What is the limit to the amount of data that can be encrypted with RSA?

Question

Typically it is recommended that RSA be used to encrypt a symmetric key, which is then used to encrypt the "payload".

What is the practical (or theoretical) limit to the amount of data that can be encrypted with RSA (I'm using a 2048 bit RSA keysize).

In particular, I'm wondering if it is safe to encrypt an RSA public key (256 bytes) with a (different) RSA public key? I'm using the Bouncy Castle crypto libraries in Java.

Answer 1

For a n-bit RSA key, direct encryption (with PKCS#1 "old-style" padding) works for arbitrary binary messages up to floor(n/8)-11 bytes. In other words, for a 1024-bit RSA key (128 bytes), up to 117 bytes. With OAEP (the PKCS#1 "new-style" padding), this is a bit less: OAEP use a hash function with output length h bits; this implies a size limit of floor(n/8)-2*ceil(h/8)-2: still for a 1024-bit RSA key, with SHA-256 as hash function (h = 256), this means binary messages up to 60 bytes.

There is no problem in encrypting a RSA key with another RSA key (there is no problem in encrypting any sequence of bytes with RSA, whatever those bytes represent), but, of course, the "outer" RSA key will have to be bigger: with old-style padding, to encrypt a 256-byte message, you will need a RSA key with a modulus of at least 2136 bits.

Hybrid modes (you encrypt data with a random symmetric key and encrypt that symmetric key with RSA) are nonetheless recommended as a general case, if only because they do not have any practical size limits, and also because they make it easier to replace the RSA part with another key exchange algorithm (e.g. Diffie-Hellman).