Proxy cryptography is a valuable tool in signature schemes, enabling a user to delegate signing capabilities to another entity in a controlled manner. Proxy functions can transform a standard signature scheme into a unidirectional variant, where the security of the resulting construction is directly linked to that of the base scheme. Our scheme introduces a random salt for each signing process and incorporates it into the computation of the encryption exponent. The construction achieves a tighter security reduction in the random oracle model, under the assumption that inverting RSA remains hard. While the scheme inherits the limitations of RSA with respect to Shor’s algorithm, it strengthens practical security in pre-quantum and transitional environments. We show how the unidirectional proxy function can be applied to the enhanced pqPFDH to obtain a generic unidirectional signature scheme that is existentially unforgeable under chosen message attacks (UF-CMA).