Our main result is a quantum public-key encryption scheme based on the Extrapolated Dihedral Coset problem (EDCP) which is equivalent, under quantum polynomial-time reductions, to the Learning With Errors (LWE) problem. For limited number of public keys (roughly linear in the security parameter), the proposed scheme is information-theoretically secure. For polynomial number of public keys, breaking the scheme is as hard as solving the LWE problem. The public keys in our scheme are quantum states of size $\tilde{O}(n)$ qubits. The key generation and decryption algorithms require $\tilde{O}(n)$ qubit operations while the encryption algorithm takes $O(1)$ qubit operations.

翻译：我们的主要结果是基于外推二元共振问题(EDCP)的量子公用钥匙加密方案,在量子多元时间缩减下,这相当于“学习错误”问题。对于数量有限的公用钥匙(安全参数中大致线性),拟议方案是信息-理论安全。对于公用钥匙的多元数,打破公用钥匙方案与解决LWE问题一样困难。我们计划中的公用钥匙是 $\ tillde{O}(n) qubit 。关键生成和解密算法需要 $\ tilde{O}(n) qubit 操作,而加密算法则需要 $(1) qubit 操作。