Practical quantum somewhat-homomorphic encryption with coherent states

Abstract

We present a scheme for implementing homomorphic encryption on coherent states encoded using phase-shift keys. The encryption operations require only rotations in phase space, which commute with computations in the codespace performed via passive linear optics, and with generalized non-linear phase operations that are polynomials of the photon-number operator in the codespace. This encoding scheme can thus be applied to any computation with coherent state inputs, and the computation proceeds via a combination of passive linear optics and generalized non-linear phase operations. An example of such a computation is matrix multiplication, whereby a vector representing coherent state amplitudes is multiplied by a matrix representing a linear optics network, yielding a new vector of coherent state amplitudes. By finding an orthogonal partitioning of the support of our encoded states, we quantify the security of our scheme via the indistinguishability of the encrypted codewords. Whilst we focus on coherent state encodings, we expect that this phase-key encoding technique could apply to any continuous-variable computation scheme where the phase-shift operator commutes with the computation.

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Cited by in corpus (8)

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• Privacy and correctness trade-offs for information-theoretically secure quantum homomorphic encryption
• Error correctable efficient quantum homomorphic encryption using Calderbank-Shor-Steane codes
• A quantum homomorphic encryption scheme for polynomial-sized circuits
• Further Limitations on Information-Theoretically Secure Quantum Homomorphic Encryption
• Quantum Search on Encrypted Data Based on Quantum Homomorphic Encryption
• Quantum preprocessing for information-theoretic security in two-party computation
• A framework for quantum homomorphic encryption with experimental demonstration