Modulus, public exponent and private material
The common two-prime form uses n=pq, with public n and exponent e and corresponding private exponent and other material. RFC 8017 also defines multi-prime RSA and CRT representations, so one file layout is not the full mathematical definition.
The raw encryption primitive computes c=m^e mod n for a representative in range. Private operations recover the corresponding representative, but modular exponentiation alone is not a secure arbitrary-message encryption scheme; valid keys and representation bounds are prerequisites.
References: [1]
Encryption and signature encodings differ
PKCS #1 separates primitives from schemes: RSAES-OAEP combines message encoding with encryption/decryption, whereas RSASSA-PSS defines signature encoding and verification. Signing is not simply private-key encryption of ordinary plaintext with any recoverable string accepted as verification.
Encoding determines length and error rules too. OAEP’s message bound depends on modulus length and hash output length, while bulk content is commonly protected symmetrically in a hybrid system. Modulus size is not unlimited payload capacity.
References: [1]
Identity and implementation remain necessary
A system must authenticate recipient keys and signer identities and control reuse across purposes. Successful arithmetic does not establish key ownership or make all decoding-error behavior harmless.
RSA’s traditional factorization-related assumptions are threatened by sufficiently capable quantum computers. This neither claims ordinary computers already break every RSA key nor makes a small size increase a post-quantum transition. Algorithms, parameters, encodings and implementations require separate assessment.