In this paper, we propose new classes of trapdoor functions to solve the bounded distance decoding problem in lattices. Specifically, we construct lattices based on properties of polynomials for which the bounded distance decoding problem is hard to solve unless some trapdoor information is revealed. We thoroughly analyze the security of our proposed functions using state-of-the-art attacks and results on lattice reductions. Finally, we describe how our functions can be used to design quantum-safe encryption schemes with reasonable public key sizes. Our encryption schemes are efficient with respect to key generation, encryption and decryption.

中文翻译：

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多项式构造格的有界距离解码问题及其密码学应用

在本文中，我们提出了新的陷门函数类来解决格中的有界距离解码问题。具体来说，我们基于多项式的属性构建格，除非揭示一些陷门信息，否则有界距离解码问题很难解决。我们使用最先进的攻击和格减少的结果彻底分析了我们提出的函数的安全性。最后，我们描述了如何使用我们的函数来设计具有合理公钥大小的量子安全加密方案。我们的加密方案在密钥生成、加密和解密方面是高效的。