KR20190071659A - Quantum encryption system for quantum signature - Google Patents

Abstract

The present invention relates to a quantum encryption system comprising: a first communication device for generating a quantum message composed of a message qubit indicating an arbitrary quantum state, encrypting the message qubit through a plurality of polarizing plates to generate a signature qubit, and generating a quantum signature pair consisting of the message qubit and the signature qubit; and a second communication device for receiving the quantum signature pair and verifying the quantum signature pair by decoding the quantum signature pair.

Description

[0001] QUANTUM ENCRYPTION SYSTEM FOR QUANTUM SIGNATURE [

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a quantum cryptography technique, and more particularly, to a quantum cryptography system for a quantum signature that provides an unforgeable quantum signature pair to ensure safety.

Quantum cryptography is a cryptographic system based on quantum mechanics, which is safe in a quantum computer environment, unlike modern cryptography. Various protocols such as BB84, B92, 6-state, SARGO04, DPS, COW, and MDI have been proposed and quantitative key distribution (QKD) QKD guarantees integrity by using a quantum channel to which quantum state superposition, uncertainty principle, non - copy principle is applied, and a one - time secret key which can be acquired through this protocol enables confidential communication. That is, QKD provides confidentiality and integrity. However, in addition to confidentiality and integrity, cryptographic systems must provide authentication and anti-tampering, and quantum signatures are required to provide such functions in quantum cryptography.

Compared to QKD, which has been studied up to the level of commercialization, quantum signatures are still under study at the theoretical and basic experimental level. The main reason is that there is no public key system in quantum cryptography. In other words, in modern cryptosystem, digital signature function is efficiently implemented and used based on public key. However, since there is no concept of public key in both, it does not apply mature technology of digital signature. Therefore, an arbitrary quantum signature and a quantum one-time signature are studied by applying a signature protocol based on a symmetric key in an alternate cipher. However, most of these quantum signature protocols are vulnerable to safety due to a vulnerability found in quanum encryption, which creates a quantum signature pair.

Korean Patent No. 10-1675674 Korean Patent No. 10-0505335

It is an object of the present invention to provide a quantum cryptography system with high freedom and ease of implementation that prevents tampering that can occur in quantum signature protocols using quantum cryptography and swap testing.

According to a first aspect of the present invention, there is provided a quantum cryptography system comprising: a quantum message generating unit configured to generate a quantum message composed of a message qubit indicating an arbitrary quantum state, encrypt the message qubit through a plurality of polarizers, A first communication device for generating a quantum signature pair comprising the message qubits and the signature qubits; And a second communication device that receives the quantum signature pair from the first communication device and decrypts the quantum signature pair to verify the quantum signature pair.

Preferably, the first communication device includes: a first polarizer for rotating the message qubit in a first axis; A second polarizer for rotating the message qubit through the first polarizer at a specific angle; And a third polarizer that rotates the message qubit through the second polarizer on a second axis.

Preferably, the first to third polarizers can encrypt the message qubit with a rotation operator such that the signature qubit is generated.

[Equation]

로서 상기 제1 및 제3 편광판에 의하여 회전된 축을 나타내는 3차원 벡터이고,

로서 3개의 파울리 연산자들로 구성되는 벡터이다.Here, I is a unit matrix,? Is an angle rotated by the second polarizer plate,

Dimensional vector representing an axis rotated by the first and third polarizing plates,

Is a vector composed of three Pauly operators.

≠2t, 및

≠0 에 해당할 수 있다.Preferably, between the first communication device and the second communication device, when the quantum signature pair transmitted from the first communication device is encrypted by an eavesdropper with a rotation operator such as the following equation, θ ≠ 2s,

≠ 2t, and

0 < / RTI >

[Equation]

는 회전된 각도,

은 회전된 축이다.Where I is a unitary matrix, s and t are integers,

Lt; / RTI >

Is a rotated axis.

Preferably, the second communication device can decrypt the quantum signature pair using the rotation operator based on the rotation angle and the rotation axis shared with the first communication device.

Preferably, the second communication device further comprises: a beam splitter for receiving and dividing photons containing information on the signature qubit and the message qubit respectively decoded in the quantum signature pair; And first and second photodetectors for detecting photons that pass through or are reflected by the beam splitter.

Preferably, the second communication apparatus may determine whether or not the signature qubits constituting the decrypted quantum signature pair and the message qubits coincide with each other according to the detection result obtained from the first and second photodetectors.

As described above, according to the present invention, authentication, integrity, and non-repudiation of the quantum signature protocol can be guaranteed by using a pair of quantum signatures that can not be falsified, and a pair of quantum signatures is generated using polarizers, There is an effect that can be implemented.

1 is a block diagram of a quantum encryption system according to a preferred embodiment of the present invention.
2 is a view of a plurality of polarizing plates according to one embodiment.
3 is a flowchart illustrating a quantum cryptography method according to an embodiment.
FIG. 4 is a block diagram of a quantum cryptography system in the case where an eavesdropper is present according to an embodiment.
5 is an exemplary view for explaining the rotation direction and the rotation angle.
6 is an exemplary diagram for explaining the security of a quantum signature performed in the quantum cryptography system according to an embodiment.

BRIEF DESCRIPTION OF THE DRAWINGS The advantages and features of the present invention and the manner of achieving them will be more apparent from the following detailed description taken in conjunction with the accompanying drawings. The present invention may, however, be embodied in many different forms and should not be construed as being limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Is provided to fully convey the scope of the invention to those skilled in the art, and the invention is only defined by the scope of the claims. Like reference numerals refer to like elements throughout the specification. "And / or" include each and every combination of one or more of the mentioned items.

Although the first, second, etc. are used to describe various elements, components and / or sections, it is needless to say that these elements, components and / or sections are not limited by these terms. These terms are only used to distinguish one element, element or section from another element, element or section. Therefore, it goes without saying that the first element, the first element or the first section mentioned below may be the second element, the second element or the second section within the technical spirit of the present invention.

Also, in each step, the identification code (e.g., a, b, c, etc.) is used for convenience of explanation, and the identification code does not describe the order of each step, Unless the order is described, it may happen differently from the stated order. That is, each step may occur in the same order as described, may be performed substantially concurrently, or may be performed in reverse order.

The terminology used herein is for the purpose of illustrating embodiments and is not intended to be limiting of the present invention. In the present specification, the singular form includes plural forms unless otherwise specified in the specification. It is noted that the terms "comprises" and / or "comprising" used in the specification are intended to be inclusive in a manner similar to the components, steps, operations, and / Or additions.

Unless defined otherwise, all terms (including technical and scientific terms) used herein may be used in a sense commonly understood by one of ordinary skill in the art to which this invention belongs. Also, commonly used predefined terms are not ideally or excessively interpreted unless explicitly defined otherwise.

In the following description of the present invention, detailed description of known functions and configurations incorporated herein will be omitted when it may make the subject matter of the present invention rather unclear. The following terms are defined in consideration of the functions in the embodiments of the present invention, which may vary depending on the intention of the user, the intention or the custom of the operator. Therefore, the definition should be based on the contents throughout this specification.

1 is a block diagram of a quantum encryption system according to a preferred embodiment of the present invention.

1, the quantum cryptography system 100 includes a first communication device 110 and a second communication device 120, and the second communication device 110 and the second communication device 120 include a quantum channel Lt; / RTI >

The first communication device 110 is a transmitting device (so-called Alice) and the second communication device 120 is a receiving device (so-called Bob). Preferably, the first communication device 110 and the second communication device 120 are communication devices that perform quantum key distribution, each of which is easily implemented by a person skilled in the art to which the present invention pertains And the implementation method can be variously modified. In addition, various methods can be applied to the quantum key distribution method performed by the first and second communication devices 110 and 120, for example, the BB84 protocol can be applied. Each of the first and second communication devices 110 and 120 has all of the basic components for performing quantum key distribution, and the components for performing quantum key distribution and the process of performing quantum key distribution are various Assuming that the conventional technique can be applied, here, the constituent elements further provided for performing quantum encryption for the quantum signature according to the present invention, and the quantum encryption method for quantum signature performed through the constituent elements, .

The first communication device 110 includes a spontaneous parametric down-conversion (SPDC) 111, a BBO (Beta Barium Borate) crystal 112 included in the SPDC 111, a single polarizer 113, 114, and one polarizing plate 115.

The SPDC 111 is a device for generating two photons having the same quantum state. Preferably, in the SPDC 111, one photon pumped out by the laser passes through the BBO crystal 112 and becomes two photons, and two photons having the same quantum state can be output from the SPDC 111 have.

One of the polarizers 113 and 115 receives each of the two photons having the same quantum state generated from the SPDC 111 and converts the photon into a quantum message state.

만큼 회전되고, 제2 편광판(114-2)에 의하여 회전각이

만큼 회전되고, 제3 편광판(114-3)에 의하여 회전축이

만큼 회전될 수 있다. 여기에서, 큐빗, 즉, 양자 상태에 대한 정보는 광자에 포함되어 각 구성요소로 전달되는 것이나, 이하에서는 설명의 편의를 위하여, 큐빗이 각 구성요소들 간에 이동 및 전달되는 것으로 표현한다.The plurality of polarizing plates 114 are for encrypting a message qubit (Qbit) indicating any quantum state constituting a quantum message, and can preferably rotate the message qubit to a specific angle on a specific axis. More specifically, referring to FIG. 2, the plurality of polarizing plates 114 may include a first polarizing plate 114-1, a second polarizing plate 114-2, and a third polarizing plate 114-3. For example, when a message qubit is input to the plurality of polarizers 114, each of the message qubits passes through the first to third polarizers 114-1 to 114-3 and is transmitted to the first polarizer 114-1 Therefore,

, And the rotation angle of the second polarizer plate 114-2

And the third polarizing plate 114-3 rotates the rotation axis

. Here, the information on the qubit, that is, the quantum state is included in the photon and is transmitted to each component. Hereinafter, for convenience of explanation, the qubit is expressed as being moved and transferred between the respective components.

The second communication device 120 includes a plurality of polarizing plates 121, a beam splitter 122, a first photodetector 123, and a second photodetector 124. [ Here, the beam splitter 122, the first photodetector 123, and the second photodetector 124 convert the quantum signature pair transmitted from the first communication device 110 to a Hong-Ou- Mandel < / RTI > interferometer. In addition, the second communication device 120 can confirm by using a swap test how much the quantum states of any two photons transmitted from the first communication device 110 match, On a linear optic basis, the exchange inspection can be implemented using the Hong-Ou-Mandel interferometer.

이고, 제2 편광판(114-2)의 회전각의 회전값이

이고, 제3 편광판(114-3)의 회전축의 회전값이

인 경우, 제2 통신장치(120)의 복수의 편광판(121)의 제1 편광판의 회전축의 회전값은

이고, 제2 편광판의 회전각의 회전값은

이고, 제3 편광판의 회전축의 회전값은

이 될 수 있다.The plurality of polarizing plates 121 receives and quantizes the quantum signature pairs received from the first communication device 110 and is similar to the plurality of polarizing plates 114 of the first communication device 110, And a polarizing plate. More specifically, the plurality of polarizing plates 121 include first to third polarizing plates arranged as shown in FIG. 2, and the first and third polarizing plates of the plurality of polarizing plates 121 are disposed on the first communication device 110 And the rotation values of the rotation angles of the second polarizing plates of the plurality of polarizing plates 121 are set to be the same as the rotation values of the first and third polarizing plates 114-1 and 114-3 of the first communication device Can be set inversely to the rotation value of the rotation angle of the second polarizer plate 114-2 of the second polarizer plate 110. [ For example, if the rotation value of the rotation axis of the first polarizing plate 114-1 of the first communication device 110 is

, And the rotation value of the rotation angle of the second polarizer plate 114-2 is

, And the rotation value of the rotation axis of the third polarizing plate 114-3 is

, The rotation value of the rotation axis of the first polarizer of the plurality of polarizers 121 of the second communication device 120 is

, And the rotation value of the rotation angle of the second polarizer plate is

, And the rotation value of the rotation axis of the third polarizer plate is

.

The beam splitter 122 receives and divides the signature qubits and the message qubits decrypted through the plurality of polarizers 121 of the quantum signature pairs and preferably transmits the photons and the message qubits containing information on the decrypted signature qubits And then divides the received photon.

The first and second photodetectors 123 and 124 detect photons that pass through or are reflected by the beam splitter 122. The control unit of the second communication device 120 (not shown) It is possible to verify the quantum signature pair by checking whether the signature qubits and the message qubits decoded according to the information on the photons detected through the two photodetectors 123 and 124, respectively.

3 is a flowchart illustrating a quantum cryptography method according to an embodiment.

The process of quantum encryption for quantum signature through the components of the first communication device 110 and the second communication device 120 of FIG. 1 will be described in more detail with reference to FIG.

The first communication device 110 generates a quantum message (step S310). Here, the quantum message is composed of message qubits representing an arbitrary quantum state, information about a quantum message composed of message qubits is included in the photon, but it is expressed that the quantum message itself is transmitted for convenience of explanation do. More specifically, when a photon is generated in the SPDC 111 of the first communication device 110, the photon is split while passing through the BBO crystal 112 to pass through the two paths, and the polarizer 113 and 115, the photons are converted to a quantum message state. In addition, one of the two paths transmits the quantum message to the second communication apparatus 120, and the other path transmits the quantum message directly to the second communication apparatus 120 without encryption.

Referring to the process in which the quantum message is encrypted and transmitted to the second communication device 120, the plurality of polarizers 114 of the first communication device 110 encrypt the quantum message to generate a quantum pair (step S320). More specifically, each of the message qubits constituting the quantum message is rotated on the first axis through the first polarizing plate 114-1 constituting the plurality of polarizing plates 114, and transmitted through the second polarizing plate 114-2 And is rotated on the second axis through the third polarizing plate 114-3. That is, by the first to third polarizers 114-1 to 114-3, each message qubit constituting the quantum message is encrypted by the rotation operator as shown in [Equation 1].

[Formula 1]

로서 상기 제1 및 제3 편광판(114-1 및 114-3)에 의하여 회전된 축을 나타내는 3차원 벡터이고,

로서 3개의 파울리 연산자(Pauli operator)들로 구성되는 벡터이다. [식 1]의 회전연산자는 비 교환관계(non-commutation relation)를 가지고 있는 것으로서 파울리 연산자들의 선형 결합에 해당한다. 또한, 회전연산자

는 회전축과 회전각으로 큐빗을 블로흐 스피어(Bloch sphere) 표면상의 원하는 지점으로 옮길 수 있으며, 이는 회전연산자

가 2차원 유티타리

와 동일하다는 것을 의미한다. 회전연산자에 대한 보다 구체적인 설명은 이하에서 한다.Here, I is a unit matrix,? Is an angle rotated by the second polarizing plate 114-2,

Dimensional vector representing an axis rotated by the first and third polarizing plates 114-1 and 114-3,

Is a vector consisting of three Pauli operators. The rotation operator in [Equation 1] has a non-commutation relation and corresponds to the linear combination of the Pauly operators. In addition,

Can move the qubit to the desired point on the surface of the Bloch sphere with the rotation axis and the rotation angle,

A two-dimensional utilitarian

. ≪ / RTI > A more detailed description of the rotation operator will be given below.

Preferably, the message qubits encrypted with the rotation operator of Equation (1) are called signature qubits, and the message qubits and signature qubits constitute a pair of quantum signatures. That is, the quantum signature pair consists of a quantum message, i.e., a message qubit, and an encrypted quantum message, i.e., a signature qubit, transmitted to the second communication device 120 via each of the two paths, (2).

[Formula 2]

및

은 메시지 큐빗으로서, 보다 상세하게

은 메시지이고,

은 메시지에 대응하는 양자 상태를 나타내는 것이고,

은 서명 큐빗 이다. From here,

And

Quot; is a message < RTI ID = 0.0 >

Is a message,

Represents a quantum state corresponding to a message,

Is a signature qubit.

The first communication device 110 transmits the quantum signature pair to the second communication device 120 (step S330). Here, the message qubits and the signature qubits that constitute the pair of quantum signatures may be transmitted to the second communication device 120 through different quantum channels, respectively.

The second communication device 120 decrypts the quantum signature pair received from the first communication device 110 (step S340). Preferably, the second communication device 120 receives both the encrypted quantum message and the unencrypted quantum message from the first communication device 110 via different paths, and decrypts the encrypted quantum message Can be performed.

More specifically, the plurality of polarizers 121 of the second communication device 120 rotate the signature qubits constituting the pair of quantum signatures based on the rotation angle and the rotation axis which are shared with the first communication device 110, Decrypt the signature pair. Here, it is pre-shared between the first and second communication apparatuses 110 and 120 as to what rotation axis the message qubit in the first communication apparatus 110 is to be encrypted by using the rotation angle. Each of the signature qubits is rotated through a first 'polarizer plate constituting a plurality of polarizers 121, rotated at a specific angle' through a second 'polarizer plate, and transmitted through a third' polarizer plate to a second ' . That is, by the first to third polarizers, each signature qubit is decoded by a rotation operator as in [Equation 3].

[Formula 3]

The second communication device 120 verifies the decrypted quantum signature pair (step S350). Here, the decrypted quantum signature pair is composed of an unencrypted quantum message, i.e., a message qubit, transmitted from the first communication device 110, and a signature qubit, decrypted after being transmitted from the first communication device 110. Preferably, a Hong-Ou-Mandel interferometer may be used for the verification of the quantum signature pair.

More specifically, the beam splitter 122 of the second communication device 120 receives the decoded signature qubits and the message qubits constituting the decrypted quantum signature pair. That is, the photons containing the information about the decoded signature qubit and the message qubit are input to the beam splitter 122. Photons that enter the beam splitter 122 and then pass through or are reflected by the beam splitter 122 are detected through the first and second photodetectors 123 and 124 and the first and second photodetectors 123 and 124, It is determined whether or not the decoded signature qubits constituting the decrypted quantum signature pair and the message qubits coincide with each other.

Preferably, an electrical signal is generated when the signature qubit and the message qubit pass through the Hong-Ou-Mandel interferometer configured in the second communication device 120, reaching the first and second photodetectors 123 and 124. If the signature qubits do not coincide with the message qubits according to the degree of coincidence between the signature qubits and the message qubits, an electrical signal is generated simultaneously with the first and second optical detectors 123 and 124 to generate coincidence counts, If the qubit and the message qubit match, no electrical signal is generated at the first and second photodetectors 123 and 124 at the same time, and no coincidence count occurs. That is, if the signature qubits and the message qubits are not completely perpendicular to each other, the coincidence count is maximized, and the coincidence count can be reduced or minimized depending on the degree of coincidence. Here, if it is determined that there is a match, the quantum signature pair is verified to be secure.

According to the above-described quantum encryption method for quantum signature, a polling signature pair is generated by using a rotation operator in a non-exchange relationship, so that the first communication device 110 and the second communication device 120 communicate with each other, In the case of encrypting the quantum message and the quantum signature pair transmitted from the first communication apparatus 110, it can be determined that the presence of the eavesdropper, that is, the quantum signature pair is falsified in the process of verifying the quantum signature pair. Hereinafter, this will be described in more detail with reference to FIG.

FIG. 4 is a block diagram of a quantum cryptography system in the case where an eavesdropper is present according to an embodiment.

4, the third communication device 130 further includes an eavesdropper 130 between the first communication device 110 and the second communication device 120. The third communication device 130 includes a first communication device And a plurality of polarization plates 131 and 132 for encrypting the quantum signature pair transmitted from the apparatus 110. [ Here, since the first and second communication apparatuses 110 and 120 have been described above, they are omitted here. In addition, the quantum encryption method performed through the first and second communication devices 110 and 120 described above is also applied here, and therefore, will be briefly described.

In the process of generating a quantum signature pair expressed by [Equation 2] by the first communication device 110 and transmitting the quantum signature pair to the second communication device 120, the third communication device 130 transmits the quantum signature pair Receive input. Each of the plurality of polarizers 131 and 132 of the third communication device 130 can encrypt each of the signature qubits and the message qubits constituting the pair of quantum signatures with a rotation operator corresponding to [Equation 4]. Each of the plurality of polarizing plates 131 and 132 may be composed of first to third polarizing plates similar to the plurality of polarizing plates 114 of the first communication device 110, The method of encrypting by the rotation operator of [Equation 4] by the 3 '' polarizing plates is the same as described above.

[Formula 4]

는 회전된 각도,

은 회전된 축이고,

로서 3개의 파울리 연산자(Pauli operator)들로 구성되는 벡터이다.Here, I is a unitary matrix,

Lt; / RTI >

Is a rotated axis,

Is a vector consisting of three Pauli operators.

The quantum signature pair encrypted in the third communication device 130 by the [Equation 4] and then transmitted to the second communication device 120 can be expressed as [Equation 5].

[Formula 5]

The second communication apparatus 120 decodes the quantum signature pairs received from the third communication apparatus 130 through the plurality of polarizing plates 121 by using the rotation operator of [Equation 3] as shown in [Equation 6].

[Formula 6]

과 복호화된 서명 큐빗에 해당하는

가 일치하는지 여부가 확인된다. 여기에서는, 도청자의 제3 통신장치(130)에 의한 양자서명 쌍의 위조가 있었으므로, 메시지 큐빗과 복호화된 서명 큐빗이 일치하지 않는 것으로 확인되어야, 본 발명에 따른 양자 암호화 방법이 도청자에 대하여 안전한 것에 해당한다.The second communication device 120 then receives the beam quadrature corresponding to the message qubits in the beam splitter 122 and the quantum signature pair decoded through the first and second optical detectors 123 and 124

And a decrypted signature qubit

Are matched. Here, since the quantum signature pair has been falsified by the third communication device 130 of the eavesdropper, it is confirmed that the message qubit and the decoded signature qubit do not coincide with each other, so that the quantum encryption method according to the present invention It is safe.

과

이 서로 비교환의 관계에 있어야 하고, 비교환 관계를 만족하기 위해서는 [식 7]을 만족하는 경우로서,

,

, 또는

의 경우에 해당한다. 여기에서, s 및 t는 정수이다.That is, in order to be safe from forgery by the eavesdropper, for [Equation 1] and [Equation 4]

and

Exchange relationship, and in order to satisfy the non-exchange relationship, Equation (7) is satisfied,

,

, or

. Here, s and t are integers.

[Equation 7]

≠2t, 및

≠0의 조건을 만족하는 경우라면, 회전연산자는 비교환 관계를 갖게 되므로, 도청자에 의하여 임의의 회전연산자로 암호화되더라도 양자서명 쌍의 검증 단계에서 복호화된 서명 큐빗과 메시지 큐빗이 일치하지 않는 것으로 판단되어 도청자의 유무가 판단될 수 있다. Therefore, between the rotation operator used for encryption in the first communication device 110 and the rotation operator used for encryption in the third communication device 110 of the eavesdropper, θ ≠ 2s,

≠ 2t, and

≠ 0, the rotation operator has a non-exchange relationship. Therefore, even if it is encrypted with an arbitrary rotation operator by the eavesdropper, the signature qubit and the message qubit that are decrypted in the verification step of the quantum signature pair do not match The presence or absence of an eavesdropper can be judged.

Hereinafter, in order to prove that the quantum encryption method according to the present invention is safe for the eavesdropper, the degree of coincidence between the message qubits and the signature qubits is quantified to quantum reliability (fidelity).

과

의 일치함의 정도는 양자 신뢰도 F(A, B)로서, [식 8]과 같이 표현될 수 있다.In the quantum estimation theory,

and

Is the quantum reliability F (A, B) and can be expressed as [Equation 8].

[Equation 8]

If both qubits (A, B) are pure states, the quantum reliability can be expressed as Uhlmann's fidelity as in Eq. (9).

[Equation 9]

Referring to [Equation 9], it can be seen that the reliability has a range from 0 to 1, and if the two qubits are completely different, the reliability is 0, In addition, the mechanism of the Hong-Ou-Mandel interferometer that performs the verification of the coincidence of the two qubits described above, that is, the mechanism in which the coincidence count is changed according to the degree of coincidence of two qubits is completely in agreement with the fidelity, Using the fidelity, it can be accurately determined whether the encrypted quantum signature pair is secure according to the quantum encryption method according to the present invention.

의 회전축을 고정한 상태에서, 제3 통신장치(130)에서 이용할 수 있는 회전연산자

의 가능한 모든 경우를 고려하여 나타낸 것이다. 도 5에서,

은 회전축

을 z축으로, 회전각

을 π/2로 설정한 것이고,

은 회전축의 방위각(azimuthal angle)은 π/4로, 편각(polar angle)

는 모든 범위로 설정한 것이고, 회전각도 모든 범위로 설정한 것이다. 도 5와 같이 제1 통신장치(110)에서의 회전연산자에 의한 암호화와 제3 통신장치(110)에서의 회전연산자에 의한 암호화가 적용된 순수 상태인

과

의 일치하는 정도를 울만의 신뢰도로 계산한 결과는 도 6에 도시된 바와 같다. In one embodiment, referring to Figure 5,

In the state where the rotation axis of the third communication device 130 is fixed,

In all possible cases. 5,

And

To the z-axis, the rotation angle

Is set to? / 2,

The azimuthal angle of the rotation axis is? / 4, the polar angle is?

Is set to the whole range, and is set to the whole range of the rotation angle. As shown in Fig. 5, in the first communication device 110, the encryption by the rotation operator and the encryption by the rotation operator in the third communication device 110 are applied in a pure state

and

The results of the calculation of the degree of coincidence with the reliability of Woolman are as shown in FIG.

Referring to FIG. 6, (a) of FIG. 6 represents a mean reliability in a three-dimensional graph and corresponds to about 0.85, and since the average reliability does not correspond to 1, a quantum signature pair to which the quantum encryption method according to the present invention is applied It is safe to forgery by eavesdroppers.

의 회전축 편각

를 π로 고정한 경우의 결과이다. 도 6의 (b)에서 볼 수 있듯이, 회전연산자

의 회전각(Rotation Angle)

가 0 또는 2π일 때 평균 신뢰도가 거의 1에 가깝게 나오지만, 이때 회전연산자

는 단위행렬 I에 해당하는 것으로서, 도청자가 아무것도 하지 않은 경우, 즉, 도청자가 양자서명 쌍에 대하여 암호화를 하지 않은 경우에 해당한다. 또한, 회전연산자

의 회전각

가 π일 때, 평균 신뢰도는 대략 0.34에 해당하므로, 본 발명에 따른 양자서명을 위한 양자 암호화 방법에 의하면, 도청자에 의한 위조가 불가능 함을 보여준다.6 (b) is a result of verifying the FIG. 6 (a) by the experiment, and it is made in the same situation as the condition of FIG. 5. In order to verify the section of FIG. 6 (a)

Rotation axis deflection angle

Is fixed to?. As can be seen in Figure 6 (b)

Rotation Angle < RTI ID = 0.0 >

0 < / RTI > or 2 < RTI ID = 0.0 > pi, < / RTI >

Corresponds to the unit matrix I and corresponds to a case where the eavesdropper does not do anything, that is, the eavesdropper does not encrypt the pair of the signatures. In addition,

Rotation angle

The average reliability is approximately 0.34, so that the quantum encryption method for quantum signature according to the present invention shows that forgery by the eavesdropper is impossible.

Hereinafter, the process of acquiring the rotation operator in the non-exchange relationship will be described in detail.

로 표현될 수 있고, 여기에서, 일부 실수들 α와 θ, 및 실수 3차원 단위 벡터

에 대하여,

이다. Lemma 1. Let U be a 2X2 arbitrary single-qubit unit operator, U is

, Where some real numbers alpha and &thetas; and a real three-dimensional unit vector < RTI ID = 0.0 >

about,

to be.

로 표현되고, 여기에서, a와 b는 복소수 이다. 행렬 U의 행렬식은

이다. U는

로 표현될 수 있고, 여기에서, V는 단위 연산자이다.

이므로,

이다. V는 단위 연산자 이므로, 이것은 고유값

, 즉

과 함께 정규 직교 기저(orthnormal basis)를 따라 대각 행렬로 될 수 있다. 따라서,

이다. 2X2 임의의 연산자 V는 (1)과 같이 파울리 기저를 이용하여 특정한 방법으로 분해될 수 있다.Proof) If U is a 2X2 unit operator,

, Where a and b are complex numbers. The determinant of the matrix U is

to be. U is

, Where V is a unit operator.

Because of,

to be. Since V is a unit operator,

, In other words

And may be a diagonal matrix along a normal orthogonal basis. therefore,

to be. 2X2 An arbitrary operator V can be decomposed in a particular way using the Fourier basis as in (1).

- (1)

- (One)

는 복소수이고,

및

는 실수들이다.

이고

이므로, 연산자 V는 (2)와 같이 표현될 수 있다.From here,

Is a complex number,

And

Are mistakes.

ego

, The operator V can be expressed as (2).

- (2)

- (2)

및

는 3차원의 실수 단위 벡터이고,

는 파울리 행렬들의 3개의 성분 벡터를 나타낸다. 단위 연산자의

정의로부터, (3)의 결과가 획득될 수 있다. 수식(3)에 대한 상세한 계산 과정은 이하에서 기재한다.From here,

And

Is a three-dimensional real unit vector,

Denotes the three component vectors of the Pauligrees. Of unit operator

From the definition, the result of (3) can be obtained. The detailed calculation procedure for equation (3) is described below.

- (3)

- (3)

는 외적을 의미한다. 상기의 결과들로부터, (4) 및 (5)가 만족될 수 있다.From here,

Means external. From the above results, (4) and (5) can be satisfied.

- (4)

- (4)

- (5)

- (5)

이고, 따라서

이거나, 또는

에 해당한다. 만약,

이고

이면,

는

로 고정되고, 여기에서,

은 정수이나, 이러한 경우는 본 발명에서는 고려하지 않는다. 만약,

이고

이면,

이다. 이런 이유로, 단위 벡터

이고, 여기에서,

은 (6)과 같은 실수 3차원 단위 벡터에 해당한다.From equation (5)

And therefore

Or

. if,

ego

If so,

The

Lt; RTI ID = 0.0 >

But this case is not considered in the present invention. if,

ego

If so,

to be. For this reason,

Lt; / RTI >

Corresponds to a real three-dimensional unit vector such as (6).

- (6)

- (6)

로 표현되고, 여기에서,

은 임의의 회전연산자 이다.

은

로 나타내어 지고, 여기에서,

에 대하여,

는 파울리 연산자 이고

는 실수이다.

는 파울리 연산자 계수로 불린다. Using the lemma 1 above, any single qubit unit operator U

, ≪ / RTI >

Is an arbitrary rotation operator.

silver

, Where < RTI ID = 0.0 >

about,

Is the Pauli operator

Is a mistake.

Is called the Paulownian operator coefficient.

와

를 임의의 단위 연산자들이라고 하면, 보조정리 1을 이용하여, 실수들 α, β, θ, 및

, 및 실수 3차원 단위 벡터들

및

에 대하여

및

로 표현할 수 있다.

Wow

Let L be the arbitrary unit operator, and use lemma 1 to calculate the real numbers a,

, And real three-dimensional unit vectors

And

about

And

.

Generally, a unit group is a non-abelian group, but some of its elements are interchangeable or semi-interchangeable. The following propositions and theorems provide explicit conditions for anti-commutation and commute.

및

를 임의의 단위 연산자들이라고 하자. 만약

이면 쌍

는 교환의 단위 쌍으로 불린다. 쌍

는, 만약

이면, 반교환(anti-commutative)의 단위 쌍으로 불린다. 만약

이 교환의 단위 쌍 및 반교환의 단위 쌍이 모두 아니면,

는 비교환(non-commutative) 단위 쌍으로 불린다. Definition 1.

And

Let be the arbitrary unit operators. if

Pair

Is called the unit pair of exchange. pair

If

, It is called an anti-commutative unit pair. if

If the unit pair of this exchange and the unit pair of half exchange are not both,

Is called a non-commutative unit pair.

이면,

는 교환의 단위 쌍이다. Proposition 1. If,

If so,

Is the unit pair of exchange.

및

가 동일하거나, 또는 원점에 대하여 대칭적이면, 임의의 회전 연산자들

및

는 항상 서로 교환이 가능하다. Proof) If axes

And

Lt; / RTI > are the same, or symmetric about the origin, any rotation operators

And

Are always interchangeable.

이고

이면,

는 교환적 관계의 단위 쌍이다. Proposition 2. If even r, s

ego

If so,

Is a unit pair of exchangeable relations.

이 반교환 관계의 단위쌍이라고 가정하면, 아래의 (7)이 획득된다.

Assuming that this is a unit pair of half exchange, the following (7) is obtained.

- (7)

- (7)

Further, at k = x, y, z, the following expressions (8) and (9) are obtained.

- (8)

- (8)

- (9)

- (9)

이고,

이고

이면,

은 반교환 관계의 단위쌍이다. 상기 (8) 및 (9)에 의하여 증명되었다. Proposition 3 . If odd r, s

ego,

ego

If so,

Is the unit pair of half exchange. (8) and (9) above.

또는

이면, 반교환 관계의 단위 쌍은 없다. Proposition 4 . If r and s are integers

or

, There is no unit pair of half exchange relation.

이 존재한다고 가정한다. 상기 (8) 및 (9)에 의하여, k=x, y, z에 대해 아래의 (10) 및 (11)이 획득될 수 있다.Proof) Unit pair of half exchange

Are present. According to (8) and (9), the following (10) and (11) can be obtained for k = x, y, z.

- (10)

- (10)

- (11)

- (11)

이면, p, q가 정수일 때,

또는

이고, 일반성을 잃지 않고,

로 할 수 있다. 그러면,

또는 3차원 단위 벡터

를 가질 수 이다. 이것은 가정(assumption)과 3차원 단위 벡터

에 의한 모순이다.if,

, When p and q are integers,

or

, Without losing generality,

. then,

Or a three-dimensional unit vector

. This assumption and three-dimensional unit vector

.

또는

이면, 나머지 증명은 상기에서 설명된 바와 유사하다.if

or

, The remaining proofs are similar to those described above.

및

이면,

이고, 아래의 (12)가 획득될 수 있다.After all, if

And

If so,

(12) below can be obtained.

- (12)

- (12)

However, there is no solution satisfying (12).

및

가 임의의 단위 연산자들이라 하자. 만약 아래의 두 조건들(조건 1 및 조건 2) 중 적어도 하나에 해당하면,

및

는 교환적 관계의 단위쌍이다. Theorem 1 .

And

Are arbitrary unit operators. If at least one of the following two conditions (Condition 1 and Condition 2) is met,

And

Is a unit pair of exchangeable relations.

Condition 1 .

또는

Condition 2 . About odd r, s

or

이면, 명제1. 에 의하여

는 교환적 관계의 단위쌍이다. 만약 r 및 s가 홀수들일 때,

또는

이면, 명제 2. 에 의하여

는

와 교환적 관계이다.Proof) If

If so, proposition 1. By

Is a unit pair of exchangeable relations. If r and s are odd numbers,

or

, Then by proposition 2

The

And the exchange relationship.

이 존재한다고 가정하면,

이다.Unit pair of exchangeable relations

Assuming that there exists,

to be.

이고

이다. 만약, r 및 s가 홀수일 때

또는

이면,

는

와 교환적 관계이다. r 및 s가 홀수일 때

및

가 증명되었다. 상기 식 (7)에 의하여 아래의 (13)이 획득된다.From here,

ego

to be. If r and s are odd

or

If so,

The

And the exchange relationship. When r and s are odd

And

. The following equation (13) is obtained by the above equation (7).

- (13)

- (13)

The simultaneous equations in equation (8) can be solved as follows (14) and (15) by expressing them in a spherical coordinate system.

- (14)

- (14)

- (15)

- (15)

이고

이다. 그러면, (16)과 같다.From here,

ego

to be. Then, it is the same as (16).

- (16)

- (16)

및

가 임의의 단위 연산자들이라고 한다. 다음의 4개의 조건들(조건 1 내지 4)는

및

를 비교환적 관계의 단위쌍

으로 만든다. Results (Corollary) 1.

And

Are arbitrary unit operators. The following four conditions (conditions 1 to 4)

And

The unit pair of the comparative transit relation

.

,

, 및

Condition 1. For odd r and non-integer s,

,

, And

,

, 및

Condition 2. For non-constant r and odd s,

,

, And

,

, 및

Condition 3. For non-constant r and s,

,

, And

,

,

, 및

Condition 4. For odd r and s,

,

,

, And

는 몇몇 경우들을 제외하고는, 어떠한 임의의 단위 연산자

와도 비교환적이다. 결과 1을 만족하지 않는 대표적인 예는 다음과 같다. 첫째, 만약 임의의 회전 연산자

의 회전축

이 임의의 회전 연산자

의 회전축

와 동일하거나, 또는 축들

및

이 원점에 대하여 대칭적인 경우에, 임의의 연산자

는 임의의 연산자

와 교환이 가능하다. 둘째, 만약

,

이면,

및

이다. 따라서, 임의의 연산자

는 임의의 연산자

와 교환적 관계에 있다. 셋째,

,

, 및

이면,

는

와 반교환적 관계에 있다. 결과 1로부터 도출된 사실을 이용하여 교환검사(swap test)를 이용하는 양자서명 프로토콜을 기본으로 하는 양자 암호 방식이 안전하다는 것은 보장된다. According to result 1, any unit operator

≪ RTI ID = 0.0 > except for some cases,

It is also a comparative transit. A representative example that does not satisfy the result 1 is as follows. First, if an arbitrary rotation operator

The rotation axis

This arbitrary rotation operator

The rotation axis

Or < / RTI >

And

In the case of symmetry with respect to this origin,

Is an arbitrary operator

Can be exchanged with. Second, if

,

If so,

And

to be. Thus, any operator

Is an arbitrary operator

And is in an exchangeable relationship. third,

,

, And

If so,

The

And is in a semi-interrelated relationship. Using the fact derived from the result 1, it is guaranteed that the quantum cryptography based on the quantum signature protocol using the swap test is safe.

를 임의의 큐빗

에 적용하기 위하여, 이전의 회전 각도

와 실수 3차원 단위 벡터

를 공유해야 한다. 이 정보를 모르는 도청자로부터, 암호화된 큐빗은 (17)과 같이 최대한으로 뒤섞인 상태에 있다. 수식(17)에 대한 상세한 계산과정은 이하에서 기재한다.In quantum communication, users can use any rotation operator

A random qubit

The previous rotation angle < RTI ID = 0.0 >

And real three-dimensional unit vector

. From an eavesdropper who does not know this information, the encrypted qubit is in the state of being mixed up to the maximum as in (17). The detailed calculation procedure for Equation (17) will be described below.

- (17)

- (17)

은 블로흐 스피어에서 연속 균등 분포(continuous uniform distribution)의 확률밀도함수 이고,

는 연속 균등 분포

의 확률밀도함수와 함께 순수 상태

의 총체이다. 만약 통신 구성원들이 임의의 회전 연산자들

를 임의의 큐빗들

의 복합 시스템에 적용한다면, 도청자로부터 암호화된 큐빗

의 복합 시스템은 최대한으로 뒤섞인 상태

이다. 따라서, 임의의 회전 연산자를 이용하는 본 발명에 따른 양자 암호화 방법은 절대적으로 안전하다.

Is the probability density function of the continuous uniform distribution in the Bloch sphere,

Lt; RTI ID = 0.0 >

With a probability density function of < RTI ID = 0.0 >

. If the communication members have any rotation operators

Lt; RTI ID = 0.0 >

, The encrypted qubit from the eavesdropper

Of the complex system is maximally scrambled

to be. Thus, the quantum encryption method according to the present invention using any rotation operator is absolutely secure.

에 대한 정보를 포함해야 하고, 결과 1. 을 만족시키는

및

일 때, 실수 3차원 단위 벡터

는 양자서명 쌍을 암호화 하기 위하여 임의의 단위 연산자

에 사용된다. 여기에서, 서명키는 메시지 큐빗을 서명 큐빗으로 변환하는데 이용되는 회전연산자의 변수를 결정하기 위한 회전각 및 회전축에 대한 정보를 포함하는 것으로서, 서명키는 통신 구성원들 간에 미리 공유될 수 있다. 이에 더하여, 서명자, 수신자, 및 검증자는 블로흐 스피어 상의 회전각도와 회전 축들을 구별하는 것이 불가능하기 때문에,

의 범위 및

의 정의역(domain)에 대하여 동의해야 한다. 만약 통신 구성원들이

회전 각도들 중 하나를 사용하고

회전 축들 중 하나를 사용하면, 연역적으로 그들은

비트 키를 공유해 왔던 것이 된다. 즉, 통신 구성원들이 사용할 수 있는 회전각도와 회전축은 무한하나, 실제로는 회전각도와 회전축의 사용범위를 미리 설정하여 사용하므로, 예를 들어, 통신 구성원들은 0~360도의 회전각 범위에서 {0, 10, 20, ..., 350}도 중에서 하나를 선택하여 사용하는 것으로 미리 약속하는 것이다. 그러면, 도청자의 위조 확률

는

이고, 여기에서, m 과 t 중 적어도 하나는 0보다 커야 한다. 만약 회전 각도들

및 회전 축들

의 전체 범위 중 하나가 사용되면, 도청자가

의 정보를 획득하는 확률

는 매우 낮고, 특히

이다. 그러나, 이 경우에는 무한대 사이즈의 키가 큐빗을 암호화하기 위하여 필요하다. 반대로, 만약

회전 각도들 및

회전 축들(여기에서, m=1, t=0) 또는

회전 각도 및

회전 축들(여기에서 m=0, t=1)이 사용되면, 공유된 키의 사이즈는

로 줄어들고, 여기에서 m+t=1이다. 그러나, 위조 확률

는 1/2로 증가한다. 따라서, 도청자가 큐빗을 위조할 확률의 범위는

이다. 예를 들어, 만약

의 극한값이 10°로 나누어지고 3개의 회전 축들

중 하나가 사용되면, 약

비트들이

와

를 표현하기 위하여 필요하다. 도청자가 이러한 사실을 알고 있는 것을 가정하면, 도청자가 정확하게

및

의 값을 추측할 수 있는 확률은

이다.The procedure for executing this method in the password for the quantum signature is as follows. The signer used hereinafter corresponds to the first communication device 110, the receiver and the verifier correspond to the second communication device 120, and the eavesdropper corresponds to the third communication device 130. [ In one embodiment, the recipient and the verifier may be separate, and one entity may be the recipient and the verifier. Signer's signature key is the angle of rotation

And should satisfy the result 1. < RTI ID = 0.0 >

And

, The real three-dimensional unit vector

Lt; RTI ID = 0.0 > unitary < / RTI > operator

. Here, the signature key includes information about a rotation angle and a rotation axis for determining a variable of a rotation operator used to convert a message qubit into a signature qubit, and the signature key can be pre-shared among communication members. In addition, since the signer, receiver, and verifier are unable to distinguish between rotation angles and rotation axes on the Bloch sphere,

And

You must agree to the domain of. If communication members

Using one of the rotation angles

Using one of the rotation axes,

Bit key. In other words, the rotation angle and the rotation axis that can be used by the communication members are infinite but actually, the rotation angle and the use range of the rotation axis are set in advance. For example, 10, 20, ..., 350} degrees. Then, the eavesdropper's forged probability

The

, Where at least one of m and t must be greater than zero. If the rotation angles

And rotation axes

Is used, the eavesdropper

The probability of obtaining the information of

Is very low, especially

to be. However, in this case an infinite size key is needed to encrypt the qubit. Conversely, if

The rotation angles and

Rotation axes (where m = 1, t = 0) or

Rotation angle and

If the rotation axes (where m = 0, t = 1) are used, the size of the shared key is

, Where m + t = 1. However,

Increases to 1/2. Thus, the range of probability that an eavesdropper fakes a qubit is

to be. For example, if

Is divided by 10 degrees and the three rotation axes

If one of these is used,

The bits

Wow

. Assuming the eavesdropper knows this, the eavesdropper

And

The probability of guessing the value of

to be.

Detailed calculation process for equation (3)

The unit operator V can be expressed as:

및

는 3차원의 실수 단위 벡터들이고,

는 파울리 행렬(Pauli matrices)의 3개의 성분 벡터

를 나타낸다. 단위 연산자자의

정의로부터, 다음과 같은 결과들이 획득된다.From here,

And

Are real-valued three-dimensional unit vectors,

Are the three component vectors of the Pauli matrices

. Unit operator

From the definition, the following results are obtained.

는 외적을 의미한다.From here,

Means external.

The detailed calculation process for equation (17)

를 임의의 큐빗

에 적용하기 위하여, 이전의 회전 각도

와 실수 3차원 단위 벡터

를 공유해야 한다.In quantum communication, users can use any rotation operator

A random qubit

The previous rotation angle < RTI ID = 0.0 >

And real three-dimensional unit vector

.

이다. 이 정보를 모르는 도청자로부터, 암호화된 큐빗은 최대한으로 뒤섞인 상태에 있다. From here,

to be. From an eavesdropper who does not know this information, the encrypted qubits are in a state of scrambling as much as possible.

은 연속변수(continuous variable)이고, 여기에서,

이다.Rotation angles

Is a continuous variable,

to be.

는 블로흐 스피어에 대한 연속균등분포(continuous uniform distribution)의 확률밀도함수(probability density function)이고, 여기에서,

및

는 연속균등분포

의 확률밀도함수와 함께 순수 상태들

의 총체이다.

Is the probability density function of the continuous uniform distribution over the Bloch sphere,

And

Lt; RTI ID = 0.0 >

The probability density functions of the pure states

.

Although the preferred embodiments of the quantum cryptography system according to the present invention have been described above, the present invention is not limited thereto, but can be modified and embodied in various ways within the scope of the claims, the detailed description of the invention and the accompanying drawings This also belongs to the present invention.

100: Quantum cryptography system
110: first communication device 120: second communication device
111: Source 112: BBO crystal
113 and 115: 114: a plurality of polarizers
121: plural polarizing plates 122: beam splitter
123: first photodetector 124: second photodetector
114-1: first flat panel plate 114-2: second polarizer plate
114-3: Third polarizer plate
130: Communication devices 131 and 132 of an eavesdropper: a plurality of polarizers

Claims (7)

Generating a quantum message constituted by a message qubit indicating an arbitrary quantum state, encrypting the quantum message with a plurality of polarizers whose rotation angles are θ ≠ 2s (s is an integer) so that the message qubit has a non-exchange relationship with an arbitrary rotation operator, A first communication device for generating a signature qubit, and generating a quantum signature pair comprising the message qubit and the signature qubit; And
And a second communication device that receives the quantum signature pair from the first communication device and decrypts the quantum signature pair to verify the quantum signature pair.
The communication apparatus according to claim 1,
A first polarizer rotating the message qubit in a first axis;
A second polarizer for rotating the message qubit through the first polarizer at a specific angle; And
And a third polarizer for rotating the message qubit passing through the second polarizer on a second axis.
3. The method of claim 2,
Wherein the message qubits are encrypted by a rotation operator such that the sign qubits are generated by the first through third polarizers.
[Equation]

Here, I is a unit matrix,? Is an angle rotated by the second polarizer plate,

Dimensional vector representing an axis rotated by the first and third polarizing plates,

Is a vector composed of three Pauly operators.
The method of claim 3,
Between the first communication device and the second communication device, when the quantum signature pair transmitted from the first communication device is encrypted by an eavesdropper with a rotation operator such as the following equation, θ ≠ 2s,

≠ 2t, and

0 < / RTI >
[Equation]

Where I is a unitary matrix, s and t are integers,

Lt; / RTI >

Is a rotated axis.
The communication apparatus according to claim 3,
And decrypts the quantum signature pair using the rotation operator based on a rotation angle and a rotation axis shared with the first communication apparatus.
6. The communication device according to claim 5,
A beam splitter for receiving and dividing photons containing information about the signature qubit and the message qubit respectively decoded in the quantum signature pair; And
And a first and a second photodetector for detecting photons passing through or reflected from the beam splitter.
7. The communication system according to claim 6,
And judges whether or not the signature qubits constituting the decrypted quantum signature pair and the message qubits coincide with each other according to the detection result obtained from the first and second photodetectors.

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