After this lesson, you will be able to: Explain public/private key pairs, how RSA and elliptic curve cryptography work at a conceptual level, and why ECC is preferred for new systems.
Asymmetric (public-key) cryptography solves the problem symmetric crypto cannot: communicating securely with someone you have never shared a key with. This lesson covers key pairs and the public/private relationship, RSA, elliptic curve cryptography, and why ECC has become the default for new systems.
Each party has a key pair: a public key they share freely and a private key they guard. The magic is the asymmetry: data encrypted with the public key can only be decrypted with the private key, and data signed with the private key can be verified with the public key. This lets anyone send you a secret (encrypt with your public key) and lets you prove authorship (sign with your private key) without ever sharing a secret in advance.
RSA, the classic public-key algorithm, rests on the difficulty of factoring the product of two large primes. It works but needs large keys (2048 or 3072 bits) for security, which makes it slower and bulkier. RSA is still everywhere (certificates, signatures), but its key sizes are a drawback as security requirements rise. You will encounter it constantly even as new systems move away from it.
ECC achieves the same security as RSA with far smaller keys: a 256-bit ECC key is roughly as strong as a 3072-bit RSA key. Smaller keys mean faster operations, less bandwidth, and lower power use, which matters enormously for mobile and IoT. ECC underpins modern signatures (ECDSA, Ed25519) and key exchange (ECDH). It rests on the hardness of the elliptic-curve discrete logarithm problem.
Asymmetric crypto is slow and not meant for bulk data. So real protocols use it only to establish a shared symmetric key (or to sign), then switch to fast symmetric encryption for the actual data. TLS does exactly this: an asymmetric handshake agrees on a symmetric session key, then AES or ChaCha20 encrypts the traffic. Understanding this hybrid pattern explains how nearly all secure communication works.
Pick the best reason.
Using RSA to encrypt large data directly instead of a symmetric key (it is slow and size-limited). Choosing tiny RSA keys (1024-bit is broken). Mixing up which key does what (encrypt with the recipient's public key; sign with your own private key). Generating keys with weak randomness. Assuming asymmetric crypto replaces symmetric (they work together). Not protecting the private key, which is the entire security of the pair.
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