a25d18cc0672fe3488eefb058231daf17a570382ffb56e490b1e5003284ca5a8978aa4c09d3e9a11eae379bd66fe86999c10fbe1eb6763d1b6b4f277e8347462e91f127a0f2fe8a9a16381452e3515608e950587f74e1f85b10ab32e667248f8764d90a8b92eb6bcce14cf7306fa56bc7852a0f2811651665f2121a6253e3e4bfecb12b54c8cd11a54d74346c3b9f2c8c7b71ea60fce8eb1d3badcea909b7f082e4e4a4ad4e2a501b2fd3a4c7acd48b416706dc3fbda180cec831bacd558fc15cfa3e19347bb5297ac7a4b931b6e19f9b0dfb0c07696727402c1c5215c0822776147a9a9c7c10bc04d23d6cee974fc37a32fd758cd09bff9f0b1cdd9e09734aa0abe0dc9f3a74415c411ce2b07369445d6e4929a0132db60024cf260b17fb3401beb794a5a365a3be92677fb68f60e091cb5cfc5d767290c4655d6922c2bd194671d5b
Bob public key: 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
Now exchange the public keys (e.g. through Internet)
Alice shared key: 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
Bob shared key: 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
Equal shared keys: True
Enjoy to modify and experiment with the above code to learn the DHKE protocol.