A key encapsulation mechanism (KEM) can be used to construct a “hybrid” cryptosystems. In these cryptosystems symmetric keys (e.g. for AES) are encrypted using asymmetric keys. The symmetric key is used for encrypting data.
A naive KEM built using RSA primitives could use “textbook” RSA to encrypt a randomly generated symmetric key but this has some significant flaws:
-
If
eis small (e.g.e=3), the symmetric key may not be reduced by the modulus after exponentiation. This means the “encrypted” key would be trivially decrypted by taking theeth-root of the ciphertext. -
Unpadded RSA ciphertexts can be manipulated in predicatable ways. The paper “When Textbook RSA is Used to Protect the Privacy of Hundreds of Millions of Users” describes a fantastic attack on an unpadded RSA-based KEM where captured encrypted keys were decrypted by replaying ciphertexts with clever bit-shifts.
These issues could be alleviated by using a secure padding scheme like OAEP. However, there is a secure KEM that is just about as simple as the textbook KEM called RSA-KEM.
RSA-KEM works by generating a random integer r in (0, N-1) (where N is
the modulus of the key) and encrypting/encapsulating r. The symmetric key is
then derived by throwing r into a key derivation function (KDF).
As I understand it, OAEP is emulating a construction like RSA-KEM in that it
attempts to converts a message into a r-like value. The extra complexity that
OAEP introduces is to handle messages that are not necessarily evenly
distributed in (0, N-1) and the padding step needs to be reversible.