Public/private keypairs, prime integer arithmetic, RSA key generation proof, and Elliptic Curve security benefits.
1. Asymmetric Model Concept
2. Mathematical Principles & RSA Keygen Proof
RSA (Rivest-Shamir-Adleman) relies on the Trapdoor One-Way Function of prime factorization: multiplying two large primes is easy, but factoring the resulting modulus back into primes is computationally infeasible.
3. Elliptic Curve Cryptography (ECC)
Stronger security bounds using curve coordinates (y² = x³ + ax + b) with significantly smaller key sizes.
| Security Strength (Bits) | Symmetric Key Size (AES) | Equivalent RSA Key size | Equivalent ECC Key size |
|---|---|---|---|
| 80 (Legacy) | 80 bits | 1024 bits | 160 bits |
| 112 (Deprecated) | 112 bits | 2048 bits | 224 bits |
| 128 (Secure) | 128 bits | 3072 bits | 256 bits |
| 256 (Highly Secure) | 256 bits | 15360 bits | 512 bits |
By shifting to 256-bit ECC, devices gain equivalent security to 3072-bit RSA while reducing processing overhead, transmission packet sizes, and memory usage. This is critical for mobile networks, smart cards, and IoT sensors.