KR20140060022A - Quantum signature method using arbitrator and system using it - Google Patents

Abstract

A quantum signature method by an arbitrator and a system using the same are disclosed. The quantum signature method by the arbitrator according to the present invention comprises the steps of: sharing a bell state and a private key previously generated among a signer device, an arbitrator device and a receiver device; encrypting a message to be transmitted by the signer device, generating an encrypted quantum message and a signature corresponding to the encrypted quantum message and transmitting a message-signature pair to the arbitrator device based on them; making the arbitrator device verify validity of the signature on the encrypted quantum message provided by the signer device and transmit a verification result and the message-signature pair to the receiver device; and making the receiver device check the message-signature pair and the verification result and decrypt the encrypted quantum message by using the previously shared private key according to the check result.

Description

TECHNICAL FIELD [0001] The present invention relates to a quantum signature method using an arbitrator and a system using the same,

In particular, the present invention relates to a quantum signature method, and more particularly to a method and system for a signer to generate an encrypted quantum message for a quantum message as well as a digital message and a signature corresponding to the encrypted quantum message, And a system for using the quantum signature by a mediator that enables a recipient who has finally received a verification result of an arbiter to reconstruct the original message by verifying the validity of the quantum message using the provided message-signature pair.

The quantum signature technique is one of the most important issues in the field of quantum cryptography. When a quantum message is sent over an unsecured quantum channel, it is assured that the message has not been transformed like a digital signature, And does not allow the sender of the message to deny that he or she has signed it. Unlike the digital signature scheme, the quantum signature scheme can provide unconditional security by using the principles of quantum mechanics such as the no-cloning theory and the uncertainty principle.

The two conditions required for such a quantum signature are as follows.

The first condition is that the signature should not be forged. Specifically, the signature verifier or other attacker should not be able to forge signatures or create signatures for new messages. It also means that the signatures that are created and used once should not be re-used by others.

The second condition is that denial of signing should not be possible. Specifically, the recipient must not be able to deny that the signer who signed it signed it later. In addition, the recipient must also be able to deny that they have received the signature.

The first known quantum signature protocol was introduced by Gottesman and Chuang in 2001, which is a quantum signature protocol for digital messages. The first signature protocol for quantum messages was first introduced by Zeng and Keitel in 2002 as a quantum signature protocol by the moderator. This protocol was highlighted by Curty and Lutkenhaus in 2008, and some of its problems were supplemented by Zeng.

Since then, Li has introduced a more efficient quantum signature protocol in 2009. In 2010, Zou and Qiu introduced a more efficient quantum signature protocol than Li et al. However, in 2011, Choi pointed out the problem of almost all quantum signature protocols for quantum messages, and Gao et al. Pointed out the same problems as independent results.

Accordingly, an object of the present invention is to provide a signer that not only generates a digital message but also an encrypted quantum message for a quantum message and a signature corresponding to the encrypted quantum message, And a system for using the quantum signature method by an arbitrator for providing the pair to the arbiter and verifying the validity of the quantum message using the message-signature pair provided by the arbiter, and for allowing the recipient to finally recover the original message. .

However, the objects of the present invention are not limited to those mentioned above, and other objects not mentioned can be clearly understood by those skilled in the art from the following description.

According to an aspect of the present invention, there is provided a method for quantum signing by an arbitrator, comprising: sharing a generated bell state and a secret key between a signer device, a mediator device, and a recipient device; Encrypting a quantum message to be sent by the signer apparatus to generate a signature corresponding to the encrypted quantum message, and transmitting a message-signature pair to the arbitrator apparatus based on the generated signature; Verifying the validity of the signature for the encrypted quantum message provided by the moderator device from the signer device and sending the verified result and the message-signature pair to the recipient device; And decrypting the encrypted quantum message using the secret key that is shared according to a result of the verification of the message-signature pair and the verification result value by the recipient device.

Advantageously, the step of sharing includes the steps of the signer device generating three pairs of Bell states and sharing the three pairs of Bell states generated with the moderator device; The arbiter apparatus generating three pairs of Bell states and sharing the generated three pairs of Bell states with the recipient apparatus; And a step in which the signer apparatus generates a secret key and shares the generated secret key with the arbiter apparatus and the receiver apparatus.

Advantageously, the step of transmitting to the moderator apparatus comprises: the signer apparatus generating three quantum messages and encrypting the generated three quantum messages; The signature device generating two signatures for the encrypted quantum message; And the signature device sending a message-signature pair to the moderator device.

Advantageously, the step of transmitting to the recipient device includes the steps of the moderator device generating a quantum message for verification from a signature using the secret key; Verifying the validity of the signature using the quantum message for verification; The moderator apparatus generating a signature for verification using the quantum message for verification; And providing the receiver apparatus with the message-signature pair and the verified result value provided from the signer apparatus by the intermediary apparatus.

Preferably, the decrypting step comprises: checking the message-signature pair and the verification result value received from the intermediary device; And decrypting the encrypted quantum message using the secret key if the verification result from the arbiter apparatus is true as a result of the confirmation by the receiver apparatus.

According to another aspect of the present invention, a system using a quantum signature method by a moderator encrypts a quantum message to be sent by a signer, generates a signature corresponding to the encrypted quantum message, and transmits a message- Signer device; A moderator apparatus for verifying validity of a signature on the provided encrypted quantum message and transmitting the verified result value and the message-signature pair; And a receiver apparatus for verifying the provided message-signature pair and the verification result value and decrypting the encrypted quantum message using a secret key that is shared based on the verification result.

Preferably, the signer device generates three pairs of Bell states, shares the generated three pairs of Bell states with the arbitrator device and the recipient device, generates a secret key, and transmits the generated secret key to the arbiter device, .

Preferably, the signer device generates three quantum messages and encrypts the generated three quantum messages to generate two signatures for the encrypted quantum messages, and the three quantum messages encrypted and the two signatures Signature pair to the arbiter apparatus.

Preferably, the arbiter apparatus generates a quantum message for verification from the signature using the secret key, verifies the validity of the signature using the generated quantum message for verification and the encrypted quantum message, To generate two verification signatures, and provides the message-signature pair provided from the signer device and the verified result value to the recipient device.

Preferably, the decrypting step comprises: checking the message-signature pair and the verification result value received from the intermediary device; And decrypting the encrypted quantum message using the secret key if the verification result from the arbiter apparatus is true as a result of the confirmation by the receiver apparatus.

Accordingly, the present invention allows a signer to generate an encrypted quantum message and a signature corresponding to the encrypted quantum message, to provide a message-signature pair to the arbiter based on the generated quantum message, and to use the message- By validating the validity of the message, it is possible to sign a quantum message as well as a digital message.

In addition, the present invention has an effect that it is safe to attack through a verification process by modifying a given message-signature pair, unlike a signature protocol for most known quantum messages.

In addition, the present invention has the effect that even when a signer sends a known quantum message by encrypting a quantum message with a secret key shared by a receiver and sends an encrypted quantum message, the mediator in the middle can not read the message.

1 is a schematic diagram of an overall system according to an embodiment of the present invention.
2 is a diagram illustrating a quantum signature method by an arbitrator according to an embodiment of the present invention.
FIG. 3 is a diagram for explaining in detail the process of sharing the bell state and the secret key shown in FIG.
FIG. 4 is a diagram for explaining a process of transmitting the message-signature pair shown in FIG. 2 in detail.
FIG. 5 is a diagram for explaining the process of verifying the validity of the signature shown in FIG. 2 in detail.
FIG. 6 is a diagram for explaining a process of decoding the quantum message shown in FIG. 2 in detail.

Hereinafter, a quantum signature method by a mediator according to an embodiment of the present invention and a system using the same will be described with reference to FIGS. 1 to 6. FIG. The present invention will be described in detail with reference to the portions necessary for understanding the operation and operation according to the present invention. If the message to be signed is a digital message, the signer can easily convert a given digital message into a quantum message.

In describing the constituent elements of the present invention, the same reference numerals may be given to constituent elements having the same name, and the same reference numerals may be given thereto even though they are different from each other. However, even in such a case, it does not mean that the corresponding component has different functions according to the embodiment, or does not mean that the different components have the same function. It should be judged based on the description of each component in the example.

In particular, according to the present invention, a signer generates not only a digital message but also an encrypted quantum message for a quantum message and a signature corresponding to the encrypted quantum message, and provides a message-signature pair to the arbiter based on the generated quantum message, - We propose a new quantum signature method that verifies the validity of a quantum message using a signature pair and finally allows the recipient to receive the verification result to restore the original message.

1 is a schematic diagram of an overall system according to an embodiment of the present invention.

1, the overall system according to the present invention may include an alice device 110, a trent device 120, a bob device 130, and the like . Participants of the system thus configured, that is, the signer device, the moderator device, and the recipient device, can be used for quantum key distribution, quantum teleportation, quantum one-time encryption, quantum state comparison).

The signer device 110 may generate three pairs of Bell states and share a portion of the Bell state with the arbiter device over the quantum authentication channel. Signer device 110 may encrypt the message to send to generate an encrypted quantum message and generate a secure signature corresponding to the encrypted quantum message to send the message-signature pair to the moderator device.

The moderator apparatus 120 may generate three pairs of bell states and share a portion of the bell state with the recipient apparatus through the quantum authentication channel. The moderator apparatus 120 can verify the validity of the two signatures for the encrypted quantum message provided from the signer apparatus 110 and transmit the verification result to the recipient apparatus

The recipient apparatus 130 can confirm the message-signature pair and the verification result and decrypt the encrypted quantum message using the secret key that has been shared according to the confirmation result.

2 is a diagram illustrating a quantum signature method by an arbitrator according to an embodiment of the present invention.

2, the participants according to the present invention may share a bell state and a secret key (S210). This will be described with reference to FIG.

FIG. 3 is a diagram for explaining in detail the process of sharing the bell state and the secret key shown in FIG.

As shown in FIG. 3, the signer device generates three pairs of bell states and transmits the generated three pairs of bell states to the intermediary device through the quantum authentication channel to share a part of the bell state with the intermediary device (211).

The moderator terminal generates three pairs of bell states and transmits the generated three pairs of bell states to the receiver apparatus through the quantum authentication channel to share a part of the bell state with the receiver apparatus (S212).

At this time, the signer device shares the secret key K _AT1 and K _AT2 with the arbiter device using the quantum key distribution protocol such as the BB84 protocol, which has been proven to be unconditionally stable, and shares the secret key K _AB in the same manner with the receiver device (S213).

Here K _AB ∈ {00,01,10,11}, K _AT1 ∈ {0,1}, K _AT2 ∈ {0,1} can be defined.

Next, the signer device may encrypt the quantum message to be sent and generate a signature corresponding to the encrypted quantum message to transmit the message-signature pair to the moderator device (S220). This will be described with reference to FIG.

FIG. 4 is a diagram for explaining a process of transmitting the message-signature pair shown in FIG. 2 in detail.

As shown in FIG. 4, the signer apparatus can generate the same three quantum messages including the quantum message to be sent and the two quantum messages, which are copies thereof, according to Equation (1) (S221).

[Equation 1]

At this time, the quantum message is divided into a known message and an unknown message.

A known message in a generic quantum signature protocol is a message that a recipient can read in a quantum message received as a classic message. That is, if the base of the quantum message is already known in advance so that it can read the received quantum message.

An unknown message is a message whose base of a quantum message is unknown to the recipient. That is, the recipient can not read the quantum message without error before receiving the base of the message.

The signer apparatus can encrypt the same three quantum messages using the secret key K _AB between the signer apparatus and the receiver apparatus using Equation (2) (S222).

&Quot; (2) "

Here, E _KAB is a quantum one-time encryption method, and can be expressed by the following Equation (3).

&Quot; (3) "

Here, K _j is the j-th bit of the secret key K, and σ _x and σ _z represent pauli matrices, and the Pauli matrices σ _x and σ _z can be expressed by the following Equation (4).

&Quot; (4) "

와

을 생성할 수 있다(S223).The signer device sends a random rotation R _K with two signatures corresponding to the encrypted quantum message P >> using the secret keys K _AT1 and K _AT2 with the moderator device

Wow

(S223).

The random rotation R _K described herein can be expressed by the following equation (5).

&Quot; (5) "

The signer device can transmit the generated (| P '>, | S ₁ >, | S ₂ >) based on the ring status shared with the intermediary device to the intermediary device using the quantum teleportation through the quantum channel (S 224) .

At this time, the transmission of the quantum state through the quantum teleportation can be performed as follows.

로 나타내고 보내려는 양자 상태를 |Q〉라고 가정하면 다음의 [수학식 6]과 같이 정의할 수 있다.The ring status shared between the signer device and the moderator device

And the quantum state to be transmitted is | Q>, it can be defined as the following Equation (6).

&Quot; (6) "

이다.here,

to be.

The result of measuring the bell state for quantum teleportation can be defined as the following equation (7).

&Quot; (7) "

The signer device can send M _A ∈ {00,01,10,11} obtained from the above-mentioned formula (7) to a public board. These public bulletin boards assume that anyone can see the message but can not transform it.

So the moderator can get the quantum state | Q> again using the public bulletin board.

Next, the intermediary apparatus can verify the validity of the two signatures for the encrypted quantum message provided from the signer apparatus and transmit the verification result to the recipient apparatus (S230). This will be described with reference to FIG.

FIG. 5 is a diagram for explaining the process of verifying the validity of the signature shown in FIG. 2 in detail.

과

를 생성할 수 있다(S231).As shown in FIG. 5, the mediator apparatus receives secret keys K _AT1 and K K shared by the signer apparatus to verify the validity of the signature from the signer apparatus (| P '>, | S ₁ >, | S ₂ > S ₂ > from the signatures S ₁ > and S ₂ > using the _{AT 2}

and

(S231).

The moderator can verify the validity of the signature by performing a quantum identity test for | P '> and | P ₁ '> and a quantum identity test for | P '> and | P ₂ '> (S232).

If the modulator device determines that the signature is valid or valid and judges that the given quantum states are equal to each other in both cases, it records as | V> = | 1>, and if it is determined that the given quantum states are different from each other even once It can be written as " V > = | 0 "

과

를 생성할 수 있다(S233).After the two tests have been completed, the moderator device applies the secret key to the random rotation that was used for the first time,

and

(S233).

And the mediator device may store the signature S ₂ '> for non-repudiation.

The mediator device can then transmit the message-signature pair and the verification result values (| P '>, | S ₁ '>, | V>) to the recipient device via the bilateral channel (S234).

Next, the recipient apparatus confirms the message-signature pair and the verification result, and decrypts the encrypted quantum message using the shared secret key according to the verification result (S240). This will be described with reference to FIG.

FIG. 6 is a diagram for explaining a process of decoding the quantum message shown in FIG. 2 in detail.

6, the receiver apparatus receives the message-signature pair and the verification result values (| P '>, | S ₁ '>, | V>) (S 241) P '>, | S ₁ '>, | V>) (S242).

을 얻을 수 있다(S243).If | V> = | 1> as a result of the confirmation, the receiver apparatus decrypts the encrypted quantum message using the secret key K _AB and outputs a quantum message

(S243).

On the other hand, the receiver apparatus can end the entire process if | V> = | 0> as a result of the confirmation (S244).

가 아니라 다음의 [수학식 8]과 같이 얽힘 상태를 표함하고 있는 좀더 일반적인 양자 메시지인 멀티 큐빗 메시지 예컨대, n-큐빗 메시지일 수 있다.On the other hand, if the quantum message to be sent by the signer device is a qubit message

But may be a multi-qubit message, for example, an n-qubit message, which is a more general quantum message expressing a entangled state as shown in the following equation (8).

&Quot; (8) "

를 대신하여 다음의 [수학식 9]를 사용한다.In this case, K _AB ∈ {0,1} ²ⁿ , K _AT1 ∈ {0,1} ⁿ and K _AT2 ∈ {0,1} ⁿ are required and six 2n-qubit GHZ states (Greenberger-Horne-Zeilinger State) And is a quantum one-time encryption

The following equation (9) is used.

&Quot; (9) "

,

이다.here,

,

to be.

을 대신하여 다음의 [수학식 10]을 사용한다.The random rotation R _K

The following equation (10) is used.

&Quot; (10) "

It is also possible to test the identity of each of the qubit messages using a product test that verifies that the product is in a product state in the case of a quantum identity test.

It is to be understood that the present invention is not limited to these embodiments, and all of the elements constituting the embodiments of the present invention described above may be combined or operated in one operation. That is, within the scope of the present invention, all of the components may be selectively coupled to one or more of them. In addition, although all of the components may be implemented as one independent hardware, some or all of the components may be selectively combined to perform a part or all of the functions in one or a plurality of hardware. As shown in FIG. In addition, such a computer program may be stored in a computer-readable medium such as a USB memory, a CD disk, a flash memory, etc., and read and executed by a computer, thereby implementing embodiments of the present invention. As the storage medium of the computer program, a magnetic recording medium, an optical recording medium, a carrier wave medium, or the like may be included.

It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or essential characteristics thereof. Therefore, the embodiments disclosed in the present invention are intended to illustrate rather than limit the scope of the present invention, and the scope of the technical idea of the present invention is not limited by these embodiments. The scope of protection of the present invention should be construed according to the following claims, and all technical ideas falling within the scope of the same shall be construed as falling within the scope of the present invention.

110: signer device
120: moderator device
130: Receiver device

Claims (1)

Sharing a pre-generated ring status and a secret key between a signer device, an intermediary device, and a recipient device;
Encrypting a message to be sent by the signer apparatus to generate an encrypted quantum message and a signature corresponding to the encrypted quantum message, and transmitting a message-signature pair to the arbitrator apparatus based on the generated signature;
Verifying the validity of the signature for the encrypted quantum message provided by the moderator device from the signer device and sending the verified result and the message-signature pair to the recipient device; And
Decrypting the encrypted quantum message using the secret key shared by the recipient device according to a result of checking the message-signature pair and the verification result value;
A method for quantum signing by an arbitrator comprising:

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