In 2010, Resch and Plank proposed a computationally secure secret sharing scheme, called AONT-RS. We present a generalisation of their scheme and discuss two ways in which information is leaked if used to distribute small ciphertexts. We discuss how to prevent such leakage and provide a proof of computational privacy in the random oracle model. Next, we extend the scheme to be robust and prove the robust AONT-RS achieves computational privacy in the random oracle model and computational recoverability under standard assumptions. Finally, we compare the security, share size and complexity of the AONT-RS scheme with Krawczyk's SSMS scheme.