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Cryptography
Cryptography
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- Basic Example of Key Exchange Protocols
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What are Key Exchange Protocols?
Key Exchange Protocols are essential mechanisms in cryptography that facilitate secure communication over insecure channels. These protocols enable two or more parties to establish a shared cryptographic key without it being intercepted by malicious entities. The key exchange protocols ensure confidentiality, integrity, and authenticity of data by allowing entities to agree on a secret key securely. Popular key exchange protocols include Diffie-Hellman, RSA (Rivest-Shamir-Adleman), and Elliptic Curve Diffie-Hellman (ECDH), each offering different levels of security and efficiency.
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Basic Example of Key Exchange Protocols
# Diffie-Hellman Key Exchange Example
# Prime number and base shared publicly
p = 23 # Prime number
g = 5 # Base
# Alice's private key (a) and public key (A)
a = 6
A = (g ** a) % p
# Bob's private key (b) and public key (B)
b = 15
B = (g ** b) % p
# Secret key calculation
# Alice computes secret key
secret_key_A = (B ** a) % p
# Bob computes secret key
secret_key_B = (A ** b) % p
# Both should have the same secret key
print("Secret key computed by Alice:", secret_key_A)
print("Secret key computed by Bob:", secret_key_B)
Explanation:
- p and g are shared publicly. p is a prime number, and g is a base.
- Alice and Bob each choose a private key (a for Alice and b for Bob).
- They compute their respective public keys (A for Alice and B for Bob) using the formula (g ** private_key) % p.
- They exchange their public keys.
- Finally, they compute the shared secret key using each other's public keys and their own private keys.
This example demonstrates the basic concept of key exchange protocols using Diffie-Hellman. It illustrates how two parties can agree on a shared secret key over an insecure channel without directly exchanging the key itself.
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