Paper 2020/595

Time-Specific Encryption with Constant-Size Secret-Keys Secure under Standard Assumption

Masahito Ishizaka and Shinsaku Kiyomoto

Abstract

In Time-Specific Encryption (TSE) [Paterson and Quaglia, SCN'10] system, each secret-key (resp. ciphertext) is associated with a time period t s.t. 0<=t<=T-1 (resp. a time interval [L,R] s.t. 0<=L<=R<=T-1. A ciphertext under [L,R] is correctly decrypted by any secret-key for any time t included in the interval, i.e., L<=t<=R. TSE's generic construction from identity-based encryption (IBE) (resp. hierarchical IBE (HIBE)) from which we obtain a concrete TSE scheme with secret-keys of O(log T)|g| (resp. O(log^2 T)|g|) and ciphertexts of size O(log T)|g| (resp. O(1)|g|) has been proposed in [Paterson and Quaglia, SCN'10] (resp. [Kasamatsu et al., SCN'12]), where |g| denotes bit length of an element in a bilinear group G. In this paper, we propose another TSE's generic construction from wildcarded identity-based encryption (WIBE). Differently from the original WIBE ([Abdalla et al., ICALP'06]), we consider WIBE w/o (hierarchical) key-delegatability. By instantiating the TSE's generic construction, we obtain the first concrete scheme with constant-size secret-keys secure under a standard (static) assumption. Specifically, it has secret-keys of size O(1)|g| and ciphertexts of size O(log^2 T)|g|, and achieves security under the decisional bilinear Diffie-Hellman (DBDH) assumption.