Research on Timed-Release Encryption System Based on Multiple Time Servers
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摘要: 时控性加密(TRE)是一种被称为“向未来发送消息”的密码原语，接收方在未来指定时间之前无法解密密文。目前，大部分TRE方案采用非交互式单时间服务器方法，系统用户能够正常解密，依赖于单一时间服务器在预定解密时间计算并广播的时间陷门。如果单一的时间服务器遭受攻击，或被腐败，则容易直接威胁TRE的安全应用。因此，需要将1个时间服务器“分散”成多个。但已有多时间服务器TRE方案既没有给出安全性分析，也没有给出严格的安全性证明。为此，该文给出一种随机预言机模型下基于双线性迪菲·赫尔曼(BDH)问题的多时间服务器的TRE模型MTSTRE，构造出一种可证明安全的具体和通用方案，并严格证明所提具体方案在自适应选择明文攻击下是安全的。效率分析表明，与已有最有效的多时间服务器TRE解决方案相比，所提具体方案的计算效率也略有提高。Abstract: Timed-Release Encryption (TRE) is a cryptographic primitive called "sending messages into the future", the receiver can not decrypt the ciphertext until a designed time in the future. Currently, most TRE schemes use a non-interactive single time server approach, where the system user is able to decrypt properly, relying on a time trapdoor calculated and broadcast by a time server at the designed decryption time. If the single time server is attacked or corrupted, it is prone to directly threaten the TRE security application. Therefore, a single time server needs to be “distributed” into multiple ones. However, existing multiple time servers TRE schemes do not provide neither the security analysis nor the strict formal security proofs. To deal with this problem, a new Multiple Time Servers TRE (MTSTRE) scheme based on Bilinear Diffie-Hellman (BDH) problem in the random oracle model is proposed, a concrete scheme with provable security and a general scheme is proposed, and then it is strictly proved that the concrete scheme is security under adaptive chosen-plaintext attack. Efficiency analysis shows that compared with the most effective existing multiple time servers TRE scheme, the calculation efficiency of the concrete scheme is slightly improved.
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表 1 其他基本运算相对于PMec运算的相对耗时统计表
基本运算操作 标识符号 相对耗时(PMT) 双线性对运算 BP 3.7870 G1群上的点乘运算 PMec 1 G1群上的点加运算 PAec 0.0074 G2群上的幂运算 Expdl 0.3409 G2群上的乘运算 Muldl 0.0026 $ \mathbb{Z}_q^* $上的模逆运算 Inv 0.0029 $ {H_1} $函数：${\{ 0,1\} ^*} \to {G_1}$ H1 0.3214 $ {H_2} $函数：${G_2} \to {\{ 0,1\} ^{ { {\log}_{2} }q} }$ H2 0.0784 
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