Ideal Secret Sharing Schemes with Share Selectability

Abstract. In this paper, we investigate a new concept, called share selectable secret sharing, where no unauthorized set can obtain information of the secret (in the information-theoretic sense) even if shares are selectable as arbitrary values which are independent of the secret. We propose two totally selectable (i.e., all users' shares are selectable) secret sharing schemes with unanimous structure. We also propose a quasiselectable (i.e., a part of each user's share is selectable) secret sharing scheme with certain hierarchical structures which contains special cases of the hierarchical threshold structures introduced by Tamir Tassa in TCC2004 (or its full version (J. Cryptology2007)). If all selectable shares are randomly chosen, then our schemes are perfect. Finally, we discuss the effect of the leakage information of the secret if a weak secret is indicated as a selectable share

Probably secure threshold public-key encryption with adaptive security and short ciphertexts

10.1016/j.ins.2012.04.038Threshold public-key encryption is a cryptographic primitive allowing decryption control in group-oriented encryption applications. Existing TPKE schemes suffer from long ciphertexts with size linear in the number of authorized users or can only achieve non-adaptive security, which is too weak to capture the capacity of the attackers in the real world. In this paper, we propose an efficient TPKE scheme with constant-size ciphertexts and adaptive security. Security is proven under the decision Bilinear Diffie-Hellman Exponentiation assumption in the standard model. Then we extend our basic construction with efficient trade-offs between the key size and the ciphertext size. Finally, we illustrate improvements to transmit multiple secret session keys in one session with almost no extra cost