From Fixed-Length to Arbitrary-Length RSA Encoding Schemes Revisited

To sign with RSA, one usually encodes the message m as μ(m) and then raises the result to the private exponent modulo N . In Asiacrypt 2000, Coron et al. showed how to build a secure RSA encoding scheme μ′(m) for signing arbitrarily long messages from a secure encoding scheme μ(m) capable of handling only fixed-size messages, without making any additional assumptions. However, their construction required that the input size of μ be larger than the modulus size. In this paper we present a construction for which the input size of μ does not have to be larger than N . Our construction shows that the difficulty in building a secure encoding for RSA signatures is not in handling messages of arbitrary length, but rather in finding a secure encoding function for short messages, which remains an open problem in the standard model.