Efficient Quantum Public-Key Encryption From Learning With Errors

05/26/2021

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by   Javad Doliskani, et al.

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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 Õ(n) qubits. The key generation and decryption algorithms require Õ(n) qubit operations while the encryption algorithm takes O(1) qubit operations.