Public Key Summary

Cryptography · Axiom Academy

Key takeaways from the Public Key Cryptography unit Key Distribution Problem Solved: Before 1976, secure communication required sharing secret keys in person—impractical at scale Diffie-Hellman-Merkle: First public key exchange protocol, based on the discrete logarithm problem (DLP) Shared Secrets Without Meeting: Two parties can establish a shared secret over an insecure channel Foundation for Modern Security: Enabled the secure internet we use today RSA (1978): Most famous algorithm, based on integer factorization, supports both encryption and digital signatures ElGamal (1985): DLP-based encryption with semantic security properties Hybrid Encryption: Practical systems use public key to share a symmetric key, then symmetric crypto for bulk data Real Performance: RSA is ~1000x slower than AES, making hybrid approaches essential Alice Generates Keys: Creates a public-private key pair using RSA or ECC Public Distribution: Alice shares her public key openly—no secrecy required Bob Encrypts: Bob uses Alice's public key to encrypt a message only Alice can read Alice Decrypts: Only Alice's private key can decrypt the message Signatures Work Reverse: Alice signs with her private key; anyone verifies with her public key One-Way Functions: Functions that are easy to compute but hard to invert without special information Trapdoor Functions: One-way functions where inversion is easy with a secret key (the trapdoor)

This is the written version of the interactive lesson above. See the full Cryptography course.