Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1710.03968 · Physical Review A

Practical somewhat-secure quantum somewhat-homomorphic encryption with coherent states

Si-Hui Tan, Yingkai Ouyang, Peter P. Rohde

Published Apr 5, 2018• 20 citations
arXivHTMLPDF

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 code space performed via passive linear optics, and with generalized nonlinear phase operations that are polynomials of the photon-number operator in the code space. 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 nonlinear 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 code words. While 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.

DOI
10.1103/physreva.97.042308

Related papers

Homomorphic encryption of linear optics quantum computation on almost arbitrary states of light with asymptotically perfect security

Ouyang, Y., Tan, S.-H., Fitzsimons, J. +1 more

Future quantum computers are likely to be expensive and affordable outright\nby few, motivating client/server models for outsourced computation. However,\nthe applications for quantum computing will often involve sensitive data, and\nthe client would like to keep her data secret, both from eavesdroppers and the\nserver itself. Homomorphic encryption is an approach for encrypted, outsourced\nquantum computation, where the client's data remains secret, even during\nexecution of the computation. We present a scheme for the homomorphic\nencryption of arbitrary quantum states of light with no more than a fixed\nnumber of photons, under the evolution of both passive and adaptive linear\noptics, the latter of which is universal for quantum computation. The scheme\nuses random coherent displacements in phase-space to obfuscate client data. In\nthe limit of large coherent displacements, the protocol exhibits asymptotically\nperfect information-theoretic secrecy. The experimental requirements are\nmodest, and easily implementable using present-day technology.

•Feb 28, 2019•15 citations

Homomorphic encryption of linear optics quantum computation on almost arbitrary states of light with asymptotically perfect security

Yingkai Ouyang, Si-Hui Tan, Joseph Fitzsimons +1 more

The authors quantify how indistinguishable any pair of quantum states with constrained energy can be after they both experience a random displacement in phase space. This continuous variable analogue of a quantum one-time pad allows one to securely delegate quantum optical computation and is easy to implement with present-day technology.

arXiv:1902.10972•Physical Review Research•Mar 18, 2020•14 citations

Non-interactive protocols for processing encrypted data (Conference Presentation)

Si-Hui Tan

Homomorphic encryption is a cryptographic primitive that enables information processing on encrypted data. Such primitives are useful in a delegated computing setting in which a client delegates processing to a server, but does not trust the server fully with her information. Here, I discuss a way of performing quantum homomorphic encryption. A homomorphic encryption protocol comprises of four algorithms: random key generation, encryption, evaluation, and decryption. Our technique requires that a pair of commuting operators be used to implement the encryption and evaluation. The client randomly selects the former, while the server implements the latter. Then post-evaluation, if the client decrypts using the inverse of the encryption, he retrieves the input state with the desired computation implemented. The code space has to be chosen carefully so that non-trivial evaluations can be performed on the logical qubits. Since the encryption key is not known to the server, the randomness introduced by key generation hides some information about the encoded data despite it being put into the hands of the server. This framework is powerful because it gives a general description for implementing quantum homomorphic encryption. For example, families of commuting groups of operators are known to exist via the Schur-Weyl duality. However, it is limited by a no-go theorem that states that an exponential overhead is needed if arbitrary computation and perfect security are desired. Nonetheless, our protocols are still interesting as an application for near-term quantum computers, especially when the computational tasks require only low-depth circuits.

Quantum Communications and Quantum Imaging•Nov 6, 2018•0 citations

Quantum encryption in phase space with displacement operators

Randy Kuang, Adrian Chan

Abstract In photonic computing, the quantum systems consist of coherent states and squeezed coherent states. Common quantum gates found in these systems are: phase shift, displacement, and squeezing gates. These gates are all unitary and reversible. Outside of quantum systems, coherent states also plays a significant role in coherent optical communications with speeds of hundreds of gigabits per second. Secure optical communications is generally implemented at the data layer with classical symmetric encryption such as Advanced Standard Encryption or AES. This inevitably allows any wiretapping to capture the transmitted data either in the plaintext mode or in the encrypted ciphertext mode in the optical infrastructure. The recent and rapid developments in Quantum computing further lift up the need for quantum secure communications in the optical infrastructure. This paper proposes a novel quantum encryption in the coherent optical domain utilizing a displacement operator and implementing with IQ-MZM optical modules, called Quantum Encryption in Phase Space or QEPS. The communication peers share a secret used to seed cryptographic pseudo random number generators to produce a synchronized random number at both the transmitter and receiver. The synchronized random numbers are used to establish displacement operators to encrypt the coherent states at the transmission and decrypt the cipher coherent states at the receiver. Therefore, malicious parties tapping along the fibre line would not extract the message in transit from optical domain due to a high Bit Error Rate or BER. The optimal displacement operator is split into a standard 16-QAM and a random phase shift operator to enhance the transmission security. We analysis the transmission security with the wiretap channel model for semantic security. We have simulated the QEPS encryption and decryption for two data modulation schemes: QPSK and 16-QAM over 80 km for transmission speeds of 56 Gbps for QPSK and 112 Gbps for 16-QAM.

EPJ Quantum Technology•Jun 29, 2023•11 citations

Quantum Encryption in Phase Space for Coherent Optical Communications

Chan, Adrian, Mostafa Khalil, Kh Arif Shahriar +3 more

Optical layer attacks on communication networks are one of the weakest reinforced areas of the network, allowing attackers to overcome security when proper safeguards are not put into place. Here, we present our solution or Quantum Encryption in Phase Space (QEPS), a physical layer encryption method to secure data over the optical fiber, based on our novel round-trip Coherent-based Two-Field Quantum Key Distribution (CTF-QKD) scheme. We perform a theoretical study through simulation and provide an experimental demonstration. The same encryption is used for QEPS as CTF-QKD but achieved through a pre-shared key and one-directional transmission design. QEPS is uniquely different from traditional technology where encryption is performed at the optical domain with coherent states by applying a quantum phase-shifting operator. The pre-shared secret is used to seed a deterministic random number generator and control the phase modulator at the transmitter for encryption and at the receiver for decryption. Using commercially available simulation software, we study two preventative measures for different modulation formats which will prevent an eavesdropper from obtaining any data. QEPS demonstrates that it is secure against tapping attacks when attackers have no information of the phase modulator and pre-shared key. Finally, an experiment with commercial components demonstrates QEPS system integrability.

arXiv:2301.06113•Jan 15, 2023•0 citations

Quantum Homomorphic Encryption Based on Quantum Obfuscation

Yuanjing Zhang, Tao Shang, Jianwei Liu +1 more

Homomorphic encryption enables computation on encrypted data while maintaining secrecy. This leads to an important open question whether quantum computation can be delegated and verified in a non-interactive manner or not. In this paper, we affirmatively answer this question by constructing the quantum homomorphic encryption scheme with quantum obfuscation. It takes advantage of the interchangeability of the unitary operator, and exchanges the evaluation operator and the encryption operator by means of equivalent multiplication to complete homomorphic encryption. The correctness of the proposed scheme is proved theoretically. The evaluator does not know the decryption key and does not require a regular interaction with a user. Because of key transmission after quantum obfuscation, the encrypting party and the decrypting party can be different users. The output state has the property of complete mixture, which guarantees the scheme security. Moreover, the security level of the quantum homomorphic encryption scheme depends on quantum obfuscation and encryption operators.

International Wireless Communications and Mobile Computing Conference (IWCMC)•Jun 1, 2020•8 citations
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 code space performed via passive linear optics, and with generalized nonlinear phase operations that are polynomials of the photon-number operator in the code space. 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 nonlinear 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 code words. While 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.
Future quantum computers are likely to be expensive and affordable outright\nby few, motivating client/server models for outsourced computation. However,\nthe applications for quantum computing will often involve sensitive data, and\nthe client would like to keep her data secret, both from eavesdroppers and the\nserver itself. Homomorphic encryption is an approach for encrypted, outsourced\nquantum computation, where the client's data remains secret, even during\nexecution of the computation. We present a scheme for the homomorphic\nencryption of arbitrary quantum states of light with no more than a fixed\nnumber of photons, under the evolution of both passive and adaptive linear\noptics, the latter of which is universal for quantum computation. The scheme\nuses random coherent displacements in phase-space to obfuscate client data. In\nthe limit of large coherent displacements, the protocol exhibits asymptotically\nperfect information-theoretic secrecy. The experimental requirements are\nmodest, and easily implementable using present-day technology.
Homomorphic encryption is a cryptographic primitive that enables information processing on encrypted data. Such primitives are useful in a delegated computing setting in which a client delegates processing to a server, but does not trust the server fully with her information. Here, I discuss a way of performing quantum homomorphic encryption. A homomorphic encryption protocol comprises of four algorithms: random key generation, encryption, evaluation, and decryption. Our technique requires that a pair of commuting operators be used to implement the encryption and evaluation. The client randomly selects the former, while the server implements the latter. Then post-evaluation, if the client decrypts using the inverse of the encryption, he retrieves the input state with the desired computation implemented. The code space has to be chosen carefully so that non-trivial evaluations can be performed on the logical qubits. Since the encryption key is not known to the server, the randomness introduced by key generation hides some information about the encoded data despite it being put into the hands of the server. This framework is powerful because it gives a general description for implementing quantum homomorphic encryption. For example, families of commuting groups of operators are known to exist via the Schur-Weyl duality. However, it is limited by a no-go theorem that states that an exponential overhead is needed if arbitrary computation and perfect security are desired. Nonetheless, our protocols are still interesting as an application for near-term quantum computers, especially when the computational tasks require only low-depth circuits.
Abstract In photonic computing, the quantum systems consist of coherent states and squeezed coherent states. Common quantum gates found in these systems are: phase shift, displacement, and squeezing gates. These gates are all unitary and reversible. Outside of quantum systems, coherent states also plays a significant role in coherent optical communications with speeds of hundreds of gigabits per second. Secure optical communications is generally implemented at the data layer with classical symmetric encryption such as Advanced Standard Encryption or AES. This inevitably allows any wiretapping to capture the transmitted data either in the plaintext mode or in the encrypted ciphertext mode in the optical infrastructure. The recent and rapid developments in Quantum computing further lift up the need for quantum secure communications in the optical infrastructure. This paper proposes a novel quantum encryption in the coherent optical domain utilizing a displacement operator and implementing with IQ-MZM optical modules, called Quantum Encryption in Phase Space or QEPS. The communication peers share a secret used to seed cryptographic pseudo random number generators to produce a synchronized random number at both the transmitter and receiver. The synchronized random numbers are used to establish displacement operators to encrypt the coherent states at the transmission and decrypt the cipher coherent states at the receiver. Therefore, malicious parties tapping along the fibre line would not extract the message in transit from optical domain due to a high Bit Error Rate or BER. The optimal displacement operator is split into a standard 16-QAM and a random phase shift operator to enhance the transmission security. We analysis the transmission security with the wiretap channel model for semantic security. We have simulated the QEPS encryption and decryption for two data modulation schemes: QPSK and 16-QAM over 80 km for transmission speeds of 56 Gbps for QPSK and 112 Gbps for 16-QAM.
Optical layer attacks on communication networks are one of the weakest reinforced areas of the network, allowing attackers to overcome security when proper safeguards are not put into place. Here, we present our solution or Quantum Encryption in Phase Space (QEPS), a physical layer encryption method to secure data over the optical fiber, based on our novel round-trip Coherent-based Two-Field Quantum Key Distribution (CTF-QKD) scheme. We perform a theoretical study through simulation and provide an experimental demonstration. The same encryption is used for QEPS as CTF-QKD but achieved through a pre-shared key and one-directional transmission design. QEPS is uniquely different from traditional technology where encryption is performed at the optical domain with coherent states by applying a quantum phase-shifting operator. The pre-shared secret is used to seed a deterministic random number generator and control the phase modulator at the transmitter for encryption and at the receiver for decryption. Using commercially available simulation software, we study two preventative measures for different modulation formats which will prevent an eavesdropper from obtaining any data. QEPS demonstrates that it is secure against tapping attacks when attackers have no information of the phase modulator and pre-shared key. Finally, an experiment with commercial components demonstrates QEPS system integrability.
Homomorphic encryption enables computation on encrypted data while maintaining secrecy. This leads to an important open question whether quantum computation can be delegated and verified in a non-interactive manner or not. In this paper, we affirmatively answer this question by constructing the quantum homomorphic encryption scheme with quantum obfuscation. It takes advantage of the interchangeability of the unitary operator, and exchanges the evaluation operator and the encryption operator by means of equivalent multiplication to complete homomorphic encryption. The correctness of the proposed scheme is proved theoretically. The evaluator does not know the decryption key and does not require a regular interaction with a user. Because of key transmission after quantum obfuscation, the encrypting party and the decrypting party can be different users. The output state has the property of complete mixture, which guarantees the scheme security. Moreover, the security level of the quantum homomorphic encryption scheme depends on quantum obfuscation and encryption operators.