Semi-quantum secret sharing method based on counting operation

Abstract

The invention relates to the field of quantum communication and quantum cryptography, in particular to a counting operation-based semi-quantum secret sharing method, which comprises the following steps that: a secret distributor converts a secret into a binary string; the distributor prepares a plurality of groups of corresponding direct product states according to the binary secret string and a coding rule; the distributor disrupts the sequence of particles in each group of direct product states, prepares decoy particles, selects one particle in each group of direct product states to form a sequence string, and sends the sequence string to the corresponding reconstructor; the distributor publishes the position and the base of the decoy particles to the reconstructor, and the reconstructor measures the corresponding particles to calculate the error rate; the reconstructor disrupts and returns the decoy particles to the distributor, and the distributor executes corresponding measurement operation on the received decoy particles and performs another round of error rate calculation; and if the two rounds of error rates are within the threshold range, all reconstructors measure the remaining quantum in the hands and record the measurement result, and a binary secret string can be deduced according to the measurement result of the reconstructors. According to the method, the security and the reliability of the secret distribution protocol are ensured, and meanwhile, the relatively high qubit rate is also ensured.

Description

Technical Field

[0001] The invention relates to the fields of quantum communication and quantum cryptography, and in particular to a semi-quantum secret sharing method based on counting operations. Background Art

[0002] With the development and improvement of quantum information theory such as the quantum no-cloning theorem and Heisenberg uncertainty theorem, quantum cryptography, which uses quantum as an information carrier, has attracted widespread attention from researchers at home and abroad. Quantum cryptography not only has the inherent advantage of built-in security, but also has more convenient means of eavesdropping detection. This is difficult to do with classical cryptography. Quantum Secret Sharing (QSS) is an important branch of quantum information science. It involves using the principles of quantum mechanics (such as quantum entanglement and quantum superposition) to achieve information sharing and protection. In this way, multiple parties can safely share a secret information, and no single party can obtain the secret alone. It has a wide range of applications in privacy protection, multi-party computing, security authentication, and quantum computing fault tolerance.

[0003] However, the cost of quantum devices for preparing and measuring arbitrary states is relatively high. Especially in a quantum secret sharing system involving multiple parties, some nodes cannot join the quantum secret sharing system if they do not have the equipment to prepare and measure arbitrary states.

[0004] The idea of ​​semi-quantum can solve the above problems very well. In a semi-quantum system, users are divided into two types: one is a user with full quantum capabilities, who can perform arbitrary unitary operations, prepare and measure arbitrary quantum states; the other is a semi-quantum user, who can only perform preparation and measurement operations under the Z basis ({|0>,|1>}) and directly return particles. There is only one full quantum user in a system, and other users are limited to semi-quantum users, which allows semi-quantum users with only simple equipment to participate in the system. Current semi-quantum secret sharing mostly uses the method of the reconstructor performing an XOR operation to recover a secret bit in the secret recovery stage. Combined with particles used for security detection, the qubit rate reaches an exponential level. Therefore, how to design a new architecture to increase the qubit rate is an important issue. Summary of the invention

[0005] In order to solve the problems existing in the above prior art, the present invention proposes a semi-quantum secret sharing method based on counting operation, which has the advantage of simplicity in the preparation of quantum state and can improve the qubit rate. The proposed semi-quantum secret sharing method based on counting operation includes the following steps:

[0006] The users of the method include distributor Alice, reconstructors Bob1, Bob2, ..., Bob nThe user Alice has full quantum capabilities, and the users Bob1, Bob2, ..., Bob n It has only half-quantum capabilities, including performing computationally based preparation and measurement operations and directly returning particles.

[0007] Step S1, the user Alice represents the secret as a binary bit string K A , expressed as Then Alice Figure 2 The encoding rule prepares l groups of n direct product states, expressed as

[0008]

[0009] Step S2, the user Alice shuffles each group of direct product state particles, and the shuffled l groups of direct product states are expressed as

[0010]

[0011] The function τ i (j)∈{1,2,...,n}(i=1,2,...,l,j=1,2,...,n) represents the rearranged subscript. When u≠v, τ i (u)≠τ i (v); Then the user Alice constructs a share particle sequence

[0012]

[0013] Step S3, the user Alice prepares n decoy particles with a length of l, where each particle is randomly selected from the set {|0>, |1>, |+>, |->}; Alice then inserts the decoy particle into the share particle sequence S j The random positions form a new sequence S′ j Alice records the position and basis of the decoy particle and converts S′ j Sent to the user Bob j ;

[0014] Step S4, after confirming the user Bob j Receive sequence S′ j After that, the user Alice publishes the position and basis of the decoy particle; the user Bob j Select the decoy particles. Further, for the decoy particles in the {|0>,|1>} basis, the user Bob j Perform Z-based measurement and calculate the error rate. If the error rate is higher than the threshold, return to step S1; otherwise, user Bob jAfter shuffling all the decoy particles in hand, all the decoy particles are returned to the user Alice, and the order before and after the shuffling is recorded;

[0015] Step S5: After confirming that the user Alice has received the decoy particle, the user Bob j Publish the order of the decoy particles before and after the rearrangement. Further, the user Alice performs corresponding measurement operations on each decoy particle, that is, performs Z-basis measurement on decoy particles in the {|0>, |1>} basis, and performs X-basis {|+>, |->} measurement on particles in the {|+>, |->} basis. Further, the user Alice compares the measurement results of the decoy particles with the error rate calculated by their initial state. If the error rate is higher than the threshold, return to step S1; otherwise, execute step S6;

[0016] Step S6: User Bob j Perform Z-based measurement on the particle sequence in hand and record the measurement results. Assuming the measurement results |0> represents "0" and |1> represents "1", Bob j The measurement result is expressed as K j =(r j 1 , r j 2 , ..., r j l );

[0017] Step S7: the users Bob1, Bob2, ..., Bob n According to their measurements The number of "1" (or "0") in the bit string is used to recover the secret bit string K of the user Alice. A The decoding rules are as follows: Figure 3 shown.

[0018] Compared with the prior art, the present invention has the following advantages: the present invention is based on direct product states, which is simple and efficient in the preparation of quantum resources; the present invention adopts a new architecture based on counting operations, which effectively controls the consumption of inspection particles, so that the overall qubit rate of the method reaches Detailed security analysis shows that the method of the present invention can resist external and internal attacks. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 A flow chart of semi-quantum secret sharing of base counting operation adopted by the present invention;

[0020] Figure 2 A secret bit string encoding rule of the present invention;

[0021] Figure 3The present invention discloses a secret bit string decoding rule.

[0022] Figure 4 A flowchart of a semi-quantum secret sharing method based on counting operations provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0023] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0024] The flow chart of the present invention is as follows Figure 1 As shown, users are divided into full quantum user Alice, who can prepare and measure any quantum state, and semi-quantum users Bob1, Bob2, ..., Bob n , can only perform preparation and measurement operations under Z and directly return particles. In the method of the present invention, the distributor Alice pairs the binary secret bit string from low to high bits, encodes the secret into the direct product state according to the encoding rules, and inserts the decoy particle into a random position of the direct product state in combination with the eavesdropping detection technology. In Alice and Bob1, Bob2, ..., Bob n After confirming that the communication is secure, Bob1, Bob2, ..., Bob n By piecing their information together and performing counting operations, Alice's secret bit string can be recovered according to the decoding rules.

[0025] The semi-quantum secret sharing method based on counting operation specifically comprises the following steps:

[0026] Step S1: Alice, the distributor, pairs the secret bit string from low to high bits. If the highest bit has no paired bit, the highest bit is paired with zero. The paired secret bit string is expressed as According to Figure 2 The encoding rules are as follows: is 00, the prepared direct product state is when is 11, and the prepared direct product state is when is 01, the prepared direct product state is when is 10, the prepared direct product state is where i = 1, 2, ..., l, Alice prepares l groups of n direct product states, expressed as

[0027]

[0028] Step S2: for each group of direct product states Pi (i=1, 2, ..., l), Alice shuffles its particle sequence. The shuffled l groups of n direct product states are expressed as

[0029]

[0030] The function τ i (j)∈{1,2,...,n}(i=1,2,...,l,j=1,2,...,n) represents the rearranged subscript. When u≠v, τ i (u)≠τ i (v); Alice then constructs the share particle sequence

[0031]

[0032] Step S3, Alice prepares n decoy particles with a length of l, where each particle is randomly selected from the set {|0>, |1>, |+>, |->}; Alice then inserts the decoy particle into the share particle sequence S j The random positions of the new sequence S' with a length of 2l are formed j Alice records the position and basis of the decoy particle and converts S′ j Send Bob j ;

[0033] Step S4, confirm Bob j Receive sequence S′ j After that, Alice announces the position and basis of the decoy particle; Bob j The decoy particle is selected based on the position information. Further, for the decoy particle Bob in the {|0>,|1>} basis j Perform Z-based measurement and calculate the error rate. If the error rate is higher than the threshold, return to step S1; otherwise, Bob j After shuffling all the decoy particles in hand, return all the decoy particles to Alice and record the order before and after the rearrangement;

[0034] Step S5: After confirming that Alice has received the decoy particle, Bob j Publish the order of the decoy particles before and after the rearrangement. Further, Alice performs corresponding measurement operations on each decoy particle, that is, performs Z-basis measurement on decoy particles in the {|0>, |1>} basis, and performs X-basis {|+>, |->} measurement on particles in the {|+>, |->} basis. Further, the user Alice compares the measurement results of the decoy particles with the error rate calculated by their initial state. If the error rate is higher than the threshold, return to step S1; otherwise, execute step S6;

[0035] Step S6, Bobj Perform Z-based measurement on the particle sequence in hand and record the measurement results. Assuming the measurement results |0> represents "0" and |1> represents "1", Bob j The measurement results are expressed as ;

[0036] Step S7, Bob1, Bob2, ..., Bob n According to their measurements The number of "1" (or "0") in the bit string is used to recover the secret bit string K of the user Alice. A , that is, Bob1, Bob2, ..., Bob n The measurement results The number of "1" in is u-1, and the two secret bits recovered are 00; the measurement result The number of "1" in is u, and the two secret bits recovered are 11; the measurement result The number of "1" in is u+1, and the two secret bits recovered are 01; the measurement result The number of "1"s in the ciphertext is u+2, and the two secret bits recovered are 10.

[0037] Exemplarily, the technical solutions in the embodiments of the present invention are clearly and completely described below with specific examples.

[0038] S1: Assume the secret bit string of the secret distributor Alice

[0039] K A =[(0,1),(0,0),(1,0),(0,1),(1,0)]. There are 6 reconstructors, denoted as Bob1, Bob2, ..., Bob6. According to the encoding rule, the 5 groups of 6 direct product states prepared by Alice are

[0040]

[0041] S2: For each group of direct product states P i (i=1,2,...,5), Alice shuffles her particle sequence, and the 5 groups of 6 direct product states after shuffling are expressed as

[0042]

[0043]

[0044] Alice then constructs a sequence of shared particles

[0045]

[0046] S3: Alice prepares 6 decoy particles of length 5, each of which is randomly selected from the set {|0>, |1>, |+>, |->}; Alice then inserts the decoy particle into the share particle sequence S j The random positions of (j=1, 2, ..., 6) form a new sequence S' of length 10 j , expressed as

[0047] S′1=|0>|->|0>|1>|1>|0>|0>|+>|->|1〉

[0048] S′2=|1>|+>|0>|1>|1>|->|1>|1>|0>|1〉

[0049] S′3=|1>|0〉|0>|+>|0>|->|1>|1〉|1>|+>

[0050] S′4=|0>|0>|0>|->|1>|+>|1>|0〉|1>|0〉

[0051] S′5=|1>|0>|0>|1>|1>|->|+>|1>|1〉|1〉

[0052] S′6=|1〉|+>|0>|->|1>|0>|1〉|1〉|1>|0〉

[0053] Alice records the position and basis of the decoy particle and converts S′ j Send Bob j ;

[0054] S4: After confirming Bob j Receive sequence S′ j After that, Alice announces the position and basis of the decoy particle; Bob j The decoy particle is selected based on the position information. Further, for the decoy particle Bob in the {|0>,|1>} basis j Perform Z-based measurement and calculate the error rate. If the error rate is higher than the threshold, return to step S1; otherwise, Bob j After shuffling all the decoy particles in hand, return all the decoy particles to Alice and record the order before and after the rearrangement;

[0055] S5: After confirming that Alice has received the decoy particle, Bob jPublish the order of the decoy particles before and after the rearrangement. Further, Alice performs corresponding measurement operations on each decoy particle, that is, performs Z-basis measurement on decoy particles in the {|0>, |1>} basis, and performs X-basis {|+>, |->} measurement on particles in the {|+>, |->} basis. Further, the user Alice compares the measurement results of the decoy particles with the error rate calculated by their initial state. If the error rate is higher than the threshold, return to step S1; otherwise, execute step S6;

[0056] S6: Bob j Perform Z-basis measurement on the particle sequence in hand and record the measurement results. Assuming that the measurement result |0> represents "0" and |1> represents "1", the measurement results of Bob1, Bob2, ..., Bob6 are expressed as

[0057]

[0058] S7: Bob1, Bob2, ..., Bob6 according to their measurement results

[0059] The number of is 4

[0060] The number of is 2

[0061] The number of is 5

[0062] The number of is 4

[0063] The number of bits is 5, and the secret bit string K of the user Alice is restored. A =[(0,1),(0,0),(1,0),(0,1),(1,0)].

Claims

1. A semi-quantum secret sharing method based on counting operation, mainly including encoding the distributor's secret bit string into a direct product state, eavesdropping detection of the distributor and the reconstructor, and decoding the secret by the reconstructor through counting operation, characterized in that: The specific steps include: S1: The secret distributor prepares a binary secret bit string of length 2l According to the encoding rule, the secret bit string is encoded into l sets of direct product states. superior; S2: The distributor randomly rearranges the particles in each group of direct product states to produce a new direct product state: The function τ i (j)∈{1,2,...,n}(j=1,2,...,n) represents the rearranged subscript and when u≠v, τ i (u)≠τ i (v) The distributor selects one particle from each group of particles to form a shared particle sequence S3: The distributor prepares to insert the decoy particle into the share particle sequence S j In, the position and basis of the decoy particles are recorded and the new particle sequence is sent to the reconstructor; S4: The reconstructor selects decoy particles in the basis {|0>,|1>} according to the decoy particle positions and basis published by the distributor, performs Z basis measurement and calculates the first error rate. If the error rate is greater than the threshold, the process returns to step S1; otherwise, the reconstructor rearranges the order of all decoy particles in its hand and returns them to the distributor, and then executes step S5. S5: The distributor determines the measurement base according to the order of the rearrangement published by the reconstructor, and performs the corresponding measurement operation. If the error rate is lower than the threshold, the distributor performs step S6, otherwise it returns to step S1; S6: Each reconstructor performs Z-basis measurement on the remaining particles in his hand and records the measurement results. The measurement result |0> represents "0", and |1> represents "1"; Bob j The measurement results are expressed as S7: All reconstructors cooperate to calculate the number of "1" (or "0") and recover the secret bit string according to the decoding rules.

2. The semi-quantum secret sharing method based on counting operation as claimed in claim 1, characterized in that: In step S1, the encoding rule is: The secret bit string is The distributor pairs two adjacent bits from low to high. A If the highest bit has no paired bit, the highest bit is paired with zero; According to the number of reconstructors n, the secret encoding rule is is 00, the prepared direct product state is when is 11, and the prepared direct product state is when is 01, the prepared direct product state is when is 10, the prepared direct product state is in 3. The semi-quantum secret sharing method based on counting operation as claimed in claim 1, characterized in that: In step S3, the specific steps include: The distributor prepares n groups of decoy particle sequences of length l (randomly selected from the set {|0>,|1>,|+>,|->}) and j Insert the new sequence S at random position j ′; At the same time, the distributor records the decoy particle position and basis; Finally, the distributor will S j 'Send to Bob j .

4. The semi-quantum secret sharing method based on counting operation as claimed in claim 1, characterized in that: In step S7, the decoding rule is: Bob1, Bob2, ..., Bob n The measurement results The number of "1" in is u-1, and the two secret bits recovered are 00; the measurement result The number of "1"s in the measurement is u, and the two secret bits recovered are 11; the measurement result The number of "1" in is u+1, and the two secret bits recovered are 01; the measurement result The number of "1"s in the ciphertext is u+2, and the two secret bits recovered are 10.

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