In cryptography, the Full Domain Hash (FDH) is an RSA-based signature scheme that follows the hash-and-sign paradigm. It is provably secure (i.e., is existentially unforgeable under adaptive chosen-message attacks) in the random oracle model. FDH involves hashing a message using a function whose image size equals the size of the RSA modulus, and then raising the result to the secret RSA exponent.

In the random oracle model, if RSA is ${\displaystyle (t',\epsilon ')}$-secure, then the full domain hash RSA signature scheme is ${\displaystyle (t,\epsilon )}$-secure where,

For large ${\displaystyle q_{\text{sig}}}$ this reduces to ${\displaystyle \epsilon \sim \exp(1)\cdot q_{\text{sig}}\cdot \epsilon '}$.

This means that if there exists an algorithm that can forge a new FDH signature that runs in time t, computes at most ${\displaystyle q_{\text{hash}}}$ hashes, asks for at most ${\displaystyle q_{\text{sig}}}$ signatures and succeeds with probability ${\displaystyle \epsilon }$, then there must also exist an algorithm that breaks RSA with probability ${\displaystyle \epsilon '}$ in time ${\displaystyle t'}$.