CN109450630A - A kind of quantum safety direct communication method based on Omega state and ultra dense coding - Google Patents
A kind of quantum safety direct communication method based on Omega state and ultra dense coding Download PDFInfo
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- CN109450630A CN109450630A CN201811569516.2A CN201811569516A CN109450630A CN 109450630 A CN109450630 A CN 109450630A CN 201811569516 A CN201811569516 A CN 201811569516A CN 109450630 A CN109450630 A CN 109450630A
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L63/00—Network architectures or network communication protocols for network security
- H04L63/14—Network architectures or network communication protocols for network security for detecting or protecting against malicious traffic
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- 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
- H04L9/0852—Quantum cryptography
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Abstract
A kind of QSDC agreement of the quantum safety direct communication method based on Omega state and ultra dense coding.Distribution code key is a very important research topic in cryptography, it is different from traditional Encryption Algorithm based on mathematical difficulties problem, quantum secure transfer protocol is based on physics, can be proved to be theory α coefficient, original QSDC agreement, particle will be tangled and be divided into two sequences, check that sequence is used to detect intrusion behavior, message coding sequence is used to transmit ciphertext, however the mode efficiency of this intrusion detection is poor, in order to improve the efficiency of intrusion detection, the QSDC agreement based on Omega state is proposed.Sender forms message qubits sequence using the particle of Bell state, for spreading out of security information, and it will check that sequence C is inserted into qubits sequence, and its position is recorded, data block sequence T is obtained, recipient extracts from T checks sequence C, with quantum bit sequence A, and Omega measurement is carried out to verification sequence C, by the way that measured value compared with threshold value, being judged to, whether current environment is safe.
Description
Technical field
The present invention relates to a kind of quantum safety direct communication method based on Omega state, by using the measurement of comentropy,
It theoretically can be improved by the efficiency of intrusion detection.
Background technique
How to distribute code key is a very important research topic in cryptography, is uniquely proved to the code key of theory α coefficient
Transport protocol is OTP (one time pad), however OTP needs to transmit a key isometric with ciphertext, and the key without
Method multiplexing, makes it be difficult to apply, the code key distribution method being widely used today is all based on mathematical difficulties problem, passes through calculating
On complexity so that invader can not crack code key within the limited time, however the safety of this method is not theoretical
Upper proof, in 1994, Shor proposed quantum Las Vegas algorithm, it was demonstrated that traditional Encryption Algorithm will be by future
It cracks, different from traditional Encryption Algorithm based on mathematical difficulties problem, quantum secure transfer protocol is based on physics, so amount
Sub- safe transmission can be proved to be safe, and quantum communications and quantum cryptography are commonly referred to as distribution of quantum key (QKD), amount
Sub- Teleportation (QT), quantum cryptography share (QSS), safe quantum communication (QSDC) etc..
BB84 agreement is the QKD agreement of first proposition, which points out that quantum bit can substitute traditional ratio in communication
Special position.BB84 agreement and its modified agreement are still widely used in quantum communications.Compared with QKD agreement, QSDC agreement
It can not receive the loss of more quantum informations, i.e. QSDC needs safer environment.In 2002, proposition based on
Einstein-Podolsky-Rosen (EPR) pairs of QSDC agreement, usage amount blockette replace quantum information bit, so that
QSDC is theoretically easy to use.Before sending security message, one of communication party can carry out guaranteed discharge by quantal data block
The safety of sub- communication channel.Eavesdropping will lead to the bit-errors in data block.
Based on same idea, it can also will tangle particle and be divided into two sequences: check that sequence is used to detect intrusion behavior,
Message coding sequence is used to transmit ciphertext.However the mode efficiency of this intrusion detection is poor, in order to improve the effect of intrusion detection
Rate, we have proposed the QSDC agreements based on quantum Omega state, improve the detection efficiency of original agreement.
Summary of the invention
In order to improve efficiency of intrusion detection, using the QSDC agreement based on Omega state, in order to simplify our statement,
Original QSDC agreement is referred to as OPP (Original Present Protocol) agreement herein, Omega state will be based on
QSDC agreement be known as SPP (Second Present Protocol) agreement, in SPP agreement, Alice sends traditional ratio
Special information is to Bob, and Bob forms message qubits sequence A using a particle of each Bell state, for spreading out of safe letter
Breath, then Bob will check sequence C insetion sequence A at random, and record their position, thus obtain data block sequence T and send
Bob is confirmed after the receipt to Alice, Alice, Bob informs the position of Alice C, and Alice extracts verification amount from T
Sub- position, and thus obtain quantum bit sequence A and verification sequence C, Alice to verification sequence C carry out Omega measurement, if not by
Eavesdropping, then measurement result should be | and Ω >, the eavesdropping of Eve will lead to the bit error rate (ber), if ber is greater than some threshold value, then it is assumed that
Current environment is dangerous, and Alice and Bob can interrupt this and communicate and restart, and otherwise the two will continue to link up.
Detailed description of the invention
In order to illustrate more clearly of the present invention is based on the Security Proof mistakes of the quantum safety direct communication method of Omega state
Journey will make attached drawing needed in method simply introduce below.For researcher in this field, pass through this
A little attached drawings can acquire other attached under the premise of not paying creative research according to scheme specific steps and proof process
Figure.
Fig. 1 theoretical value and experiment value mean square error schematic diagram
Specific embodiment
1. the communication protocol process of recipient and sender are as follows:
Four kinds of Bell states are as follows:
The Omega state mentioned in text are as follows:
WhereinB1>∈{|Ψ±>,|Φ±>, therefore have 16 kinds
Omega state can be generated by Bell state, herein we assume that | B0>=| Φ+>, | B0>=| Φ->.We can be used | and Ω >
To enhance the efficiency of intrusion detection.
Assuming that four tenth of the twelve Earthly Branches operate { U0,U1,U2,U3The one of particle of Bell's state is operated after so that Bell's state |
Φ+> be converted into | Φ+>,|Ψ+>,|Ψ->,|Φ->.So four tenth of the twelve Earthly Branches operations can be about set to 00,01,11,10 respectively.Bob
By analyze send and receive be corresponding position Bell state variation, to analyze Alice using the what type of tenth of the twelve Earthly Branches
Operation, so that Alice and Bob completes transmission two classical bits by transmitting a qubit, this principle is exactly ultra dense volume
Code.
Recipient Bob and sender Alice is legitimate correspondence both sides, and Eve is listener-in.The communication process of entire scheme is such as
Under:
Step 1: assuming that Alice wishes that sending traditional N (bit) information has prepared sufficient Bell state work to Bob, Bob
For information sequence and corresponding Bell state information is recorded, and sufficient | Ω > be used as detection sequence C, it is assumed that during agreement carries out
The probability for being switched to control model (or being detection sequence) is c, and Bob needs to prepare cN/ (1-c) | Ω > a state and N/2
Bell state.
Step 2: as OPP, Bob forms message qubits sequence A using first particle of each Bell state,
It is used for transmission security message.Then Bob will randomly check sequence C insetion sequence A and store their position, and present Bob is obtained
The length scale for having arrived its final transmission data block sequence T, T is N/2+4cN/ (1-c).
Step 3: Bob sends T to Alice, and Alice carries out Bob by common signal channel after receiving transmission sequence T
Confirmation.Then Bob tells the position of Alice C, and Alice extracts verification quantum bit from T, obtain message quantum bit sequence A and
Verification sequence C.
Step 4: Alice is to sequence C progress Omega measurement is checked, if do not eavesdropped in ecotopia, measurement result is answered
This is always | and Ω >, the eavesdropping of EVE will lead to bit error rate ber (bit error rate).If ber is greater than some threshold value, Alice
Think that quantum communications are dangerous with Bob, they can interrupt this and communicate and restart, if the bit error rate is less than threshold value, Alice
Think that channel is safe with Bob.They will continue to link up.
Step 5: Alice and Bob confirmed the safety of quantum channel with the detection sequence C in this data block T,
Next information will be transmitted using message sequence A.The information for needing to send is selected the corresponding tenth of the twelve Earthly Branches to operate by Alice, such as
Alice thinks transmission 00, then she will select U0Carry out the sequence of operation.Carry out after all operations Alice by sequence A and oneself again
Generating | Ω > state retransmits back Bob according to step 2.After Bob receives the sequence of Alice transmission, according to the guarantor of step 4 and oneself
It stays particle to carry out Bell state measurement, is compared by the transmission result and received measurement result of reservation, to obtain Alice
Which tenth of the twelve Earthly Branches operation what is carried out is, to obtain the classical bit information that Alice is transmitted.
Step 6: Alice and Bob successfully transfers N (bit) tradition bit information, they will repeat step 1 to step 6
Until information end of transmission.
Step 7: SPP agreement terminates.
2.SPP efficiency is greater than OPP proof procedure
Our use information opinions prove the safety of SPP.Assuming that d indicates the probability that Eve is invaded, then Eve exists
Available maximum information content is in OPP
I(dopp)=- (dlog2(d)+(1-d)log2(1-d))
Eve does not know the position of sequence C, so Eve needs to implement to invade in each qubits, we can assume that,
The qubits that Eve is observed is | 1 > or | 0 >, the probability of the two is all 1/2, then the efficiency invaded is
Wherein | α |2+|β|2=1, | m |2+|n|2=1, parameter alpha, β, m, it is standardizing factor that n is determined by Eve.
In this matrix, | 1 > or | 0 > mixed state will be become,
|E|0>>=E | 0 >=α | 0 >+β | 1 >
|E|1>>=E | 1 >=m | 0 >+n | 1 >
Assuming that | Ω(0)>E=| 0000 >, after Eve invasion, | Ω(0)> will to will become a kind of mixed state as follows:
Above formula, which expand, to be obtained
|Ω(0)>E=α4|0000>+α2β2|0110>
+α2β2|1001>+β4|1111>+|Ω(0)>w
Wherein | Ω(0)>wWhat is indicated is the state that Eve obtains error result, and Eve carries out invading it as available from the above equation
Afterwards, she is still available | Ω > probability be
Using same method, it is as follows that remaining four kinds of states can be calculated
So Eve is still obtained | Ω > shape probability of state is
What above formula indicated is the probability that Eve obtains Omega identical with Alice, so the invasion quilt of the Eve in SPP can be obtained
The probability detected are as follows:
dSPP≥1-p|Ω>
It is assumed that | α |2=a, | m |2=t is so the information content I that Eve is obtained0When Bob sends 0 and I1When Bob sends 1 can be with
It calculates as follows:
I0=H (a)=- (alog2(a)+(1-a)log2(1-a))
I1=H (t)=- (tlog2(t)+(1-t)log2(1-t))
If Bob send 0 and 1 probability be it is identical, according to the symmetry of α and m, work as a=t, Eve is available at most
Information content:
It works as a=t, the available most information of Eve, and is detected with minimum probability, probability value are as follows:
dSPP=1-p|Ω>=-4a4+8a3-8a2+4a
Above formula is the unary biquadratic equation about (0,1) a ∈, and Descartes had been proven that unary biquadratic equation in 1637
There is solution in complex number space.We can be found out accordingly by computer program using Newton method or Descartes's method
Solution.In Security Proof, we, which do not need to find out a, is specifically solved, and can be indicated using kernel method.Assuming that a=k (d),
Then:
4(k(d))4-8(k(d))3+8(k(d))2- 4 (k (d))+d=0
As available from the above equation, Eve information content obtained in SPP is
I(dSPP)=H (k (d))
The difference that Eve passes through two kinds of agreement information content obtained of OPP and SPP is Δ=I (dOPP)-I(dSPP), if Δ >
0, in the identical situation of probability being detected, Eve can obtain more information content in OPP, this indicates that SPP has more
Good detection efficiency.Eve information content obtained in SPP is always less than in OPP when d ∈ (0,0.5), therefore SPP ratio OPP has
Better detection efficiency.
The Security Proof of 3.SPP
Assuming that Alice and Bob goes selection control sequence using probability value for c ∈ [0,1] and carries in message sequence
One information content, the then information content that quantum bit averagely carries in SPP are 1-c.We assume that transmission each time be all it is independent,
ciIt indicates before sending 1 quantum of information position, in control sequence transmission i quantum bit, Eve obtains 1 information by Alice and Bob
And the probability being not detected are as follows:
Therefore when Eve successfully obtains I (dspp) information shifts and when being not detected, probability size is (s1)1/I(dspp),
So if Eve obtains nI (d n quantum of information positionspp) when, her successful probability size are as follows:
When d ∈ (0,0.5), n ∈ [0,50], with the increase of n, s value can decline, and limn→∞S=0.Assuming that n is one
A possibility that value of the value of a fixation, d is bigger, and the gradient of s is bigger, therefore the probability of d invasion is bigger, is detected is bigger,
And due to the obtained information of Eve be it is random, a complete information can not be formed, so SPP agreement is safe.
We, which design one, below proves above-mentioned detection scheme based on the computer simulation experiment of monte carlo method
Correctness can fix wherein several variables by controlling the thought of variable, to reach to simplify the process of emulation experiment
To the purpose for simplifying the difficulty that experiment is implemented.
D=0.5, c=0.5 are set first, according to Newton method approach a solution a=k (d) of available current a=
0.822, the probability for eavesdropping successfully 1bit information content can be calculated at this time.
So steal the successful probability of n bit information content:
The theoretical number attempted required for stealing the success of n bit information content can be calculated simultaneously:
So we can successfully steal the number of trial required for n bit information content by emulating EveTo test
Demonstrate,prove the correctness and reasonability of the agreement.
Algorithm flow is as follows:
1. count initialized
2. repeating simulation protocol receives and dispatches process, when being detected eavesdropping, it is total to record the information that current Eve has been intercepted
Measure n '.
3. if n ' >=n, terminates current emulation, returnsOtherwise
For the similarity degree of description theory value and experiment value, can using mean square error (Mean Square Error,
MSE it) describes, formula can indicate are as follows:
Program is write using Python3, and randomizer is included using system, and setting n=5 repeats emulation experiment 300
Secondary to be averaged and calculate MSE, the results are as follows.
In Fig. 1, x-axis indicates the number that emulation experiment carries out, and value is [0,300]；The size of y-axis expression MSE.From
On figure as can be seen that when simulation times are less, the value of MSE is very big, illustrates that theoretical value and actual value are not agreed with, image fluctuation
It is very big, illustrate that there is also a large amount of randomnesss in emulation experiment.With being continuously increased for simulation times, the value of MSE is gradually reduced,
And level off to 0, illustrate that experiment value gradually agrees with theoretical value, simultaneously the fluctuation of image is also reducing, illustrate with
The increase of simulation times, influence of the randomness to result are gradually reducing.
Pass through the analysis of Fig. 1, it can be deduced that the emulation experiment meets Chebyshev's law of large numbers, illustrates emulation reality
The design and verifying tested be it is reasonable, by emulation experiment can further prove thought proposed in invention correctness and
Reasonability.
Claims (1)
1. the Quantum Secure Direct Communication agreement based on Omega state and ultra dense coding.In order to improve the efficiency of intrusion detection, propose
QSDC agreement based on Omega state.Sender forms message qubits sequence using the particle of Bell state, for spreading out of safety
Information, and will check that sequence C is inserted into qubits sequence, and record its position, data block sequence T is obtained, recipient takes out from T
Take inspection sequence C and quantum bit sequence A, and Omega measurement carried out to verification sequence C, by by measured value compared with threshold value,
Judge whether current environment is safe.It is characterized in that: receiving party carries out Omega measurement to check bit, and by measurement result
It compares with threshold value, to judge whether current communication environment is safe.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110276207A (en) * | 2019-06-27 | 2019-09-24 | 华南农业大学 | A kind of encryption method based on quantum teleportation |
| CN112929338A (en) * | 2021-01-21 | 2021-06-08 | 深圳大学 | Method for preventing quantum 2-1 from being illegally measured by careless transmission protocol receiver |
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2018
- 2018-12-21 CN CN201811569516.2A patent/CN109450630A/en active Pending
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110276207A (en) * | 2019-06-27 | 2019-09-24 | 华南农业大学 | A kind of encryption method based on quantum teleportation |
| CN110276207B (en) * | 2019-06-27 | 2020-12-11 | 华南农业大学 | Encryption method based on quantum invisible state |
| CN112929338A (en) * | 2021-01-21 | 2021-06-08 | 深圳大学 | Method for preventing quantum 2-1 from being illegally measured by careless transmission protocol receiver |
| CN112929338B (en) * | 2021-01-21 | 2022-10-25 | 深圳大学 | Method for preventing quantum 2-1 from being illegally measured by careless transmission protocol receiver |
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