Quantum cipher based on phase inversion
Methods, systems and computer readable media are disclosed for providing a quantum cipher based on phase inversion, A shared key is established between a first party and a second party. A Hadamard transformation is applied to a message intended for a second party from the first party to produce an equal superposition state. A key phase inversion is applied to the output of the Hadamard transformation. A multiple phase inversion transformation is applied to the output of the key phase inversion to produce an encrypted quantum state with a uniform probability and relative phase distributions. The result is sent to the second party.
1. A method of providing a quantum cipher based on phase inversion, the method comprising:
establishing a shared key between a first party and a second party;
applying a Hadamard transformation to a message intended for a second party from the first party to produce an equal superposition state;
applying a key phase inversion to the output of the Hadamard transformation;
applying a multiple phase inversion transformation to the output of the key phase inversion to produce an encrypted quantum state with a uniform probability and relative phase distributions; and
sending the result to the second party.
2. The method of claim 1 wherein the applying a Hadamard transformation to a message intended for a second party from the first party to produce an equal superposition state, the applying a key phase inversion to the output of the Hadamard transformation, and the applying a multiple phase inversion to the output of the key phase inversion to produce an encrypted quantum state with a uniform probability and relative phase distributions are performed by a quantum computer.
3. The method of claim 1 wherein the quantum cipher is used for communications between a UE and a core.
4. The method of claim 1 wherein the Hadamard transformation is performed in accordance with the formula
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m
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1
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0
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1
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x
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.
5. The method of claim 1 wherein the key phase inversion is performed in accordance with the formula
Λ k =I− 2| k><k|.
6. The method of claim 1 wherein the multiple phase inversion transformation is performed in accordance with the formula
|ψ c =γ k,d |ψ′ c .
7. The method of claim 1 further comprising retrieving the message from the result, the retrieving comprising:
applying a multiple phase inversion transformation to the received message;
applying a key phase inversion to the output of the multiple phase inversion transformation; and
applying a Hadamard transformation to the result from the key phase inversion.
8. A system comprising:
a UE including a first quantum computing element; and
a core network including a second quantum computing element;
wherein the first quantum computing element provides a quantum cipher based on phase inversion for a message sent from the UE to the core network;
wherein the second quantum computing element provides a quantum cipher based on phase inversion for a message sent from the core network to the UE, wherein the quantum cipher based on phase inversion is provided by the method comprising: establishing a shared key between a first party and a second party: applying a Hadamard transformation to a message intended for a second party from the first party to produce an equal superposition state; applying a key phase inversion to the output of the Hadamard transformation; applying a multiple phase inversion transformation to the output of the key phase inversion to produce an encrypted quantum state with a uniform probability and relative phase distributions; and sending the result to the second party.
9. The system of claim 8 wherein the applying a Hadamard transformation to a message intended for a second party from the first party to produce an equal superposition state, the applying a key phase inversion to the output of the Hadamard transformation, and the applying a multiple phase inversion to the output of the key phase inversion to produce an encrypted quantum state with a uniform probability and relative phase distributions are performed by a quantum computer.
10. The system of claim 8 wherein the Hadamard transformation is performed in accordance with the formula
ψ
m
〉
=
H
⊗
n
(
m
〉
)
=
1
N
∑
x
=
0
N
-
1
(
-
1
)
m
·
x
x
〉
.
11. The system of claim 8 wherein the key phase inversion is performed in accordance with the formula
Λ k =I− 2| k><k|.
12. The system of claim 8 wherein the multiple phase inversion transformation is performed in accordance with the formula
|ψ c =γ k,d |ψ′ c .
13. The system of claim 8 further comprising retrieving a message that has been transformed into a quantum cipher based on phase inversion, the retrieving comprising:
applying a multiple phase inversion transformation to the received message;
applying a key phase inversion to the output of the multiple phase inversion transformation; and
applying a Hadamard transformation to the result from the key phase inversion to obtain the original message.
14. A non-transitory computer-readable medium containing instructions which,
when executed, cause a quantum computing element to perform steps comprising:
establishing a shared key between a first party and a second party;
applying a Hadamard transformation to a message intended for a second party from the first party to produce an equal superposition state;
applying a key phase inversion to the output of the Hadamard transformation;
applying a multiple phase inversion transformation to the output of the key phase inversion to produce an encrypted quantum state with a uniform probability and relative phase distributions; and
sending the result to the second party.
15. The non-transitory computer-readable medium of claim 14 further comprising instructions wherein the applying a Hadamard transformation to a message intended for a second party from the first party to produce an equal superposition state, the applying a key phase inversion to the output of the Hadamard transformation, and the applying a multiple phase inversion to the output of the key phase inversion to produce an encrypted quantum state with a uniform probability and relative phase distributions are performed by a quantum computer.
16. The non-transitory computer-readable medium of claim 14 further comprising instructions wherein the Hadamard transformation is performed in accordance with the formula
ψ
m
〉
=
H
⊗
n
(
m
〉
)
=
1
N
∑
x
=
0
N
-
1
(
-
1
)
m
·
x
x
〉
.
17. The non-transitory computer-readable medium of claim 14 further comprising instructions wherein the key phase inversion is performed in accordance with the formula
Λ k =I− 2| k><k|.
18. The non-transitory computer-readable medium of claim 14 further comprising instructions wherein the multiple phase inversion transformation is performed in accordance with the formula
|ψ c =γ k,d |ψ′ c .
19. The non-transitory computer-readable medium of claim 14 further comprising instructions for retrieving the message from the result, the retrieving comprising:
applying a multiple phase inversion transformation to the received message;
applying a key phase inversion to the output of the multiple phase inversion transformation; and
applying a Hadamard transformation to the result from the key phase inversion.