辅助输入环境下的确定性公钥加密方案

摘要

针对辅助输入环境下确定性公钥加密方案较难构造的问题，基于d-判定性Diffie-Hellman(d-DDH)问题，应用矩阵加密、矩阵d-DDH以及有限域上的Goldreich-Levin定理，构造一个辅助输入环境下的确定性公钥加密方案，并在标准模型下证明该方案具有强不可区分私密安全性。该方案所基于的d-DDH问题比判定性Diffie-Hellman问题更难，且可以根据应用需要选择不同d值，提供不同的安全级别。%It is not easy to construct a secure Deterministic Public Key Encryption(DPKE) schemes under Auxiliary Input(AI) environment. Aiming at this problem, based on a new intractable problem named d-decisional Diffie-Hellman(d-DDH) problem introduced recently, a new DPKE scheme under AI environment is proposed in this paper. The scheme is proved to have privacy strong indistinguish-able security in the standard model under the d-DDH assumption. Some methods and theories such as matrix encryption, matrix d-DDH, and Goldreich-Levin theorem for finite fields are used in the construction and security proof of the scheme. The d-DDH problem on which the scheme is based is more intractable than decisional Diffie-Hellman Problem(DDHP). Moreover, it can select different d for different security demand of applications.