Forward-Secure Public-Key Encryption Scheme Based on SM9

In the traditional hybrid cryptosystem, an attacker can generate the previously used session key to decrypt session contents encrypted under the session key due to the leakage of the current private key. To address this issue of leakage of the private key, this paper applies the key encapsulation mechanism and proposes a forward-secure public-key encryption scheme (FS-SM9) based on identity cryptosystem SM9. This paper also proves that the scheme is IND-FS-CPA under the hardness assumption (q, n)-DBDHI in the standard model. In the encryption scheme, the lifetime of the system is divided into multiple periods which are managed by a binary tree, which reduces the overheads of the system to a logarithmic level. The time information is embedded into the ciphertext when encrypting messages. Only the private key of the specific period can decrypt the ciphertext. Each private key is updated via an updating procedure and this updating procedure is unidirectional, during which a new private key is generated while the old one is deleted, so the forward security is preserved. Moreover, as shown by the performance analysis and experimental results, the scheme only introduces negligible overheads in achieving forward security under certain conditions. Therefore, the proposed scheme is practical and can be run on specific resource-constrained devices, providing forward security for these devices.