Efficient Universal Padding Techniques for Multiplicative Trapdoor One-Way Permutation

Coron et al. proposed the ES-based scheme PSS-ES which realizes an encryption scheme and a signature scheme with a unique padding technique and key pair. The security of PSS-ES as an encryption scheme is based on the partial-domain one-wayness of the encryption permutation. In this paper, we propose new ES schemes OAEP-ES, OAEP++-ES, and REACT-ES, and prove their security under the assumption of only the one-wayness of encryption permutation. OAEP-ES, OAEP++-ES, and REACT-ES suit practical implementation because they use the same padding technique for encryption and for signature, and their security proof guarantees that we can prepare one key pair to realize encryption and signature in the same way as PSS-ES. Since one-wayness is a weaker assumption than partial-domain one-wayness, the proposed schemes offer tighter security than PSS-ES. Hence, we conclude that OAEP-ES, OAEP++-ES, and REACT-ES are more effective than PSS-ES. REACT-ES is the most practical approach in terms of the tightness of security and communication efficiency.