Asymmetric Encryption (RSA & ECC)

Introduction: The Open Padlock

Imagine a padlock that everyone can have a copy of. You can use it to lock a box, but once locked, only the owner of the physical key can open it. Even the person who locked the box can’t open it again.

This is Asymmetric (Public Key) Encryption.

• Public Key: Given to the world. Used to Encrypt.
• Private Key: Kept secret. Used to Decrypt.

What Problem does it solve?

• Key Exchange: How can two people who have never met agree on a secret AES key without a hacker seeing it?
• Identity: How can I prove that this message really came from “Luke”?

Two Major Players

1. RSA (Rivest-Shamir-Adleman)

• The Math: Based on the extreme difficulty of factoring large prime numbers. If you multiply two 1024-bit primes, it’s easy. But if I give you the result, it takes a supercomputer years to find the original primes.
• Status: The classic standard. Trusted, but requires very long keys (2048+ bits) to be safe.

2. ECC (Elliptic Curve Cryptography)

• The Math: Based on the algebraic structure of elliptic curves over finite fields.
• Why it’s better: It provides the same security as RSA but with much smaller keys. A 256-bit ECC key is as strong as a 3072-bit RSA key.
• Status: The modern standard. Used in BitCoin, Ethereum, and modern mobile apps.

Typical Business Scenarios

• ✅ SSL/TLS Certificates: When you see the lock icon in Chrome, your browser used RSA/ECC to verify the website’s identity and exchange an AES key.

• ✅ SSH Keys: Logging into a server without a password using id_rsa.

• ✅ Digital Signatures: Signing a legal document (DocuSign) or a software package to prove it hasn’t been modified.

• ❌ Encrypting Big Files: Never use RSA/ECC to encrypt a 1GB file. It is extremely slow and memory-intensive. Encrypt the file with AES, then encrypt the small AES key with RSA/ECC.

Performance & Complexity

• RSA: Fast to verify (Public Key), slow to sign/decrypt (Private Key).
• ECC: Faster and more efficient than RSA, especially on mobile devices.

Summary

"Asymmetric encryption is the 'Front Door' of security. It allows the world to send you secrets and verify your identity, while ensuring that only your Private Key can unlock the truth."