RSA
RSA is the asymmetric encryption algorithm published by Rivest, Shamir, and Adleman in 1977, based on the hardness of factoring large integers, used for encryption and digital signatures.
Purpose
It realizes asymmetric encryption and digital signatures, letting two parties communicate securely and authenticate without pre-shared keys.
Mechanism
Key generation: pick primes p and q, set n = pq and φ = (p-1)(q-1), choose e coprime to φ, and set d = e^{-1} mod φ. Encryption: c = m^e mod n; decryption: m = c^d mod n. Security rests on the difficulty of factoring n.
Use cases
- TLS certificate key exchange and signatures
- SSH public-key authentication
- PGP/GPG keys
- Code-signing certificates
Examples
- Input
n=3233, e=17, m=65Outputc=2790Encrypting 65 → 2790
Common errors
- Using keys that are too short (<2048 bits)
- Use at least 2048 bits; 3072 or 4096 recommended
Related terms
AES
The Advanced Encryption Standard (AES) is the symmetric block cipher NIST standardized in 2001, supporting 128/192/256-bit keys, and is the de facto standard of modern encryption. GLOSSARY
PKI
PKI (Public Key Infrastructure) is the system managing digital certificates and public keys, comprising CAs, registration authorities, certificate repositories, and revocation mechanisms, underpinning TLS and signatures. GLOSSARY
X.509 Certificate
An X.509 certificate binds a public key to an identity, signed by a CA for verification, containing validity, issuer, subject, and extension fields. GLOSSARY
CA
A CA (Certificate Authority) is a trusted third party that issues digital certificates binding public keys to identities, serving as the trust root of PKI. GLOSSARY