Rsas

RSAs (RSA-based algorithms) are the RSA family of public-key cryptosystems and digital signature schemes. The RSA system, introduced in 1977 by Ron Rivest, Adi Shamir, and Leonard Adleman, is built on the difficulty of factoring large composite integers. In RSA, a key pair consists of a public key used for encryption or verification and a private key used for decryption or signing. The public key is a modulus n and an exponent e; the private key includes an exponent d such that e d ≡ 1 mod φ(n), where φ(n) = (p−1)(q−1) and n = pq for primes p and q. Security relies on the computational hardness of factoring n.

RSAs include encryption and signing variants. RSAES refers to the RSA encryption scheme; RSASSA denotes RSA-based digital signatures. Practical implementations use padding schemes to secure the protocols, such as OAEP (for encryption) and PSS (for signatures). PKCS#1 is a widely used standard that defines these padding rules and signature formats.

In modern practice, RSAs typically employ keys of 2048 bits or larger, with 3072 or 4096-bit keys for higher security. RSA’s security can be compromised by weak keys, improper padding, side-channel attacks, or quantum attacks; consequently, many practitioners phase toward stronger alternatives, including elliptic-curve cryptography.

RSAs are embedded in many security protocols and standards, notably TLS, S/MIME, OpenPGP, and X.509 certificates. They continue to be widely supported, though post-quantum cryptography research is developing quantum-resistant schemes for future use.