TWI613899B - A method of quantum encryption and decryption - Google Patents

Abstract

The invention relates to a quantum encryption and decryption method, wherein the encryption method first generates a random number, converts into a quantum random number by a conversion function, and then obtains the first ciphertext by the first positive operator according to the long key encryption. And encrypting the first positive operator and the second positive operator according to the shared key to obtain the second ciphertext, and combining the first ciphertext and the second ciphertext to obtain the main The ciphertext; the decryption method is the reverse operation, and the original message P can be obtained by using the compression function, the positive operator and the measurement function to operate the ciphertext. In this way, it can become the basis of a communication protocol and effectively encrypt and protect the message.

Description

A method of quantum encryption and decryption

The invention relates to a quantum cryptography technology, in particular to a quantum encryption and decryption method, which can be used as a communication protocol by encrypting and decrypting a message by a compression function and a unitary operation. The basis is to eliminate the threat of quantum computers; and can further provide quantum authentication encryption technology in combination with existing authentication methods.

According to the encryption technology, it is widely used in the exchange of information. In particular, there are many insecure communication channels in the network. It is also necessary to transmit private or confidential information through encryption technology to make unrelated people or unscheduled transmission. The target cannot read the content in the message. The general encryption technology is divided into two types: "symmetric key encryption technology" and "asymmetric key encryption technology"; symmetric key encryption technology refers to the operation of encrypting and decrypting through a complicated calculation process using a symmetric key, usually Confusion or diffusion is used as the basis for calculation, such as Data Encryption Standard (DES) and Advanced Encryption Standard (AES); asymmetric key encryption On the contrary, the keys used for encryption and decryption are different. They are asymmetric keys. They are usually used as the basis of encryption technology by factorization or discrete logarithm. For example, RSA encryption algorithm or ElGamal encryption is derived. Algorithms, etc.

Since encryption technology has been significantly helpful for secret communication, it has been widely It is used in various communication pipes and networks. However, the rapid development of quantum computers and quantum computing in recent years has made the mathematical process of encryption more susceptible to cracking. The information to be protected will no longer be secure and hidden. Therefore, quantum encryption technology has been proposed. Based on quantum mechanics, in order to encrypt, many encryption methods have been proposed, such as Quantum Key Distribution Protocols, Quantum Direct Communication Protocols, and Quantum. Quantum Dialogue Protocols and Quantum Signature Protocols are collectively referred to as Quantum Encryption Protocols. They also derive authentication encryption technology. Although it can enhance the security of information again, encryption technology needs to be traditional. The communication pipeline is open to public discussion, so there will still be quite a lot of problems. In the rapid development of quantum computers, it has the lack of attack and crack.

The Republic of China Patent Bulletin No. TW I487308 B "Quantum Communication Method" discloses a method of message encryption and source authentication function, which shares the base key and the numerical key by the sender and the receiver, and publicly agrees on the merge rule and the hash. The function enables the transmitter and the receiver to transmit only one quantum, which can combine the message encryption and authentication functions in the communication process, and solves the problem that the previous communication data cannot have both encryption and authentication functions. However, although the current quantum cryptography technology is more convenient and efficient, it has to transmit information through traditional communication channels, and it is still insufficient in security. Therefore, research and development of a new quantum cryptography technology can make encrypted messages more capable. Resisting the attacks of quantum computers and improving the security and privacy of information has become the direction that inventors have studied.

Nowadays, the inventor is that in view of the above-mentioned existing quantum cryptography technology, there are still many defects in the actual implementation, so it is a tireless spirit, and borrowed It is improved by its extensive professional knowledge and years of practical experience, and the present invention has been developed based on this.

The main object of the present invention is to provide a quantum encryption and decryption method, which uses a compression function, a positive operator and a measurement function to encrypt and decrypt a message, and can be used as a new quantum encryption protocol in communication technology. The keys used for encryption and decryption can be reused, more efficient in message encryption, and less burdensome on communication; and have Indistinguishable and Unconditionally Security, which are attacks on quantum computers. Better resistance.

In order to achieve the above-mentioned implementation, the present invention provides a quantum encryption method, and the encryption step includes the following steps: Step 1: generate a random number r, and substitute a conversion function to convert the random number r into a quantum random number |r>, and then The first positive operator U ^{1 is} encrypted according to a long-term secret key K ₀ to obtain a first ciphertext | C ₁ 〉; Step 2: using a compression function (Compression function) to enter a random number r After the operation, a shared key K _{1 is obtained} , and then the conversion function converts the message P into a quantum message |P>; and step 3: the first positive operator U ¹ and a second positive operation Sub-U ² , encrypting the quantum message |P> according to the shared key K ₁ to obtain a second ciphertext |C ₂ 〉, combining the first ciphertext|C ₁ 〉 and the second ciphertext|C ₂ 〉 That is, the main ciphertext|C> is obtained.

In one embodiment of the invention, the transfer function is a Z-substrate qubit represented as Gen _z (.), where Z = {|0>, |1>}.

Another object of the present invention is to provide a quantum decryption method, the decrypting step comprising: Step 1: measuring and decrypting a first ciphertext|C ₁ 〉 according to a long key K ₀ according to a measurement function. Obtaining a random number r; Step 2: using a compression function to substitute a random number r operation to obtain a shared key K ₁ ; and step 3: using a first positive operator U ¹ and a second positive operator U ² decrypts a second ciphertext|C ₂ 〉 according to the shared key K ₁ to obtain a quantum message |P>, and after calculation by the measurement function, an unencrypted message P can be obtained.

In an embodiment of the present invention, the measurement function is expressed as M(.), and is measured on a Z-substrate or an X-substrate according to the value of the long key K ₀ or the value of the shared key K ₁ , where Z ={|0>,|1>}, X={|+〉,|-〉}.

{I,H}，其係依據長金鑰K₀或共享金鑰K₁的值，選擇使用I或H，且其中I=|0〉〈0|+|1〉〈1|，

In an embodiment of the present invention, the first normal operator U ¹ belongs to one of I or H, and is represented as U ¹

{I,H}, which is based on the value of the long key K ₀ or the shared key K ₁ , and optionally uses I or H, and wherein I=|0><0|+|1><1|,

{I,iσ _y }，其係依據長金鑰K₀或共享金鑰K₁的值，選擇使用I或i σ _y，且其中I=|0〉〈0|+|1〉〈1|，iσ _y =|0〉〈1|-|1〉〈0|。 In an embodiment of the present invention, the second positive operator U ² belongs to one of I or i σ _y and is represented as U ^{2 .}

{I, iσ _y }, which is based on the value of the long key K ₀ or the shared key K ₁ , and optionally uses I or i σ _y , where I=|0><0|+|1><1|, Iσ _y =|0><1|-|1><0|.

In an embodiment of the invention, the compression function is expressed as f(.), which is a compression number r.

(ES1)‧‧‧Step 1

(ES2)‧‧‧Step 2

(ES3)‧‧‧Step three

(DS1) ‧ ‧ Step 1

(DS2)‧‧‧Step 2

(DS3)‧‧‧Step three

First figure: an encryption diagram of a preferred embodiment of the present invention

Second figure: a schematic diagram of decryption of a preferred embodiment of the present invention

The object of the present invention and its structural and functional advantages will be explained in conjunction with the specific embodiments according to the structure shown in the following drawings, so that the reviewing committee can have a more in-depth and specific understanding of the present invention.

Referring to the first figure, a quantum encryption method of the present invention, the encrypting step includes the step 1 (ES1): generating a random number r, and substituting a conversion function, which is a Z-based quantum bit, denoted as Gen _z after r>, then U by a first unitary operator ¹ in accordance with a long key K ₀ encrypted |, where Z = (.) {| 0 >, | 1>}, that the random number r is converted into a quantum random number Obtain a first ciphertext|C ₁ 〉; Step 2 (ES2): substitute a random function f(.) into the random number r, obtain a shared key K ₁ after the compression operation, and then convert the message P by a conversion function. Forming a quantum message|P>; and step three (ES3): encrypting the first positive operator U ¹ and a second positive operator U ² according to the shared key K ₁ to obtain the quantum message |P> A second ciphertext|C ₂ 〉, the first ciphertext|C ₁ 〉 and the second ciphertext|C ₂ 〉 are combined to obtain the main ciphertext|C>.

Referring to the second figure, a quantum decryption method of the present invention, the decrypting step includes the step 1 (DS1): a measurement function M(.) is based on a long key K ₀ and is aligned with a Z base or an X base. The first ciphertext|C ₁ 〉 is measured and decrypted to obtain a random number r, where Z={|0>, |1>}, X={|+>, |->}; Step 2 (DS2) ): using a compression function f(.) to substitute the random number r, the compression operation to obtain a shared key K ₁ ; and the third step (DS3): using a first positive operator U ¹ and a second positive operation Sub-U ² decrypts a second ciphertext|C ₂ 〉 according to the shared key K ₁ to obtain a quantum message |P>, and after calculating by the measurement function, an unencrypted message P can be obtained; the quantum decryption method It is the reverse operation of the quantum encryption method.

{I,H}，其係依據長金鑰K₀或共享金鑰K₁的值，選擇使用I或H，且其中I=|0〉〈0|+|1〉〈1|，

；第二么正運算子U²係屬於I或i σ _y其中之一，表示為U²

{I,iσ _y }，其係依據長金鑰K₀或共享金鑰K₁的值，選擇使用I或i σ _y，且其中I=|0〉〈0|+|1〉〈1|，iσ _y =|0〉〈1|-|1〉〈0|。 Wherein, the first positive operator U ¹ of the encryption method and the decryption method belongs to one of I or H, and is expressed as U ¹

{I,H}, which is based on the value of the long key K ₀ or the shared key K ₁ , and optionally uses I or H, and wherein I=|0><0|+|1><1|,

The second positive operator U ² is one of I or i σ _y , expressed as U ²

{I, iσ _y }, which is based on the value of the long key K ₀ or the shared key K ₁ , and optionally uses I or i σ _y , where I=|0><0|+|1><1|, Iσ _y =|0><1|-|1><0|.

In addition, the scope of the invention may be further exemplified by the following specific examples, which are not intended to limit the scope of the invention.

Please continue to refer to the first figure and the second figure. The quantum encryption and decryption method of the present invention can also be called probabilistic Quantum (Probabilistic Quantum). Encryption) encrypts a random number r and the desired message by probability quantum, and then merges it into the main ciphertext, which can improve the difficulty of message cracking. In quantum mechanics, Dirac notation is often used to represent the existence of state vectors of quantum states. Dirac symbols are further divided into ket "|>" and "bra" (<|". For the corresponding conjugate transpose, it represents the state vector in Hilbert Space, which can be represented as a matrix, and the quantum state in quantum mechanics has uncertainty (uncertainty Therefore, the present invention develops a probabilistic quantum cryptography technique by using a mixed state of a plurality of quantum states, so that the attacker cannot simply calculate an accurate value to crack the encrypted message.

Quantum encryption method:

First, the message that is transmitted between the transmitting end and the receiving end is defined as P, which is Plain-text. When the transmitting end needs to encrypt the transmitted message P, it must first take the number r, and the information P can be indistinguishable. The characteristic, and the random number r is substituted by the transfer function Gen _z (.). After the Gen _z (r) conversion, the random number r becomes a quantum random number, expressed as |r>, where the transfer function Gen _z (. ) represents a Z-substrate qubit transfer function that converts general information into a state vector of quantum states, and the Z-system can be |0> or |1>;|r> is a matrix, so the positive operation The unitary operation is used to calculate the matrix. The first positive operator U ¹ encrypts the quantum random number |r> according to the long key K ₀ , and becomes the first ciphertext|C ₁ 〉, the long key K ₀ is a key shared in advance by the transmitting end and the receiving end, and according to this, the encryption of the random number r is completed.

Furthermore, the encryption of the message P is performed, and the compression function f(.) is substituted into the random number r, and the f(r) compression operation is performed to obtain a shared key K ₁ , and the shared key K ₁ generated by the compression operation can be improved. The security of the message to the extent of unconditional security, and then the message P is converted into a quantum message |P> by the conversion function Gen _z (.), the first positive operator U ¹ and the second positive operator U ² , according to the sharing The key K ₁ encrypts the quantum message |P> to obtain the second ciphertext|C ₂ 〉, and finally the first ciphertext|C ₁ 〉 and the second ciphertext|C ₂ 〉 are combined to obtain the main ciphertext| C>, after the encryption of the message P is completed, the main ciphertext|C> is transmitted to the receiving end.

Quantum decryption method:

(|C₁〉)解密後，能獲得亂數r，其中Z={|0〉,|1〉}，X={|+〉,|-〉}，而使用Z基底或X基底的時機係取決於長金鑰K₀之數值，當K₀=0時，使用Z基底，K₀=1時，則使用X基底作計算；與加密方法相同，接收端亦需要利用壓縮函數f(．)代入亂數r，藉著f(r)壓縮運算後，得到共享金鑰K₁，再將第一么正運算子U¹以及第二么正運算子U²依據共享金鑰K₁對第二密文|C₂〉解密，能得到量子訊息|P〉；最後再將量子訊息|P〉代入量測函數M(．)，以M₀(|P〉)量測計算後，則可以得到原始之訊息P，接收端能夠讀取到正確之訊息。此量子解密方法使用與加密方法同樣的長金鑰K₀以及共享金鑰K₁，並利用反向操作的方式進行解密。 When the receiving end wants to read the content of the main ciphertext|C>, it is necessary to take a measurement function M(.) according to the long key K ₀ and perform the first ciphertext|C ₁ 〉 on the Z base or the X base. Measurement and decryption,

(|C ₁ 〉) After decryption, the random number r can be obtained, where Z={|0>, |1>}, X={|+〉, |->}, and the timing of the Z-base or X-base is used. Depending on the value of the long key K ₀ , when K ₀ =0, the Z base is used, and when K ₀ =1, the X base is used for calculation; as with the encryption method, the receiving end also needs to utilize the compression function f(.) Substituting the random number r, after the f(r) compression operation, the shared key K _{1 is obtained} , and then the first positive operator U ¹ and the second positive operator U ^{2 are} paired according to the shared key K ₁ to the second Ciphertext|C ₂ 〉Decryption, can get the quantum message|P>; finally, the quantum message|P> is substituted into the measurement function M(.), and the measurement is calculated by M ₀ (|P>), then the original can be obtained. Message P, the receiver can read the correct message. This quantum decryption method uses the same long key K ₀ and shared key K ₁ as the encryption method, and decrypts by means of reverse operation.

{I,H}，第二么正運算子U²

{I,iσ _y }，其係根據長金鑰K₀或共享金鑰K₁的值作選擇。因此，以上術之量子加密方法為例，第一么正運算子U¹根據長金鑰K₀對量子亂數|r〉進行加密成第一密文|C₁〉，其過程之關係可如表一所示。 Among them, the first positive operator U ¹

{I,H}, the second positive operator U ²

{I, iσ _y }, which is selected based on the value of the long key K ₀ or the shared key K ₁ . Therefore, the quantum encryption method of the above is taken as an example. The first positive operator U ¹ encrypts the quantum random number |r> into the first ciphertext|C ₁ 〉 according to the long key K ₀ , and the relationship between the processes is as follows. Table 1 shows.

It can be seen from Table 1 that when the long key K ₀ is 0, the first positive operator U ¹ takes I, and the equation of the first ciphertext|C ₁ 〉 operation is expressed as |C ₁ 〉=I. |r>; When the long key K ₀ is 1, the first positive operator U ¹ takes H, and the equation of the first ciphertext|C ₁ 〉 operation is expressed as |C ₁ 〉=H. |r〉.

Furthermore, the first positive operator U ¹ and the second positive operator U ² each encrypt the quantum message |P> according to the shared key K ₁ to obtain the second ciphertext |C ₂ 〉, the process of which The relationship can be as shown in Table 2.

It can be seen from Table 2 that when the shared key K _{1 is} applied to the first positive operator U ¹ and the second positive operator U ² , there are four combinations. When K _{1 is} 0, the first positive operator U ¹ and the second positive operator U ² take I, and the equation of the second ciphertext|C ₂ 〉 operation is expressed as |C ₂ 〉=I. |P>; When K ₁ is 1 and 0 respectively, the first positive operator U ¹ and the second positive operator U ² take H and I respectively, and the equation of the second ciphertext|C ₂ 〉 operation is expressed as |C ₂ 〉=H. |P>; When K ₁ is 0 and ₁ , respectively, the first positive operator U ¹ and the second positive operator U ² take I and i σ _y , respectively, and the second ciphertext | C ₂ 〉 equation Expressed as |C ₂ 〉=i σ _y . |P>; When K _{1 is} 1, the first positive operator U ¹ and the second positive operator U ² take H and i σ _{y respectively} , and the second ciphertext|C ₂ 〉 equation is expressed Is |C ₂ 〉=H. i σ _y . |P〉.

Therefore, the present invention provides a new quantum encryption and decryption method, which enables the message P to be transmitted by the transmitting end and the receiving end to achieve the purpose of encryption, and is received. The terminal can also perform the decryption action to smoothly read the message P, and can effectively resist the attack of the quantum computer during the transmission process, thereby increasing the confidentiality and security of the message transmission.

It can be seen from the above description that the present invention has the following advantages compared with the prior art:

1. The present invention provides a quantum encryption and decryption method, which can protect a traditional message or a quantum message to be exchanged between a transmitting end and a receiving end by a calculation process such as a compression function, a positive operation operator, and a measurement function. Even with traditional communication pipeline transmission, it can have good security and privacy, and the invention can be used as the basis of quantum communication protocol, which is of great help to the development of quantum communication in the future.

2. The quantum encryption and decryption method of the present invention makes the transmitted ciphertext indistinguishable by the mismatching of the random number and the message to be transmitted, and cannot be correctly calculated when other quantum computers try to steal the message in the ciphertext. The required value is measured, and when the long key and the shared key have not been leaked, it can be used again at the next message transmission, making the message encryption and decryption more efficient, and the communication burden is lower.

3. A quantum encryption and decryption method of the present invention can generate a shared key by compressing a function, thereby improving the security of the message to an unconditional security level and reducing the possibility of message leakage, compared with the previously used quantum encryption technology. The quantum cryptography of the present invention is more difficult to crack.

4. The quantum encryption and decryption method of the invention can not only perform quantum encryption and decryption, but also can combine the existing authentication methods to further provide quantum authentication encryption technology, which has the functions of encryption and authentication, and is more effective in use. Convenience.

In summary, a quantum encryption and decryption method of the present invention can achieve the intended use efficiency by the above disclosed embodiments, and the present invention It has not been disclosed before the application, and Cheng has fully complied with the requirements and requirements of the Patent Law.爰Issuing an application for a patent for invention in accordance with the law, and asking for a review, and granting a patent, is truly sensible.

The illustrations and descriptions of the present invention are merely preferred embodiments of the present invention, and are not intended to limit the scope of the present invention; those skilled in the art, which are characterized by the scope of the present invention, Equivalent variations or modifications are considered to be within the scope of the design of the invention.

(ES1)‧‧‧Step 1

(ES2)‧‧‧Step 2

(ES3)‧‧‧Step three

(DS1) ‧ ‧ Step 1

(DS2)‧‧‧Step 2

(DS3)‧‧‧Step three

Claims (10)

A quantum encryption method, the steps comprising: Step one: generating a random number r, and substituted into a transfer function, so that the random number r is converted into a quantum random number | r>, then by a first unitary operator U ¹ According to a long-term secret key K ₀ encryption, a first ciphertext|C ₁ 〉 is obtained; Step 2: using a compression function to substitute the random number r operation to obtain a shared key (Session key) K ₁ , and then convert the message P into a quantum message |P> by the conversion function; and step 3: the first positive operator U ¹ and a second positive operator U ² , according to The shared key K ₁ encrypts the quantum message |P> to obtain a second ciphertext|C ₂ 〉, and the first ciphertext|C ₁ 〉 and the second ciphertext|C ₂ 〉 are combined Obtain the main ciphertext|C>. The quantum encryption method according to claim 1, wherein the conversion function is a Z-substrate qubit represented by Gen _z (.), wherein Z={|0>, |1>}. The quantum encryption method according to claim 1, wherein the first positive operator U ¹ is one of I or H, and the mathematical expression is U ¹ {I, H}, which selects to use I or H according to the value of the long key K ₀ or the shared key K ₁ , and wherein I=|0><0|+|1><1|, . The quantum encryption method according to claim 1, wherein the second positive operator U ² belongs to one of I or i σ _y , and the mathematical expression is expressed as U ² {I, iσ _y }, which is selected according to the value of the long key K ₀ or the shared key K ₁ , using I or i σ _y , and wherein I=|0><0|+|1><1 |,iσ _y =|0><1|-|1><0|. The quantum encryption method according to claim 1, wherein the compression function is expressed as f(.), and the random number r is compressed. A quantum decryption method includes the following steps: Step 1: measuring and decrypting a first ciphertext|C ₁ 〉 according to a long-term secret key K ₀ to obtain a quantum function. a random number r; step two: using a compression function (Compression function) to enter the random number r operation to obtain a shared key (Session key) K ₁ ; and step three: using a first positive operator U ¹ and A second positive operator U ² decrypts a second ciphertext|C ₂ 〉 according to the shared key K ₁ to obtain a quantum message |P>, and after being calculated by the measurement function, the unencrypted is obtained. Message P. The method for quantum decryption according to claim 6, wherein the measurement function is expressed as M(.), and according to the value of the long key K ₀ or the value of the shared key K ₁ , The X substrate was measured, where Z = {|0>, |1>}, X = {|+>, |->}. The method of claim 6, wherein the first positive operator U ¹ is one of I or H, represented as U ¹ {I, H}, which selects to use I or H according to the value of the long key K ₀ or the shared key K ₁ , and wherein I=|0><0|+|1><1|, . The method of quantum decryption according to claim 6, wherein the second positive operator U ² belongs to one of I or i σ _y and is represented as U ² {I, iσ _y }, which is selected according to the value of the long key K ₀ or the shared key K ₁ , using I or i σ _y , and wherein I=|0><0|+|1><1 |,iσ _y =|0><1|-|1><0|. The method of quantum decryption according to claim 6, wherein the compression function is expressed as f(.), and the random number r is compressed.