What is RSA Cryptography?
RSA (Rivest–Shamir–Adleman) is the most widely deployed public-key cryptosystem, invented in 1977. Its security relies on the difficulty of integer factorization — given the product of two large primes, it is computationally infeasible to recover the primes classically.
RSA is used in TLS/HTTPS certificates, digital signatures, key exchange, email encryption (PGP/S-MIME) and API authentication.
How RSA works
| Step | Operation | Description |
|---|---|---|
| Key generation | Choose primes p, q → n = p×q | Compute public exponent e and private exponent d |
| Encryption | c = me mod n | Anyone with the public key (n, e) can encrypt |
| Decryption | m = cd mod n | Only the private key holder (d) can decrypt |
Key size security levels
| Key size | Security level | NIST status | Quantum safe? |
|---|---|---|---|
| 1024-bit | ~80-bit | Prohibited since 2013 | No |
| 2048-bit | ~112-bit | Acceptable until 2030 | No |
| 3072-bit | ~128-bit | Recommended | No |
| 4096-bit | ~140-bit | Strong | No |
RSA and quantum computers
All RSA key sizes are vulnerable to Shor's algorithm running on a sufficiently powerful quantum computer. NIST recommends migrating to post-quantum alternatives — Kyber (ML-KEM) for key exchange and Dilithium (ML-DSA) for signatures — before 2030.
Try Kyber (ML-KEM) • Analyze your RSA key size • Check your domain's PQ readiness
References
- R. Rivest, A. Shamir, L. Adleman — "A Method for Obtaining Digital Signatures and Public-Key Cryptosystems" (1978)
- NIST SP 800-57 — Recommendation for Key Management
- RFC 8017 — PKCS#1 v2.2 RSA Cryptography Standard
- RSA on Wikipedia