CN110213060A - A kind of quantum Proxy Signature method and system that the nothing based on quantum walking is tangled - Google Patents
A kind of quantum Proxy Signature method and system that the nothing based on quantum walking is tangled Download PDFInfo
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- H—ELECTRICITY
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- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
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- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
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- H—ELECTRICITY
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- H—ELECTRICITY
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- H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
- H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
- H04L9/3257—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures using blind signatures
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Abstract
The invention belongs to quantum information processing technology fields, disclose a kind of quantum Proxy Signature method and system that the nothing based on quantum walking is tangled, in the coding stage of message, coding rule is blinded using four kinds of single-particle state combination message, is encoded and blinded information；During the Teleportation of encoded particles, usage amount sub-line is walked to realize the Teleportation of encoded particles, it is tangled in the spontaneous generation of Teleportation kind particle, for resisting the NAK attack of signer and the refusal attack of verifier, is also used to prevent attacker from forging a signature.The present invention includes key updating, has achieved the effect that one-time pad (OTP), this, which to carry into execution a plan next time, no longer needs to redistribute key；Safety analysis shows that the solution of the present invention satisfaction can not forge, and undeniably, the characteristic blinded, and it can also resist and tangle attack using the program is fit closely in e-commerce or electronic fare payment system.
Description
Technical field
The invention belongs to quantum information processing technology field more particularly to a kind of amounts that the nothing based on quantum walking is tangled
Sub- Proxy Signature method and system.
Background technique
Currently, the immediate prior art:
Digital signature is widely used in E-Government, electron medical treatment and electronic fare payment system.It assures that information is complete
Property and authenticity.However, classical signature scheme becomes dangerous in quantum environment with the development of quantum computer.Reason
It is that the safety of classical signature scheme depends primarily on classical difficult math question, such as big factor of an integer decomposes and discrete
Logarithm problem, when facing quantum calculation, they cracking may be cracked, such as Shor algorithm and Grover algorithm.It is classical
Digital signature be no longer regarded as safe, therefore, scientific research scholar proposes Quantum Digital Signature Research, by quantum-mechanical theory
It is added in original digital signature, classical digital signature is extended.Due to the series of characteristics of quantum state, more
It begins one's study quantum signature scheme come more scientific research scholars.
First quantum signature scheme is to be proposed by Gottesman and Chuang in 2001, they use unidirectional letter
Number is to complete signature scheme.In 2002, Barnum et al. had found the fragility of this quantum signature scheme, then pointed out
The infeasible place of this quantum signature scheme.Soon Zeng and Keitel proposes a kind of quantum arbitration based on GHZ state
Signature scheme, by the way that arbitrator is arranged, they successfully meet the theory demands of Barnum proposition.Hereafter, more and more
Quantum signature scheme is suggested.
Proxy Signature is a kind of specific type of digital signature, and wherein the true content of message blinds, until Proxy Signature
Agreement is completed.It realizes in many cryptographic protocols, and is applied to many information security fields, such as electronic fare payment system and
Protocol of Electronic Voting.2009, Wen et al., propose it is a kind of based on EPR tangle to and one-time pad weak blind signature scheme.
2010, Wang et al., it is based on quantum-mechanical fundamental characteristics, introduces a kind of new equality blind signature scheme.2013,
Shi et al. proposes a kind of quantum batch Proxy Blind Signature Scheme based on three-dimensional two particle Entangled State system.In addition, also
Many other Proxy Signature agreements based on multiparticle Entangled State.
In conclusion problem of the existing technology is:
(1) there are technology of preparing problem on obstacle in the particle state preparation stage for previous quantum blind signature scheme, many existing
Agreement mostly realize quantum blind signature scheme using the Entanglement of GHZ state or multiparticle Entangled State, however the system of Entangled State
It is standby to need to consume more resource, and be not easy to prepare under the prior art, this technology barrier makes such quantum blind signature scheme
Practicability substantially reduce.
(2) previous quantum blind signature scheme mostly completes particle using the Entanglement of GHZ state or multiparticle Entangled State
Teleportation, certain such schemes can not resist when in face of tangling attack and tangle attack, cause particle to be ravesdropping, information is let out
The consequence of dew.
(3) previous certain quantum blind signature schemes lack key self-renewing, the key updating technology of one-time pad
(OTP) the QKD key distribution before mostly executing dependent on each agreement, this process result in waste of resources.
Solve the difficulty of above-mentioned technical problem:
Currently, the preparation and storage of GHZ state or multiparticle Entangled State are all very big challenges, compared with the preparation of single-particle state
Need high equipment and more resources in face of tangling attack, multi-pass crosses overall system design to resist and tangle attack, passes through reason
By analytical proof system to the resilience for tangling attack
Most agreements are overly dependent upon the distribution of QKD key to ensure solution security, can pass through the side of update original cipher key
Formula similarly realizes the effect of one-time pad (OTP) to ensure solution security.
Solve the meaning of above-mentioned technical problem:
The preparation and storage of single-particle state are all more easy and steady compared with the preparation of GHZ state or multiparticle Entangled State and storage
It is fixed, thus promoted using the practicability of the quantum blind signature scheme of single-particle.And throughput sub-line walking system, we realize
Single-particle state is spontaneous in quantum walking process tangles, and the characteristic tangled is used for the Teleportation of particle, instead of being based on
The Teleportation of GHZ state or multiparticle Entangled State in turn ensures the safety of communication while completing telecommunication.This
Invention will inveigle the measurement result of particle to be used for the key updating of communication two party, communication by the remaining k/2 bit of eavesdropping detection
Both sides can combine the update rule appointed in advance to complete after through eavesdropping detection using remaining trick particle measurement result
Key updating, thus the dependence before reducing execution agreement every time to QKD distribution key.For based on quantum running gear
Single-particle Teleportation, the present invention have formulated coding rule and signature agreement, provide a kind of more practical based on quantum
The quantum Proxy Signature method and system that the nothing of walking is tangled.
Summary of the invention
In view of the problems of the existing technology, the present invention provides a kind of quantum that the nothing based on quantum walking is tangled is blind
Endorsement method and system.
The invention is realized in this way a kind of quantum Proxy Signature method that the nothing based on quantum walking is tangled, described to be based on
The quantum Proxy Signature method tangled of nothing of quantum walking includes:
In the coding stage of message, blind coding rule using four kinds of single-particle state combination message, carry out coding and
Blind information.
During the Teleportation of encoded particles, usage amount sub-line is walked to realize the Teleportation of encoded particles, in stealth
It passes the spontaneous generation of state kind particle to tangle, for resisting the NAK attack of signer and the refusal attack of verifier, is also used to prevent
Only attacker forges a signature.
Further, the coding rule that blinds of message includes: to blind coding stage in message, and message owner generates a string of n
The random binary character string L of bit, then using L according to character string L, M and | bc > corresponding bit value (table 1.) generate n ratio
Special raw information M two particle Bit String | b1c1>, | b2c2>, | b3c3>...|bncn>}。
Table 1. character string L, M and | bc > corresponding bit value
Table 1 is meant that two particle bit | bici> measurement base determine that and their feature vector is determined by M by L.This
Mean when L bit is 0, | bici> measurement base be X base；When L bit is 1, | bici> measurement base X base, and | bi>
XOR|ci> it is equal to Mi.Here, |+>=1/2 (| 0 >+| 1 >), | ->=1/2 (| 0 >-| 1 >).Then message preparation person sequentially extracts
| b > particle generates B=| b1b2b3...bn>, sequentially extracting | c > particle generates C=| c1c2c3...cn>.For example, if L is
0110, M is 1011, two particle Bit String | bc > can be generated for | 01 >, | -- >, |+->, | 10 > }, thus B=| 0-+1 >, C
=| 1--0 >, only do not prepare person and know exactly which the two particle bit that she prepares | bici>, B string or C string cannot infer by oneself
The information of M out.At this point, the coding that blinds of message is completed.
Further, quantum traveling method includes: the quantum sky that quantum walking runs on locational space and coin space composition
Between, it is expressed as
Wherein Hp indicate position span { n, n ∈ Z }, Hc indicate quantum walking coin direction | 0 >, | 1 > }, quantum row
The evolution of the total quantized system for each step walked is described as equation
WhereinS is known as shift operation symbol, is expressed as s=∑n| n+1><n |, and C is hard
Coin operator, when coin operator is | when 0 > state, make coin from state | n > be moved to state | n+1 >, when coin operator
For | when 1 > state, so that coin moves backward to state | n-1 >.
Further, usage amount sub-line walks to realize that the Teleportation of encoded particles includes:
The quantum running gear based on two coins is selected, by selecting suitable initial state and matched measurement
Base is successfully delivered any unknown quantum bit between two sides, and do not need preparation it is initial tangle particle.
If sender wants to give verifier's Teleportation unknown quantum bitWherein | α |2+|β|2=1.
In Teleportation, prepare two particles, A1And Ap, A1It is the unknown quantum bit that sender wants Teleportation, is designated as
Coin1, ApParticle state be locational space state.Equally, verifier prepares particle B, is designated as coin2.ApWith the initial state of B
All it is | 0 >.It walks by two step quantum, completes Teleportation.
The walking of first step quantum are as follows:
Wherein,
Formula (in, C1The operator for indicating coin1-A1, selects I operation as operator.
The walking of second step quantum are as follows:
Wherein,
In formula, H indicates to execute coin2-B particle Hadamard operation when the initial state of beta particle is | when 0 > state, this
A operator is replaced by I operation when the initial state of beta particle is | when+> state.
Sender measures A with X base1Particle, measurement result be denoted as λ 1 (|+> and | -> be denoted as 1 and -1 respectively).Then it sends
Person measures A with Q basepParticle, wherein | Q >=| -2 ' >, | -1 >, | 0 >, | 1 >, | 2 ' > }, Measurement result be denoted as λ 2 (| -2 ' >, | 0 >, | 2 ' > be denoted as -1,0,1 respectively).Sender again will measurement
As a result λ 1 and λ 2 inform that verifier, verifier make corresponding Pauli recovery operation to beta particle according to λ 1 and λ 2, complete about
A1The Teleportation of particle.
Further, the quantum Proxy Signature method that the nothing based on quantum walking is tangled further comprises:
The first step, initial phase: sender, signer and verifier prepare some particles and are used for quantum running gear.
Second step blinds the stage: sender generates the random binary character string L of n-bit, and then sender is according to blind
Change coding rule using L generate n-bit raw information M two particle Bit String | b1c1>, | b2c2>, | b3c3>...|bncn>}。
When sender generates two particle Bit String | bc > after, sender sequentially extracts | and b > particle generates B=| b1b2b3...bn>,
Sequentially extracting | c > particle generates C=| c1c2c3...cn>.At this point, the encryption that blinds of message is completed.
Third step is signed the stage: the encryption sub-information C throughput sub-line of M is walked Teleportation to signer by sender,
And the Proxy Signature for the person of asking for an autograph, signer execute Pauli to the quantum bit string received and operate to complete Proxy Signature.
Further, third step further comprises:
(1) k trick particles are randomly added to and are used to eavesdrop detection and key updating in C by sender.Sender can
To inveigle the blind information CK Teleportation of particle to tangle particle to signer, and independent of preparation her addition, wherein CK
={ c1, c2, c3...cn+k}.Sender prepare initial state be | 0 > particle ApiFor quantum teleportation, sender is by ciMake
To be needed in quantum running gear by the particle of Teleportation, wherein ci=α | 0 >+β | 1 >, | α |2+|β|2=1.Signer is
Prepare quantum bit string Cp in the particle preparation stage, by particle CpiAs the reception particle in quantum running gear, CpiIt is in |
0 > state.The original state of entire quantum running gear are as follows:
After first step quantum walking W1, whole system state becomes
|Φ>(1)=(α | 100 >+β | -110 >)p12。
After second step quantum walking W2, whole system state becomes
|Φ>(2)=(α | 200 >+α | 001 >+β | 010 >+β | -211 >)p12。
(2) sender measures c with X basei, measurement result |+> and | -> it is designated as 1 and -1 respectively.Sender continues with Q base
| Q >=| -2 ' >, | -1 >, | 0 >, | 1 >, | 2 ' > } measurement Api, whereinMeasurement result
| -2 ' >, | 0 >, | 2 ' > it is designated as -1,0,1 respectively.Finally, the measurement result sequence of X base and Q base is expressed as 1 sequence of λ
With 2 sequence of λ.
(3) sender is with key KACIt encrypts λ 1 and λ 2 and generates Sac=EKAC(λ 1, λ 2).Then, by SacInform signer.
(4) signer key KACDecrypt Sacλ 1 and λ 2 is obtained, by λ 1 and λ 2, signer is particle string Cp
Pauli recovery operation obtains target state.Signer completes the Teleportation of the Anomalous particle from sender, Cp particle
The state that the state of string converts for CK particle string.
(5) after determining that signer completes particle Teleportation, sender starts the position for announcing to inveigle particle and survey
Base is measured, signer selection is suitable to measure base to measure each trick particle, then by the measurement of the trick particle of k/2 bit
As a result and its position informs that sender, sender can assess the error rate during particle Teleportation.If error rate is super
Specified threshold epsilon is crossed, then terminates the communication, then repeats the program from the beginning, until error rate is acceptable.Otherwise,
Continue to execute signature scheme.
(6) remaining k/2 bit measurement result, signer and sender more new key KAC。
(7) after abandoning trick particle, signer is to ciProxy Signature.The random binary string G of signer generation n-bit
={ g1, g2, g3...gn, then according to giOperate Anomalous particle ciIt completes to sign, if giIt is 0, to ciIt executes Pauli and operates I
=| 0><0 |+| 1><1 |, it otherwise executes Pauli and operates σx=| 0><1 |+| 1><0 |.Record is completed unknown after Pauli is operated
Quantum string is Mc.σxThe rollover states in two measurement bases, that is,
Further, it also needs to carry out security verification after the completion of third step.
Another object of the present invention is to provide the quantum Proxy Signatures that the nothing based on quantum walking described in a kind of implementation is tangled
The quantum blind signing system that the nothing based on quantum walking of method is tangled.
Another object of the present invention is to provide the quantum Proxy Signatures that the nothing based on quantum walking described in a kind of implementation is tangled
The quantum Proxy Signature terminal that the nothing based on quantum walking of method is tangled.
Another object of the present invention is to provide a kind of computer readable storage mediums, including instruction, when it is in computer
When upper operation, so that computer executes the quantum Proxy Signature method that the nothing based on quantum walking is tangled.
In conclusion advantages of the present invention and good effect are as follows:
The present invention is a kind of quantum blind signature scheme that the nothing based on quantum walking is tangled, in the primary preparation stage
Only with single-particle.
Different from pervious quantum blind signature scheme, the specific advantage of the solution of the present invention can be summarized as follows.
First, the solution of the present invention does not need to prepare Entangled State particle when preparing original state particle, but in quantum
Make to be automatically generated between single-particle during walking to tangle, it is difficult to tangle particle preparation and can be shown that based on tangling particle
Quantum blind signature scheme application in some cases scheme be it is unworthy, after all practicability be quantum information theory
Important pursuit.
Second, the invention proposes a kind of cleverly encryptions to blind means, the information thus quilt of message owner Alice
Encryption is dexterously blinded, nobody can be inferred to origination message, and present invention demonstrates that this encryption according to single subset
Blind the robustness of mode.
Third, main information of the invention are encoded as quantum state, and the communication process of signature scheme is that throughput sub-line is walked
What Teleportation was completed, it is realized now with many successfully quantum walking experiments, either quantum calculation or quantum simulation,
Quantum walking is required for quantum communications.In addition, the program includes key updating, the effect of one-time pad (OTP) is reached
Fruit, this, which to carry into execution a plan next time, no longer needs to redistribute key.Last safety analysis shows side of the invention
Case satisfaction can not forge, undeniably, the characteristic blinded, and it can also resist and tangle attack, in e-commerce or electronics branch
It the use of the program is fit closely in the system of paying.
Detailed description of the invention
Fig. 1 is the quantum Proxy Signature method flow diagram that the nothing provided in an embodiment of the present invention based on quantum walking is tangled.
Fig. 2 is provided in an embodiment of the present invention when working as N=100,500 and 1000, the population k correctly guessed with successfully
Infer the relational graph of the probability P of entire message.
Fig. 3 is provided in an embodiment of the present invention when working as N=50,100 and 200, refuses the quantity k and rejection probability P of signatured
Between relational graph.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to embodiments, to this hair
It is bright to be further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, not
For limiting the present invention.
There are technology of preparing problem on obstacle in the particle state preparation stage for previous quantum blind signature scheme, many existing
Agreement mostly realizes quantum blind signature scheme using the Entanglement of GHZ state or multiparticle Entangled State, however the preparation of Entangled State
It needs to consume more resource, and is not easy to prepare under the prior art, this technology barrier makes such quantum blind signature scheme
Practicability substantially reduces.
The present invention is based on quantum walking technology, propose a kind of quantum Proxy Signature method that the nothing based on quantum is tangled and
System.Specifically, early in 1993, Aharonov et al. just proposes quantum walking technology, and hereafter, Ambainis et al. is mentioned
Linear quantum running gear is gone out.It is inspired by quantum running gear characteristic, the characteristic of quantum running gear is used for by the present invention
The Teleportation of Anomalous particle --- spontaneous generation is tangled between particle, prepares Entangled State in the particle preparation stage to eliminate
Particle is to complete particle Teleportation, in turn, Teleportation combination coding rule, the blind label that the present invention will be walked based on quantum
Name step completes a kind of quantum Proxy Signature method and system that the nothing based on quantum is tangled.
In view of the problems of the existing technology, the present invention provides a kind of quantum that the nothing based on quantum walking is tangled is blind
Endorsement method and system are explained in detail the present invention below with reference to technical solution.
In the quantum Proxy Signature method that nothing provided in an embodiment of the present invention based on quantum walking is tangled, in the volume of message
Code stage, the present invention cleverly encode and have blinded information using four kinds of 1. rules of single-particle state combination table.In addition, compiling
During the Teleportation of code particle, usage amount sub-line of the present invention, which is come up, realizes the Teleportation of encoded particles, in Teleportation
The spontaneous generation of kind particle is tangled, and ensure that the integrality and safety of raw information.The program can not only resist signature
The NAK attack of person and the refusal attack of verifier, can also prevent attacker from forging a signature.It specifically includes:
(1) message to blind coding rule as follows:
Coding stage is blinded in message, message owner generates the random binary character string L of a string of n-bits, then makes
With L generated according to table 1. n-bit raw information M two particle Bit String | b1c1>, | b2c2>, | b3c3>...|bncn>}。
Table 1. character string L, M and | bc > corresponding bit value
Table 2 is meant that two particle bit | bici> measurement base determine that and their feature vector is determined by M by L.This
Mean when L bit is 0, | bici> measurement base be X base；When L bit is 1, | bici> measurement base X base, and | bi>
XOR|ci> it is equal to Mi.Here, |+>=1/2 (| 0 >+| 1 >), | ->=1/2 (| 0 >-| 1 >).Then message preparation person sequentially extracts
| b > particle generates B=| b1b2b3...bn>, sequentially extracting | c > particle generates C=| c1c2c3...cn>.For example, if L is
0110, M is 1011, two particle Bit String | bc > can be generated for | 01 >, | -- >, |+->, | 10 > }, thus B=| 0-+1 >, C
=| 1--0 >, only do not prepare person and know exactly which the two particle bit that she prepares | bici>, B string or C string cannot infer by oneself
The information of M out.At this point, message blinds completion.
(2) quantum walking technology includes:
Quantum walking is the quantum simulation of classical random walk, it can be used as quantum key generator, intrinsic according to it
Uncertain chaotic sea dynamic behaviour.
Quantum walking occurs in a compound Hilbert space, is made of two main vector subspaces, respectively
It is locational space and coin space, is expressed as
Wherein Hp indicate position span { n, n ∈ X }, Hc indicate quantum walking coin direction | 0 >, | 1 > }, quantum row
The evolution of the total quantized system for each step walked can be described as equation
WhereinS is known as shift operation symbol, is expressed as s=∑n| n+1><n |, and C is hard
Coin operator, when coin operator is | when 0 > state, it makes coin from state | n > be moved to state | n+1 >, when coin operates
Symbol is | when 1 > state, it makes coin move backward to state | n-1 >.
(3) include: by the particle Teleportation that two step quantum running gears are realized
In quantum running gear, shift operator can bring tangling between locational space and coin space, therefore,
The present invention can be by this Teleportation for tangling resource and acting on particle.Concretely, the present invention select with two coins for
The quantum running gear on basis, by selecting suitable initial state and matched measurement base, the present invention can between two sides at
Transmit to function any unknown quantum bit, and do not need preparation it is initial tangle particle.
Assuming that Alice wants to give Bob Teleportation unknown quantum bitWherein | α |2+|β|2=1.For
Completion Teleportation, needs to prepare two particles, A1And Ap, A1It is the unknown quantum bit that Alice wants Teleportation, it
Also it is designated as coin1, the particle state of Ap is the state of locational space.Likewise, Bob prepares particle B, it is also designated as coin2.
The initial state of Ap and B is all | 0 >.It walks by two step quantum, Teleportation can be completed.
The walking of first step quantum can be described as:
Wherein,
In formula (3) and (4), C1Indicate that the operator of coin1-A1, agreement of the invention select I operation as behaviour
It accords with.The walking of second step quantum can be stated are as follows:
Wherein,
In formula (5), H indicates to execute coin2-B particle Hadamard operation when the initial state of beta particle is | 0 > state
When, this operator can also be replaced when the initial state of beta particle is by I operation | when+> state.
At this point, Alice measures A with X base1Particle, measurement result be denoted as λ 1 (|+> and | -> be denoted as 1 and -1 respectively).This
Afterwards, Alice measures Ap particle with Q base, wherein | Q >=| -2 ' >, | -1 >, | 0 >, | 1 >, | 2 ' > }, Measurement result be denoted as λ 2 (| -2 ' >, | 0 >, | 2 ' > be denoted as -1,0,1 respectively).Then, Alice will be surveyed
It measures result λ 1 and λ 2 and informs that Bob, Bob make corresponding Pauli recovery operation to beta particle according to λ 1 and λ 2, complete about A1Grain
The Teleportation of son.
Two step quantum walking scheme includes: under the detailed derivation of the present invention
Pass through analytical calculation, it is found that pass through W1, produce the relationship of tangling between Ap particle and A1 particle, they are answered
Close state fromBecome (a | 10 >+b | -11 >)p1, here it is the teleportations that quantum walking can be used for particle
State is without the reason of the initial stage, particle was tangled in preparation.
Now, A1It is also at Entangled State with B, when Alice measures particle A1When, according to quantum-mechanical theory, particle Ap
Corresponding state will be collapsed to B.
Then Alice measures Ap particle with Q base, and particle B can also collapse to corresponding state.
Finally, measurement result is informed Bob by Alice.According to these measurement results, Bob is executed accordingly on particle B
Pauli is operated to restore unknown quantum state.Relationship between measurement result and Pauli operation is as shown in table 2..
The relationship of table 2. measurement result and Pauli operation room
Indicated above, the intrinsic uncertain chaotic sea dynamic behaviour of coin state makes quantum walking resonable
Have the unlimited random key space of generation to resist the ability of brute force attack by upper, and then quantum walking can be studied in quantum
Application in signature.Therefore, the invention proposes a kind of quantum blind signature schemes that the nothing based on quantum walking is tangled.
With reference to the accompanying drawing and specific embodiment the invention will be further described.
Embodiment
As shown in Figure 1, the quantum Proxy Signature method that the nothing provided in an embodiment of the present invention based on quantum walking is tangled includes
Three participants, sender Alice, signer Charlie and verifier Bob.Agreement is related to four-stage: initial phase,
The blinding stage signs stage and Qualify Phase.Before agreement starts, Alice and the prior shared key K of BobAB, Alice and
The prior shared key K of CharlieAC, Bob and the prior shared key K of CharlieBC.These keys are distributed by QKD agreement.Specifically
Include:
The first step, initial phase:
In initial phase, Alice, Charlie and Bob prepare some particles and are used for quantum running gear.Alice is
Teleportation in quantum running gear prepares a string of particle sequence Ap, wherein Ap=| and 010203...0n>.Charlie prepares
A string of initial states are | the particle sequence C p of 0 > state, for the Teleportation in quantum running gear with Alice, and wherein Cp=|
010203...0n>.Bob prepare a string of initial states be | the particle sequence B p of 0 > state, in quantum running gear with Alice's
Teleportation, wherein Bp=| 010203...0n>.Bob prepares other a string of initial states | and the particle sequence B c of 0 > state is used for
The Teleportation of Charlie Proxy Signature in quantum running gear, wherein Bc=| 010203...0n>。
Second step blinds the stage:
In the stage that blinds, Alice generates the random binary character string L of n-bit, and then Alice is according to the rule of table 1.
Generated using L n-bit raw information M two particle Bit String | b1c1>, | b2c2>, | b3c3>...|bncn>}.Work as Alice
Generate two particle Bit String | bc > after, Alice is sequentially extracted | and b > particle generates B=| b1b2b3...bn>, sequentially extract |
C > particle generates C=| c1c2c3...cn>.At this point, the encryption that blinds of message is completed.
Third step is signed the stage:
In the signature stage, the encryption sub-information C throughput sub-line of M is walked Teleportation to Charlie by Alice, and is requested
The Proxy Signature of Charlie, Charlie execute Pauli to the quantum bit string received and operate to complete Proxy Signature.
(1) k trick particles are randomly added to and are used to eavesdrop detection and key updating in C by Alice.By using
Her addition can be inveigled the blind information CK Teleportation of particle to give by the quantum traveling method introduced before, Alice
Charlie, and tangle particle independent of preparation, wherein CK={ c1, c2, c3…cn+k}.The present invention is with ciThe teleportation of particle
For state.Before this, Alice has had been prepared for initial state and is | 0 > particle ApiFor quantum teleportation, Alice is by ciAs
It is needed in quantum running gear by the particle of Teleportation, wherein ci=α | 0 >+β | 1 >, | α |2+|β|2=1.Charlie exists
The particle preparation stage has prepared quantum bit string Cp, he is by particle CpiAs the reception particle in quantum running gear, CpiPlace
In | 0 > state.Now, the original state of entire quantum running gear can be written as:
After first step quantum walking W1, whole system state becomes
|Φ>(1)=(α | 100 >+β | -110 >) p12 (13)。
After second step quantum walking W2, whole system state becomes
|Φ>(2)=(α | 200 >+α | 001 >+β | 010 >+β | -211 >)p12 (14)。
(2) Alice measures c with X basei, measurement result |+> and | -> it is designated as 1 and -1 respectively.Alice continues with Q base | Q
>={ | -2 ' >, | -1 >, | 0 >, | 1 >, | 2 ' > } measurement Api, whereinMeasurement result
| -2 ' >, | 0 >, | 2 ' > it is designated as -1,0,1 respectively.Finally, the measurement result sequence of X base and Q base is expressed as 1 sequence of λ
With 2 sequence of λ.
(3) Alice key KACIt encrypts λ 1 and λ 2 and generates Sac=EKAC(λ 1, λ 2).Then, she is by SacInform Charlie.
(4) Charlie key KACDecrypt SacObtain λ1And λ2, pass through λ1And λ2, Charlie combination table 2. is to particle string
Cp does Pauli recovery operation to obtain target state.Hereafter, Charlie completes the stealth of the Anomalous particle from Alice
State is passed, the state of Cp particle string converts the state for CK particle string.
(5) after determining that Charlie completes particle Teleportation, Alice starts the position for announcing to inveigle particle and survey
Base is measured, Charlie selection is suitable to measure base to measure each trick particle, then by the measurement of the trick particle of k/2 bit
As a result and its position informs that Alice, Alice can assess the error rate during particle Teleportation.If error rate is more than
Specified threshold epsilon, then they terminate the communication, then repeat the program from the beginning, until error rate is acceptable.It is no
Then, they continue to execute signature scheme.
(6) remaining k/2 bit measurement result, Charlie and Alice are used according to the key updating rule arranged in advance
Its more new key KACTo use in the future.
(7) after abandoning trick particle, Charlie is to ciProxy Signature.The random binary string of Charlie generation n-bit
G={ g1, g2, g3...gn, then he is according to giOperate Anomalous particle ciTo complete to sign, that is, if giIt is 0, he is to ciIt executes
Pauli operates I=| 0><0 |+| 1><1 |, otherwise he executes Pauli operation σx=| 0><1 |+| 1><0 |.Record completes Pauli
Unknown quantum string is Mc after operation.σxCan in two measurement bases rollover states, that is,
σx| 0 >=| 1 >, σx| 1 >=| 0 > (15).
σx|+>=| ->, σx| ->=|+> (16).
Below with reference to Qualify Phase, the invention will be further described.
In Qualify Phase, Alice throughput sub-line walking system is by the quantum bit string B Teleportation of coding encrypting to Bob
To support Qualify Phase, then Charlie by his signature throughput sub-line walking system Teleportation to Bob, and by character string
G is also passed to Bob to support Qualify Phase.Bob measures the quantum string in his hand according to L, and according to the eap-message digest of Alice
Complete signature verification.
(1) similar with (1-6) the step of the signature stage, by using quantum running gear, Alice can be by B teleportation
State is to Bob and completes key KABUpdate to use in the future.This, Alice distinguishes γ1And γ2Indicate measurement base X and Q
Measurement result sequence.Alice is by γ1And γ2Use KABEncryption generates Sab=EKAB(γ 1, γ 2), she is by SabSend Bob to.
(2) Bob KABDecrypt Sab, the Teleportation of the Anomalous particle from Alice is completed, the state of quantum string Bp turns
Quantum string Bp after transformation is denoted as Mb by the state for becoming quantum string B.
(3) after Bob announces that his throughput sub-line walking system receives all unknown quantum states from Alice,
His signature Mc throughput sub-line walking system Teleportation to Bob, and is completed key K by CharlieBCUpdate, as sign rank
The step of section (1-6), is such.This, Charlie, which distinguishes η 1 and η 2, indicates the measurement result sequence of measurement base X and Q.Charlie
By η 1 and η 2 and random binary string G KBCEncryption generates Sbc=EKBC(η 1, η 2, G), he is by SbcSend Bob to.
(4) Bob KBCDecrypt SbcG is obtained, the Teleportation of the Anomalous particle from Charlie, particle string are completed
The state of Bc becomes the state of particle string Mc.Particle string Bc after after turning is denoted as Mc '.
(5) when the Teleportation of Bob and Alice, Charlie terminate, there are quantum string Mb and Mc' in Bob hand.Alice is passed
The defeated character string L for determining two quantum strings measurement base is to Bob and with key KABEncryption, S1=EKAB(L), Bob decrypts S1 and root
Measurement the base Z or X of each quantum bit are selected according to character string L, that is, measure in the case where the place value of L is 0 using Z base, in L
Place value be to be measured using X base in the case of 1.The measurement result of Mb and Mc' is expressed as Rb and Rc '.
(6) Bob calculates RbXOR Rc ' XOR G's as a result, and result is recorded as M'.
(7) Alice exports the hashed value of M using hash function H appropriate.Then, Alice key KABEncrypt H
(M) to generate Shm=EKAB(H (M)), and Shm is sent to Bob.
(8) Bob key KABShm is decrypted to obtain H (M).Bob calculate H (M') result and verify H (M') whether etc.
In H (M), if H (M')=H (M), Bob announce that signature is effective and receives the Proxy Signature of Charlie, otherwise he refuses
The signature of Charlie.
Below with reference to safety analysis, the invention will be further described.
Method of the invention has safety, i.e., safe quantum Proxy Signature agreement not only prevents the puppet of legal participant
It makes or refuses, moreover it is possible to prevent external eavesdropping attack.It specifically includes:
1) blind property: in the present invention, Alice Teleportation is blinded to the quantum string C of Charlie.Firstly,
Charlie only executes Pauli operation to unknown quantity substring C to complete to sign, he is unable to measure quantum string C, because only that
Alice knows the measurement base of quantum string C.Secondly, the message M of Alice is encoded as quantum string C and B, for Charlie,
They be unknown quantity substring and with encryption quantum running gear Teleportation, and measurement result needed for Teleportation by
Alice is generated and is encrypted with key.In addition, even if Charlie obtains measurement base and has measured the measurement of unknown quantity substring C
As a result, he cannot guess B by C to be inferred to the information of M, because only that Alice it is exact know that she prepares that is right
Particle.Present invention assumes that Charlie has 50% probability to hit it another particle B, can be quantitatively evaluated according to statistical data at
Function infers the probability of entire message M.
Wherein k indicates the total number of particles correctly guessed, N indicates the entire message length of M.Probability PiMeet binomial point
Cloth and binomial coefficient.
For N=100, N=500, N=1000, PiFig. 2 about k shows that for different N, there are it by Pi most
Big value, and reduce with the increase of N.It was therefore concluded that signature scheme effectively can be such that information blinds.
2) attacker can not the property eavesdropped: agreement of the invention can resist eavesdropping attack, even if attacker Eve is used
Tangle attack, and futile.
It inveigles particle for avoiding such attack firstly, the present invention is added in transmission particle, improves the safety of agreement
Property.This process is described in detail in the present invention in (1-5) the stage of signature the step of.Assuming that Eve interception was transmitted from Alice
Then any particle sequence retransmits another particle sequence to recipient.Due to Eve to inveigle particle position and
State is known nothing, and recipient can obtain incoherent measurement result, and the error rate during Particle Delivery increases, this
It will lead to the termination of a session.Therefore, the eavesdropping attack of Eve is invalid to plan of the invention.
Secondly, Eve also can not obtain information by tangling attack, because when information is transmitted in quantum channel, information
It is encoded as particle sequence and is walked with discrete time quantum to encrypt.Assuming that Eve has intercepted particle C in transmission process, it is used in combination
New particle e and C are intertwined to form a bigger Hilbert space, wherein C=| 0 >, | 1 >, |+>, | ->.
Wherein E is the single operation matrix of Eve, is expressed as
Four { the e determined by E operator00, e01, e10, e11Pure state meets normalizing condition
Because of EE*=1, a, b, a ', b ' meets following relationship
|a|2+|b|2=1, | a ' |2+|b′|2=1, ab*=(a ')*b′ (25)。
The present invention can obtain result
|a|2=| a ' |2, | b |2=| b ' |2 (26)。
If the attack particle of Eve is in Entangled State, the interference of this listener-in will inevitably introduce mistake, this
Invention can be with the presence of the Probability Detection of PE to listener-in.
PE=| b |2=1- | a |2=| b ' |2=1- | a ' |2 (27)。
If Eve is not desired to introduce error, total particle must be related with direct product state to the auxiliary particle of Eve.However,
Under direct product state, there is no any correlation between auxiliary particle e and C particle, therefore Eve does not obtain any useful information, this card
Be illustrated tangle attack be futile.
3) non repudiation of signatory: assuming that signer Charlie wants to deny his signed information, due to verifying
The step of stage (3,4), the Teleportation that Bob needs the measurement result η 1 of Charlie and η 2 to walk with performance sub-line, measurement
As a result the η 1 and key K of η 2BCEncryption, key KBCDistributed for the first time by QKD agreement and is updated in eavesdropping detection process.Cause
This, other members are difficult to obtain KBCKey, KBCPlay the role of authentication, therefore Charlie cannot deny his signature.
In addition, can deny that possibility is quantitatively evaluated to Charlie according to statistical data.Assuming that Charlie
Agree to or deny that his signature has 1/2 a possibility that, his may be calculated P a possibility that denyingd。
Wherein k indicates the quantity of the signature for the Charlie refusal that Bob is received, and N indicates the length of all signatures received.
Probability PdMeet bi-distribution and binomial coefficient.
The present invention has found P in Fig. 3dRelationship between k, respectively in N=50, N=100, N=200, the figure
Show PdReduce for different N there is maximum value and with the increase of N.
4) verifier can not rejection: in agreement of the invention, Bob can not deny his throughput sub-line walking system
Obtain the signature of Chalie and the quantum bit string B of Alice.If Bob rejection signature, he can not obtain any good
Place.Because Bob needs the signature Mc and random string G of Charlie to verify signature in (6) the Qualify Phase the step of
Integrality, and G key KBCEncryption, the information can only be decrypted by Bob.Key KBCIt will update in eavesdropping detection process with reality
The effect of existing one-time pad (OTP).On the other hand, if Bob has received some signatures but do not recognized the correct of signature
Property, that is to say, that Bob states H (M') ≠ H (M) in Qualify Phase, even if H (M')=H (M).However, this deny to Bob
There is no any benefit.Once he claims H (M') ≠ H (M), in Chalie, he will be considered that signature has been stolen hearer's interception.
Therefore, Chalie will make signature invalid and terminate communication, and the signature that Bob is obtained will be utterly useless.Equally, Bob cannot deny him
Quantum bit string B is obtained from Alice hand by Teleportation.Bob is in order to complete signature verification, Alice throughput sub-line
Walking system gives quantum bit string B Teleportation to Bob, measurement result γ 1 and γ 2 key KABEncryption, KABIt can only be solved by Bob
It is close.If Bob denies that he obtains quantum bit string B by Teleportation from Alice hand, he will be unable to complete to sign to test
Card.
5) unforgeable: assuming that dishonest member Alice, Bob or attacker Eve attempt to forge Charlie's
Proxy Signature.For Alice, her purpose is that Charlie is allowed to complete Proxy Signature, even if she is from (3,4) of Qualify Phase
Step obtains the string of binary characters G of Charlie, she can not also modify the quantum signature Mc of Charlie.Because related to Mc
For the quantum bit string B of connection in Bob hand, it has been sent to Bob before Charlie completes signature.If Alice is repaired
Signature Mc is changed, Mc is then sent to Bob again, this will be unable to by finally verifying, because of H (M') ≠ H (M).She needs
Again another sub- Bit String B' of string quantity is sent to Bob, this is clearly not permitted by agreement.
For Bob, people may worry that his permission is too big, he knows the measurement of G and two quantum bit string
As a result.In fact, Bob cannot modify signature information Mc by G to complete to verify, because of the survey of quantum string B associated with Mc
Amount is the result is that determine, and G is unique time flow sequence.If Bob modifies Mc, final verification result may be unable to complete,
Because of H (M') ≠ H (M).
For attacker Eve, if he wants to forge a signature, need to intercept the institute of Teleportation in entire signature process
There is particle.But the present invention can not prove in attack before this in the property eavesdropped, even if using attack is tangled, Eve can not be stolen
It takes particle or obtains useful information.Therefore, the particle that he can not intercept anyone completes signature forgery.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention
Made any modifications, equivalent replacements, and improvements etc., should all be included in the protection scope of the present invention within mind and principle.
Claims (10)
1. a kind of quantum Proxy Signature method for tangling of nothing based on quantum walking, which is characterized in that described based on quantum walking
Include: without the quantum Proxy Signature method tangled
In the coding stage of message, coding rule is blinded using four kinds of single-particle state combination message, is encoded and is blinded
Information；
During the Teleportation of encoded particles, usage amount sub-line is walked to realize the Teleportation of encoded particles, realizes in stealth
It passes the spontaneous generation of state kind particle to tangle, resists the NAK attack of signer and the refusal attack of verifier, and prevent from attacking
Person forges a signature.
2. the quantum Proxy Signature method that the nothing as described in claim 1 based on quantum walking is tangled, which is characterized in that message
Blinding coding rule includes: to blind coding stage in message, and message owner generates the random binary character string of a string of n-bits
L, then generated using L n-bit raw information M two particle Bit String | b1c1>,|b2c2>,|b3c3>...|bncn>}。
3. the quantum Proxy Signature method that the nothing as described in claim 1 based on quantum walking is tangled, which is characterized in that quantum row
Walking method includes: the vector subspace that quantum walking runs on locational space and coin space composition, is expressed as
Wherein Hp indicate position span { n, n ∈ Z }, Hc indicate quantum walking coin direction | 0 >, | 1 > }, quantum walking it is every
The evolution of total quantized system of a step is described as equation
WhereinS is known as shift operation symbol, is expressed as S=∑n| n+1><n |, and C is coin behaviour
It accords with, when coin operator is | when 0 > state, make coin from state | n > be moved to state | n+1 >, when coin operator is | 1 > state
When, so that coin moves backward to state | n-1 >.
4. the quantum Proxy Signature method that the nothing as described in claim 1 based on quantum walking is tangled, which is characterized in that usage amount
Sub-line walks to realize that the Teleportation of encoded particles includes:
The quantum running gear based on two coins is selected, by selecting suitable initial state and matched measurement base,
Any unknown quantum bit is successfully delivered between two sides, and do not need preparation it is initial tangle particle；
If sender wants to give recipient's Teleportation unknown quantum bitWherein | α |2+|β|2=1；In stealth
It passes in state, prepares two particles, A1And Ap, A1It is the unknown quantum bit that sender wants Teleportation, is designated as coin1, Ap
Particle state be locational space state；Equally, recipient prepares particle B, is designated as coin2；ApInitial state with B is all | 0 >；
It walks by two step quantum, completes Teleportation；
The walking of first step quantum are as follows:
Wherein,
Formula (in, C1The operator for indicating coin1-A1, selects I operation as operator；
The walking of second step quantum are as follows:
Wherein,
In formula, H indicates to execute coin2-B particle Hadamard operation when the initial state of beta particle is | when 0 > state, this behaviour
Accord with and being replaced by I operation when the initial state of beta particle is | when+> state；
Sender measures A with X base1Particle, measurement result be denoted as λ 1 (|+> and | -> be denoted as 1 and -1 respectively)；Then sender is surveyed with Q base
Measure ApParticle, wherein | Q >=| -2' >, | -1 >, | 0 >, | 1 >, | 2' > }, Measurement
As a result be denoted as λ 2 (| -2' >, | 0 >, | 2' > be denoted as -1,0,1 respectively)；Measurement result λ 1 and λ 2 is informed recipient again by sender,
Recipient makes corresponding Pauli recovery operation to beta particle according to λ 1 and λ 2, completes about A1The Teleportation of particle.
5. the quantum Proxy Signature method that the nothing as described in claim 1 based on quantum walking is tangled, which is characterized in that the base
Further comprise in the quantum Proxy Signature method that the nothing of quantum walking is tangled:
The first step, initial phase: sender, signer and verifier prepare some particles and are used for quantum running gear；
Second step blinds the stage: sender generate n-bit random binary character string L, then sender according to blind coding
Regular (table 1.) generated using L n-bit raw information M two particle Bit String | b1c1>,|b2c2>,|b3c3>...|bncn>}；
When sender generates two particle Bit String | bc > after, sender sequentially extracts | and b > particle generates B=| b1b2b3...bn>,
Sequentially extracting | c > particle generates C=| c1c2c3...cn>；At this point, the encryption that blinds of message is completed；
Third step, sign the stage: the encryption sub-information C throughput sub-line of M is walked Teleportation to signer by sender, and is requested
The Proxy Signature of signer, signer execute Pauli to the quantum bit string received and operate to complete Proxy Signature.
6. the quantum Proxy Signature method that the nothing as claimed in claim 5 based on quantum walking is tangled, which is characterized in that third step
Further comprise:
(1) k trick particles are randomly added to and are used to eavesdrop detection and key updating in C by sender；Sender can incite somebody to action
Her addition inveigles the blind information CK Teleportation of particle to tangle particle to signer, and independent of preparation, wherein CK=
{c1,c2,c3...cn+k}；Sender prepare initial state be | 0 > particle ApiFor quantum teleportation, sender is by ciAs
It is needed in quantum running gear by the particle of Teleportation, wherein ci=α | 0 >+β | 1 >, | α |2+|β|2=1；Signer is in grain
The sub- preparation stage prepares quantum bit string Cp, by particle CpiAs the reception particle in quantum running gear, CpiIt is in | 0 > state；
The original state of entire quantum running gear are as follows:
After first step quantum walking W1, whole system state becomes
|Φ>(1)=(α | 100 >+β | -110 >)p12；
After second step quantum walking W2, whole system state becomes
|Φ>(2)=(α | 200 >+α | 001 >+β | 010 >+β | -211 >)p12；
(2) sender measures c with X basei, measurement result |+> and | -> it is designated as 1 and -1 respectively；Sender continues with Q base | and Q >=
| -2' >, | -1 >, | 0 >, | 1 >, | 2' > } measurement Api, whereinMeasurement result | -2'
>, | 0 >, | 2' > it is designated as -1,0,1 respectively；Finally, the measurement result sequence of X base and Q base is expressed as 1 sequence of λ and 2 sequence of λ
Column；
(3) sender is with key KACIt encrypts λ 1 and λ 2 and generates Sac=EKAC(λ1,λ2)；Then, by SacInform signer；
(4) signer key KACDecrypt Sacλ 1 and λ 2 is obtained, by λ 1 and λ 2, signer does Pauli recovery to particle string Cp
Operation is to obtain target state；Signer completes the Teleportation of the Anomalous particle from sender, CpThe state of particle string converts
For the state of CK particle string；
(5) after determining that signer completes particle Teleportation, sender starts the position for announcing to inveigle particle and measurement base,
The suitable measurement base of signer selection measures each trick particle, then by the measurement result of the trick particle of k/2 bit and
Inform that sender, sender can assess the error rate during particle Teleportation in its position；If error rate is more than specified
Threshold epsilon, then terminate the communication, then repeat the program from the beginning, until error rate is acceptable；Otherwise, continue to hold
Row signature scheme；
(6) measurement result is used for by remaining k/2 bit measurement result, signer and sender according to the rule appointed in advance
More new key KAC；
(7) after abandoning trick particle, signer is to ciProxy Signature；The random binary string G={ g of signer generation n-bit1,
g2,g3...gn, Anomalous particle c is then operated according to giiIt completes to sign, if giIt is 0, to ciExecute Pauli and operate I=| 0><
0 |+| 1><1 |, it otherwise executes Pauli and operates σx=| 0><1 |+| 1><0 |；Record completes quantum string unknown after Pauli is operated
For Mc；σxThe rollover states in two measurement bases, that is,
σx| 0 >=| 1 >, σx| 1 >=| 0 >；
σx|+>=| ->, σx| ->=|+>.
7. the quantum Proxy Signature method that the nothing as claimed in claim 5 based on quantum walking is tangled, which is characterized in that third step
It also needs to carry out security verification after the completion.
8. a kind of quantum Proxy Signature method that the nothing implemented based on quantum walking described in claim 1 is tangled is walked based on quantum
The quantum blind signing system that tangles of nothing.
9. a kind of quantum Proxy Signature method that the nothing implemented based on quantum walking described in claim 1 is tangled is walked based on quantum
The quantum Proxy Signature terminal tangled of nothing.
10. a kind of computer readable storage medium, including instruction, when run on a computer, so that computer executes such as
The quantum Proxy Signature method that nothing based on quantum walking described in claim 1-7 any one is tangled.
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| CN114448522B (en) * | 2022-02-22 | 2023-09-22 | 中国海洋大学 | Noise quantum network transmission control method and system based on quantum Shor code |
| CN114465670B (en) * | 2022-02-22 | 2023-10-27 | 中国海洋大学 | Multipartite quantum invisible state communication method and system based on quantum surface code |
| CN115865343A (en) * | 2022-12-06 | 2023-03-28 | 西藏民族大学 | Quantum voting method based on GHZ state |
| CN115865343B (en) * | 2022-12-06 | 2023-07-14 | 西藏民族大学 | Quantum voting method based on GHZ state |
| CN116996237A (en) * | 2023-09-29 | 2023-11-03 | 山东高速建设管理集团有限公司 | Distributed management method and system based on quantum threshold signature |
| CN116996237B (en) * | 2023-09-29 | 2023-12-08 | 山东高速建设管理集团有限公司 | Distributed management method and system based on quantum threshold signature |
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