If you use a block cipher, you input must be an exact multiple of the block bit length.
In order to encipher arbitrary length data, you need first to pad you data to a multiple of the block length. This can be done with any method, but there are a number of standards. PKCS7 is one which is quite common, you can see an overview on the wikipedia article on padding.
Since block cipers operate on blocks, you also need to come up with a way of concatenating the encrypted blocks. This is very important, since naive techniques greatly reduce the strength of the encryption. There is also a wikipedia article on this.
What you did was to try to encrypt (or decrypt) data of a length which didn’t match the block length of the cipher, and you also explicitly asked for no padding and also no chaining mode of operation.
Consequently the block cipher could not be applied to your data, and you got the reported exception.
UPDATE:
As a response to your update and GregS’s remark, I would like to acknowledge that GregS was right (I did not know this about RSA), and elaborate a bit:
RSA does not operate on bits, it operates on integer numbers. In order to use RSA you therefore need to convert your string message into an integer m: 0 < m < n, where n is the modulus of the two distinct primes chosen in the generation process. The size of a key in the RSA algorithm typically refers to n. More details on this can be found on the wikipedia article on RSA.
The process of converting a string message to an integer, without loss (for instance truncating initial zeroes), the PKCS#1 standard is usually followed. This process also adds some other information for message integrity (a hash digest), semantical security (an IV) ed cetera. With this extra data, the maximum number of bytes which can be supplied to the RSA/None/PKCS1Padding is (keylength – 11). I do not know how PKCS#1 maps the input data to the output integer range, but
my impression is that it can take any length input less than or equal to keylength – 11 and produce a valid integer for the RSA encryption.
If you use no padding, your input will simply be interpreted as a number. Your example input, {0xbe, 0xef} will most probably be interpreted as {10111110 +o 11101111} = 1011111011101111_2 = 48879_10 = beef_16 (sic!). Since 0 < beef_16 < d46f473a2d746537de2056ae3092c451_16, your encryption will succeed. It should succeed with any number less than d46f473a2d746537de2056ae3092c451_16.
This is mentioned in the bouncycastle FAQ. They also state the following:
The RSA implementation that ships with
Bouncy Castle only allows the
encrypting of a single block of data.
The RSA algorithm is not suited to
streaming data and should not be used
that way. In a situation like this you
should encrypt the data using a
randomly generated key and a symmetric
cipher, after that you should encrypt
the randomly generated key using RSA,
and then send the encrypted data and
the encrypted random key to the other
end where they can reverse the process
(ie. decrypt the random key using
their RSA private key and then decrypt
the data).