Sign with RSA-1024 an SHA-256 digest: what is the size?

Question

I was wondering: 1) if I compute the digest of some datas with SHA-512 => resulting in a hash of 64 bytes 2) and then I sign this hash with RSA-1024 => so a block of 128 bytes, which is bigger than the 64 bytes of the digest

=> does it mean in the end my signed hash will be exactly 128 bytes?

Thanks a lot for any info.

Answer 1

With RSA, as specified by PKCS#1, the data to be signed is first hashed with a hash function, then the result is padded (a more or less complex operation which transforms the hash result into a modular integer), and then the mathematical operation of RSA is applied on that number. The result is a n-bit integer, where n is the length in bits of the "modulus", usually called "the RSA key size". Basically, for RSA-1024, n is 1024. A 1024-bit integer is encoded as 128 bytes, exactly, as per the encoding method described in PKCS#1 (PKCS#1 is very readable and not too long).

Whether a n-bit RSA key can be used to sign data with a hash function which produces outputs of length m depends on the details of the padding. As the name suggests, padding involves adding some extra data around the hash output, hence n must be greater than m, leaving some room for the extra data. A 1024-bit key can be used with SHA-512 (which produces 512-bit strings). You could not use a 640-bit key with SHA-512 (and you would not, anyway, since 640-bit RSA keys can be broken -- albeit not trivially).