Every public-key encryption scheme has to incorporate a certain amount of randomness into its ciphertexts to provide semantic security against chosen ciphertext attacks (IND-CCA). The difference between the length of a ciphertext and the embedded message is called the ciphertext overhead. While a generic brute-force adversary running in 2t steps gives a theoretical lower bound of t bits on the ciphertext overhead for IND-CPA security, the best known IND-CCA secure schemes demand roughly 2t bits even in the random oracle model. Is the t-bit gap essential for achieving IND-CCA security? We close the gap by proposing an IND-CCA secure scheme whose ciphertext overhead matches the generic lower bound up to a small constant. Our scheme uses a variation of a four-round Feistel network in the random oracle model and hence belongs to the family of OAEP-based schemes. Maybe of independent interest is a new efficient method to encrypt long messages exceeding the length of the permutation while retaining the minimal overhead.

In this paper, we propose a rational m-out-of-n secret sharing scheme, a dealer wishes to entrust a secret with a group of n players such that any subset of m or more players can reconstruct the secret, but a subset of less than m players cannot learn anything about the secret. The reconstruction protocol of our scheme is fair and stable in the rational settings, allowing all players to obtain the designated secret. Our scheme is based on RSA-OAEP with the distributed decryption. The security of our scheme relies on a computational assumption and uses the random oracles. The size of each share in our scheme is independent of the utility function and the computation cost of the reconstruction protocol is constant. Moreover, our scheme prevents the attacks with at most m-1 coalitions.

Recently a framework called Tag-KEM/DEM was introduced to construct efficient hybrid encryption schemes. Although it is known that generic encode-then-encrypt construction of chosen ciphertext secure public-key encryption also applies to secure Tag-KEM construction and some known encoding method like OAEP can be used for this purpose, it is worth pursuing more efficient encoding method dedicated for Tag-KEM construction. This paper proposes an encoding method that yields efficient Tag-KEM schemes when combined with set partial one-way permutations such as RSA and Rabin's encryption scheme. To our knowledge, this leads to the most practical hybrid encryption scheme of this type. We also present an efficient Tag-KEM which is CCA-secure under general factoring assumption rather than Blum factoring assumption.

We first model the variants of OAEP and SAEP by changing a construction and position of a redundancy, and establish a universal proof technique in the random oracle model, the comprehensive event dividing tree. We then make a taxonomical security consideration of the variants of OAEP and SAEP, based on the assumptions of one-wayness and partial-domain one-wayness of the encryption permutation, by applying the tree. Furthermore, we demonstrate the concrete attack procedures against all insecure schemes; we insist that the security proof failure leads to some attacks. From the security consideration, we find that one of the variants leads to a scheme without the redundancy; the scheme is not PA (plaintext aware) but IND-CCA2 secure. Finally, we conclude that some of them are practical in terms of security tightness and short bandwidth.

The new concept of ES (Encryption-Signature) schemes which realize an encryption scheme and a signature scheme with a unique padding technique and key pair, was proposed by Coron et al. They also gave a proof of PSS-ES. In this paper, first, we discuss the methodology for the construction for ES schemes by using padding techniques of encryption schemes, and propose a new ES scheme, OAEP-ES, adopting this methodology. It is proven that OAEP-ES scheme can be constructed under the assumption of the one-wayness of the encryption permutation, while the security of PSS-ES utilized as an encryption scheme is based on the partial-domain one-wayness; which is a theoretical progress since the one-wayness is more general assumption than the partial-domain one-wayness. It is shown that OAEP-ES attains tighter security than PSS-ES, which is a practical interest.