无陷门格基签密方案

现有的格基签密方案以陷门产生算法和原像取样算法为核心算法。但是，这两个算法都很复杂，运算量较大，严重影响格基签密方案的执行效率。该文运用无陷门格基签名及其签名压缩技术，结合基于带错学习问题的加密方法，提出第1个基于格理论的、不依赖于陷门产生算法和原像取样算法的签密方案。方案在带错学习问题和小整数解问题的难解性假设下，达到了自适应选择密文攻击下的不可区分性和自适应选择消息攻击下的不可伪造性。方案在抗量子攻击的同时，保证了较高的执行效率。

A Lattice-based Signcryption Scheme Without Trapdoors

The existing lattice-based signcryption schemes are based on trapdoor generation algorithm and preimage sample algorithm. However, both algorithms are complex, require a lot of time to run, and affect the efficiency of latticed-based signcryption schemes deeply. To solve this problem, the first lattice-based signcryption scheme without trapdoor generation algorithm and preimage sample algorithm is proposed, with the help of the technique of lattice signatures without trapdoors and the associated signature compression technique, as well as the encryption method based on the learning with errors assumption. The scheme achieves indistinguishability against adaptive chosen ciphertext attacks under the learning with errors assumption. It also achieves existential unforgeability against adaptive chosen message attacks under the small integer solution assumption. The proposed scheme is not only quantum resistant, but also efficient.