CN112769858B - Quantum learning-based safe non-random superposition coding method in wireless communication - Google Patents

Quantum learning-based safe non-random superposition coding method in wireless communication Download PDF

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CN112769858B
CN112769858B CN202110091042.0A CN202110091042A CN112769858B CN 112769858 B CN112769858 B CN 112769858B CN 202110091042 A CN202110091042 A CN 202110091042A CN 112769858 B CN112769858 B CN 112769858B
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subcarrier
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attack
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CN112769858A (en
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徐东阳
任品毅
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Xian Jiaotong University
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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
    • H04L63/1441—Countermeasures against malicious traffic
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2602—Signal structure
    • H04L27/261—Details of reference signals
    • 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

A secure non-random superposition coding method based on quantum learning in wireless communication is characterized in that original pilot signals appointed by each unauthorized activation-free user are randomized and coded into Subcarrier Activation Patterns (SAPs), and the coded SAPs can be separated, identified and reliably decoded into code words and finally converted into corresponding pilot signals although being covered by malicious signals and overlapped and interfered with each other in a wireless environment, so that unauthorized access is guaranteed. The invention constructs a safe non-random superposition coding technology based on quantum learning. The process of identifying the attacker code words in the decoding process is analyzed, the process is successfully modeled into a quantum black box model, the algebraic structure of the black box model is given, and a quantum acceleration method based on quantum learning is provided. The invention can effectively learn and remove the influence of complex attack behaviors through the support of the safe non-random superposition coding technology based on quantum learning.

Description

Quantum learning-based safe non-random superposition coding method in wireless communication
Technical Field
The invention relates to the field of wireless communication, in particular to a safe non-random superposition coding method based on quantum learning in wireless communication.
Background
With the increasing development of wireless communication technology, on one hand, the performance requirements of a future communication network on high reliability, low time delay and large connection are increased; on the other hand, the broadcast nature of the wireless channel brings with it an increasing risk of security. The wireless access security is used as a first security defense line of wireless communication, and a security protection mechanism based on a high-level password encryption and decryption system is widely adopted to protect wireless data generated in the access process. However, with the development of quantum computer technology, the mechanism faces the risk of being decoded, and meanwhile, the post-quantum cryptography system is not mature, and the security threat of wireless access is increased sharply, so that a more advanced underlying information coding technology needs to be adopted to ensure the security of data in the wireless access process.
A wireless security access mechanism capable of preventing pilot frequency attack in the wireless access process of an OFDM system is researched. In the OFDM system, the pilot frequency is an important guarantee of the authorization-free wireless access, and through a pilot frequency sharing mechanism of a transmitting end and a receiving end, the system can accurately acquire the identity of the access equipment activated in the authorization-free access process through measuring the pilot frequency signal, so that the normal wireless access is guaranteed. The existing pilot sharing mechanism is based on the public known pilot and is public and deterministic. Therefore, the pilot signals can be known by an attacker, when the attacker learns the frame synchronization information and the pilot information of a legal transceiver, the attacker can accurately launch pilot attack, and further paralyze wireless data transmission service in the wireless access process by sending a specific pilot signal synchronously with a certain legal user so as to interfere with a pilot sharing mechanism between the pairing of the legal transceiver. Attack can be effectively resisted by coding random pilot frequency information, and the existing research mostly adopts a subcarrier coding mode to carry and transmit the pilot frequency information. However, in these studies, the complexity of the pilot decoding process is high, and it is difficult to capture the impact of the pilot attack, and the security performance is limited. Therefore, the key point is how to design a more efficient and accurate pilot decoding scheme, and how to design a secure wireless access mechanism to weaken the influence of pilot sensing attack in an unlicensed OFDM access system.
Disclosure of Invention
The invention aims to provide a secure non-random superposition coding method based on quantum learning in wireless communication, so as to solve the problems.
In order to achieve the purpose, the invention adopts the following technical scheme:
a secure non-random superposition coding method based on quantum learning in wireless communication comprises the following steps:
step 1, establishing a system model; adopting a random pilot frequency mechanism, wherein a plurality of activated uplink transmitters adopt random pilot frequencies to carry out wireless communication access, and an active attacker adopts a hybrid attack mode which comprises the following steps: part of frequency bands interfere the access of legal users, and full frequency bands interfere the access of the legal users and keep silent;
and 2, creating a code frequency domain by encoding each subcarrier activation mode, and constructing a non-random superposition encoding rule based on quantum learning.
Further, in step 1, in the system model, K activated uplink transmitters, a receiver and a pilot sensing attacker are considered to generate K +1 uplink communication links in total, which are the uplink transmitters respectively→ receiver, pilot aware attacker → receiver; the receiver has NTThe root antenna, the activated uplink transmitter and the pilot frequency perception attacker are all single antennas; in a frequency domain, each antenna of each uplink occupies N subcarriers in each OFDM symbol simultaneously; each activated uplink transmitter randomly transmits random pilot signals on different frequency points, a pilot perception attacker randomly transmits random pilot signals on different frequency points, and the pilot signal on the ith subcarrier is
Figure BDA0002912489580000021
Where ρ isAFor its pilot transmission power, the pilot transmission power,
Figure BDA0002912489580000023
and the pilot phase on the ith subcarrier at the kth OFDM symbol time is shown, and the subcarrier activation modes on different frequency points follow a mixed attack mode.
Further, the pilot signal is configured to: the pilot signal of the mth active uplink transmitter on the ith subcarrier during the kth OFDM symbol is
Figure BDA0002912489580000022
Where ρ isL,mFor its pilot transmission power, phik,mAnd pilot frequency phase in the kth OFDM symbol time is represented, and the subcarrier activation modes on different frequency points follow the coding mode of the non-random superposition coding technology.
Further, in step 2, K +2 OFDM symbol times are considered, where K represents the number of users; carrying out energy detection on signals received by any single subcarrier, and realizing accurate signal number detection on each subcarrier by configuring a detection threshold, wherein if the signals exist, the subcarrier is coded to be 1, otherwise, the subcarrier is 0; according to the obtained binary code, a binary code word vector set is obtained as follows: s1＝{s1＝[s1,m]|s1,m∈{0,1},1≤m≤LsIn which s is1,mRepresents the m-th binary codeword unit; l issExpressing the length of the code word, and obtaining the M +1 element code word vector set S2＝{s2|s2,m∈{0,...,M},1≤m≤Ls}，s2,mRepresents the M + 1-th element code word unit;
the establishment of the code frequency domain is:
Figure BDA0002912489580000034
wherein b represents the position of the code word s corresponding to the frequency domain, wherein N represents the number of occupied sub-carriers; obtaining a binary codebook C ═ C of NxCi,j]The ith code word in the codebook is defined as ci＝[c1,i … cN,i]T；
And constructing a non-random superposition coding rule based on quantum learning, wherein the non-random superposition coding rule specifically comprises a coding rule and a decoding rule.
Further, in the step 2,
and (3) encoding criterion: one nxc binary codebook C ═ bi,j]Referred to as a non-random superposition coding matrix, if and only if the following properties are satisfied:
for any two sets of vectors
Figure BDA0002912489580000031
There is an ith row i e {1,2
Figure BDA0002912489580000032
If the code word length is greater than the preset value, L is an artificially set variable, C is the size of the code book, and B is the length of the code word;
first, C is uniformly divided into K sub-codebooks, denoted as CiI is more than or equal to 1 and less than or equal to K, and then, the ith uplink transmission is characterized
The activation mode of the sub-carrier adopted by the transmitter is bi∈CiIf the subcarrier activation mode adopted by the attacker is c, then the superposition phenomenon generated by the signals generated by the K +1 nodes is characterized as follows:
b1∨…∨bK＝bS,K,bS,K∨c＝bI
and is
m1+…+mK＝mS,K,mS,K+c＝mI
Wherein, bS,K,mS,KRepresenting the mutual superposition of independent subcarrier activation patterns generated by K nodes; c is a subcarrier activation mode adopted by an attacker, and satisfies the following conditions:
Figure BDA0002912489580000033
bI,mIthen the receiver is the only two codes that can be obtained finally; all possible column vectors bS,KForm a code matrix BKIs also bS，KIs BKA certain column of vectors; for the same reason, for BKAny column vector code word can be uniquely decomposed into a group of code words bi，1≤i≤K。
Further, in the step 2,
decoding criterion: the decoding process is as follows:
1) traversing N sub-carriers to obtain a differential coding matrix D ═ Dj∈[1，N]]Wherein d isj＝[d1，j … dN，j]；
2) Identifying the currently encountered attack type from the three attack types;
3) decoding is performed according to the identified attack type.
Further, the specific process of step 2) is as follows:
judgment bIAnd D, judging whether all elements in D are 1, if yes, indicating that full-band attack occurs, and outputting a code word bI(ii) a Otherwise, executing the next operation;
judgment bIWhether or not it is BKIf not, partial frequency band attack occurs, and code word b is outputIIf yes, continuing to execute the next operation;
if m is presentI＝mS，KKnowing that the attacker currently keeps the silent state, the code word b is outputS，KOtherwise, judging that partial frequency band attack currently occurs, and outputting a code word bI。
Further, the specific process of step 3) is as follows:
if the attack pattern is a full-band attack and remains silent, Alice decodes b directlyI；
If the attack mode is partial frequency band attack, the jth subcarrier is taken as a reference subcarrier, and the signal independence characteristics of different devices between adjacent subcarriers are extracted through a signal difference inner product technology to obtain a binary code word
Figure BDA0002912489580000041
The base station end establishes a function f1(. o) its functional compartment is a check bIWhether or not it belongs to BK+1If so, f1(. o) output 0, otherwise f1(. output 1; if b isIBelong to BK+1Further performing the function f2(. h), which functions as: at the j frequency point, if
Figure BDA0002912489580000042
Belong to BKThe column vector of (2), then f2Output of 0, otherwise f2(. o) output 1, if bINot belonging to BK+1The column vector of (2), then the function f is executed3(. h), which functions as: judgment of
Figure BDA0002912489580000043
If the column vector belongs to B, then f3(. o) output 1, otherwise f3(. cndot.) is 0;
the quantum learning mathematical model is as follows:
modeling the f interval in the step III as an independent variable of {0, 1}nThe boolean function f, satisfies the following:
f：{0，1}n→{0，1}
defining c as a set of possible Boolean functions; quantum learning on c is defined as a series of unitary transformations U1，Uf，U2，Uf，U3，Uf…, wherein UiIs a unitary matrix, U, independent of a set of Boolean functionsfThen represents a quantum circuit, defined as:
Figure BDA0002912489580000051
where x ∈ {01}n，y∈{0，1}；
The identification process of the attacker code word is essentially a Boolean function c, and the corresponding quantum circuit is defined as UfModeling the codeword identification process of an attacker as:
Figure BDA0002912489580000052
where | x > represents the control qubit, | y > represents the target qubit; by using the model to carry out quantum accelerated learning, the uncertain behavior of the attacker is accurately captured.
Compared with the prior art, the invention has the following technical effects:
the invention successfully models the pilot frequency decoding process based on the non-random superposition coding technology into a black box model for the first time, and further adopts the quantum learning technology to the model, so that the uncertainty in the pilot frequency decoding process affected by the attack can be quickly and accurately captured and eliminated, the decoding accuracy in the attack environment is improved, and the decoding complexity is greatly reduced. By using the model to carry out quantum accelerated learning, the uncertain behaviors of the attacker can be accurately captured, and the computational complexity is doubled.
Drawings
FIG. 1 is a system model diagram.
Fig. 2 is a coding framework diagram.
Fig. 3 is a decoding framework diagram.
Fig. 4 is a graph of code rate as a function of the number of subcarriers.
Figure 5 algebraic structure diagram of the decoding process.
Detailed Description
The invention is further described below with reference to the accompanying drawings:
FIG. 1 shows a system model diagram, considering K activationsThe uplink transmitter, the receiver and the pilot frequency perception attacker jointly generate K +1 uplink communication links which are the uplink transmitter → the receiver and the pilot frequency perception attacker → the receiver respectively; the receiver has NTThe root antenna, the activated uplink transmitter and the pilot frequency perception attacker are all single antennas; in the frequency domain, each antenna of each uplink occupies N subcarriers simultaneously in each OFDM symbol. Each activated uplink transmitter randomly transmits a random pilot signal on different frequency points, and the pilot signal is configured as follows: the pilot signal of the mth active uplink transmitter on the ith subcarrier during the kth OFDM symbol is
Figure BDA0002912489580000061
Where ρ isL,mFor its pilot transmission power, phik,mThe pilot frequency phase in the kth OFDM symbol time is represented, and the subcarrier activation modes on different frequency points follow the coding mode of the non-random superposition coding technology; the pilot frequency perception attacker randomly transmits random pilot frequency signals on different frequency points, and the pilot frequency signal on the ith subcarrier is
Figure BDA0002912489580000062
Where ρ isAFor its pilot transmission power, the pilot transmission power,
Figure BDA0002912489580000063
and the pilot phase on the ith subcarrier at the kth OFDM symbol time is shown, and the subcarrier activation modes on different frequency points follow a mixed attack mode.
Fig. 2 presents a proposed coding framework diagram, comprising the following steps:
step 1, considering K +2 OFDM symbol time, wherein K represents the number of users; carrying out energy detection on signals received by any single subcarrier, and realizing accurate signal number detection on each subcarrier by configuring a detection threshold, wherein if the signals exist, the subcarrier is coded to be 1, otherwise, the subcarrier is 0; according to the obtained binary code, a binary code word vector set is obtained as follows: s1＝{s1＝[s1,m]|s1,m∈{0,1},1≤m≤LsIn which s1,mRepresents the m-th binary codeword unit; l is a radical of an alcoholsExpressing the length of the code word, and obtaining the M +1 element code word vector set S2＝{s2|s2,m∈{0,...,M},1≤m≤Ls}，s2,mRepresents the M + 1-th element code word unit;
the establishment of the code frequency domain is:
Figure BDA0002912489580000064
wherein b represents the position of the code word s corresponding to the frequency domain, wherein N represents the number of occupied sub-carriers; obtaining a binary codebook C ═ C of NxCi,j]The ith code word in the codebook is defined as ci＝[c1,i … cN,i]T；
And Step 2, constructing a safe non-random superposition coding technology rule based on quantum learning, wherein the safe non-random superposition coding technology rule specifically comprises a coding rule and a decoding rule.
And (3) encoding criterion: one nxc binary codebook C ═ bi,j]Referred to as a non-random superposition coding matrix, if and only if the following properties are satisfied:
for any two sets of vectors
Figure BDA0002912489580000071
There is an ith row i e {1,2
Figure BDA0002912489580000072
If the code word length is greater than the preset value, L is an artificially set variable, C is the size of the code book, and B is the length of the code word;
first, C is uniformly divided into K sub-codebooks, denoted as CiI is more than or equal to 1 and less than or equal to K, and then the activation mode of the subcarrier adopted by the ith uplink transmitter is represented as bi∈CiIf the subcarrier activation mode adopted by the attacker is c, then the superposition phenomenon generated by the signals generated by the K +1 nodes is characterized as follows:
b1∨…∨bK＝bS,K,bS,K∨c＝bI
and is
m1+…+mK＝mS,K,mS,K+c＝mI
Wherein, bS,K,mS,KRepresenting the mutual superposition of independent subcarrier activation patterns generated by K nodes; c is a subcarrier activation mode adopted by an attacker, and satisfies the following conditions:
Figure BDA0002912489580000073
bI,mIit is the only two codes that the receiver can finally obtain; all possible column vectors bS,KForm a code matrix BKI.e. bS,KIs BKA certain column of vectors; for the same reason, for BKAny column vector code word can be uniquely decomposed into a group of code words bi,1≤i≤K；
Fig. 3 gives the proposed decoding criteria: the decoding process is as follows:
1) traversing N sub-carriers to obtain a differential coding matrix D ═ Dj∈[1,N]]Wherein d isj＝[d1,j … dN,j]；
2) Identifying the currently encountered attack type from the three attack types; the specific process comprises the following steps:
I) judgment bIAnd D, judging whether all elements in D are 1, if yes, indicating that full-band attack occurs, and outputting a code word bI(ii) a Otherwise, executing the next operation;
II) determination of bIWhether or not it is BKIf not, partial frequency band attack occurs, and code word b is outputIIf yes, continuing to execute the next operation
III) if m is presentI＝mS,KKnowing that the attacker currently keeps the silent state, the code word b is outputS,KOtherwise, judging that partial frequency band attack currently occurs, and outputting a code word bI；
3) Decoding according to the identified attack type;
I) if the attack pattern is a full band attack and remains silent,then Alice decodes b directlyI；
If the attack mode is partial frequency band attack, the jth subcarrier is taken as a reference subcarrier, and the signal independence characteristics of different devices between adjacent subcarriers are extracted through a signal difference inner product technology to obtain a binary code word
Figure BDA0002912489580000081
The base station end establishes a function f1(. o) its functional compartment is a check bIWhether or not it belongs to BK+1If so, f1(. o) output 0, otherwise f1(. output 1; if b isIBelong to BK+1Further performing the function f2(. h), which functions as: at the j frequency point, if
Figure BDA0002912489580000082
Belong to BKThe column vector of (2), then f2Output of 0, otherwise f2(. o) output 1, if bINot belonging to BK+1The column vector of (2), then the function f is executed3(. h), which functions as: judgment of
Figure BDA0002912489580000086
If the column vector belongs to B, then f3(. o) output 1, otherwise f3And (·) is 0. The following figure shows the algebraic structure of the decoding process. Wherein, the input variable of the black box model f (x) is x, x belongs to {0, 1}, the output is f (x), f (x) belongs to {0, 1}, if the input variable is x, x belongs to {0, 1}, the output is f (x), f (x) belongs to {0, 1}, and if the input variable is x, x belongs to {0, 1}, the output is x, x belongs to
Figure BDA0002912489580000083
If the value is zero, it can be confirmed that the received signal at the frequency point j belongs to an attacker, otherwise, the received signal does not belong to the attacker, and obviously, f (0) and f (1) need to be calculated respectively in order to distinguish the attacker.
II) a quantum learning mathematical model:
modeling the f interval in the step III as an independent variable of {0, 1}nThe boolean function f, satisfies the following:
f：{0，1}n→{0，1}
we define c as the set of possible boolean functions. Quantum learning on c is defined as a series of unitary transformations U1，Uf，U2，Uf，U3，Uf…, wherein UiIs a unitary matrix, U, independent of a set of Boolean functionsfThen represents a quantum circuit, defined as:
Figure BDA0002912489580000084
where x ∈ {01}n，y∈{0，1}。
The identification process of the attacker code word is essentially a Boolean function c, and the corresponding quantum circuit is defined as UfModeling the codeword identification process of an attacker as:
Figure BDA0002912489580000085
where | x > represents the control qubit and | y > represents the target qubit. By using the model to carry out quantum accelerated learning, the uncertain behaviors of the attacker can be accurately captured, and the computational complexity is doubled.

Claims (4)

1. A secure non-random superposition coding method based on quantum learning in wireless communication is characterized by comprising the following steps:
step 1, establishing a system model; adopting a random pilot frequency mechanism, wherein a plurality of activated uplink transmitters adopt random pilot frequencies to carry out wireless communication access, and an active attacker adopts a hybrid attack mode which comprises the following steps: part of frequency bands interfere the access of legal users, and full frequency bands interfere the access of the legal users and keep silent;
step 2, a code frequency domain is created through coding of each subcarrier activation mode, and a non-random superposition coding rule based on quantum learning is constructed;
in step 1, K active uplink transmitters, a receiver and a pilot are considered in the system modelSensing attackers to generate K +1 uplink communication links which are an uplink transmitter → a receiver and a pilot frequency sensing attacker → the receiver respectively; the receiver has NTThe root antenna, the activated uplink transmitter and the pilot frequency perception attacker are all single antennas; in a frequency domain, each antenna of each uplink occupies N subcarriers in each OFDM symbol simultaneously; each activated uplink transmitter randomly transmits random pilot signals on different frequency points, a pilot perception attacker randomly transmits random pilot signals on different frequency points, and the pilot signal on the ith subcarrier is
Figure FDA0003538667950000011
Where ρ isAFor its pilot transmission power, the pilot transmission power,
Figure FDA0003538667950000012
the pilot frequency phase on the ith subcarrier at the kth OFDM symbol time is represented, and the subcarrier activation modes on different frequency points follow a mixed attack mode;
in step 2, k +2 OFDM symbol times are considered; carrying out energy detection on signals received by any single subcarrier, and realizing accurate signal number detection on each subcarrier by configuring a detection threshold, wherein if the signals exist, the subcarrier is coded to be 1, otherwise, the subcarrier is 0; according to the obtained binary code, a binary code word vector set is obtained as follows: s1＝{s1＝[s1,m]|s1,m∈{0,1},1≤m≤LsIn which s is1,mRepresents the m-th binary codeword unit; b represents the length of the code word, and an M +1 element code word vector set S is obtained in the same way2＝{s2|s2,m∈{0,...,M},1≤m≤Ls}，s2,mRepresents the M + 1-th element code word unit;
the establishment of the code frequency domain is:
Figure FDA0003538667950000013
wherein b represents the position of the code word s corresponding to the frequency domain, wherein N represents the number of occupied sub-carriers; obtaining a binary codebook C ═ b of NxCi,j]Code bookWherein the ith codeword is defined as ci＝[b1,i… bN,i]T；
Constructing a non-random superposition coding rule based on quantum learning, wherein the non-random superposition coding rule specifically comprises a coding rule and a decoding rule;
in the step (2), the first step is that,
decoding criterion: the decoding process is as follows:
1) traversing N sub-carriers to obtain a differential coding matrix D ═ Dj∈[1,N]]Wherein d isj＝[d1,j … dN,j]；
2) Identifying the currently encountered attack type from the three attack types;
3) decoding according to the identified attack type;
the specific decoding process according to the identified attack type comprises the following steps:
if the attack pattern is a full-band attack and remains silent, Alice decodes b directlyI；
If the attack mode is partial frequency band attack, the jth subcarrier is taken as a reference subcarrier, and the signal independence characteristics of different devices between adjacent subcarriers are extracted through a signal difference inner product technology to obtain a binary code word
Figure FDA0003538667950000021
The base station end establishes a function f1(. h) its function is to check bIWhether or not it belongs to BK+1If so, f1(. o) output 0, otherwise f1(. output 1; if b isIBelong to BK+1Further performing the function f2(. h), which functions as: at the j frequency point, if
Figure FDA0003538667950000022
Belong to BKThe column vector of (2), then f2Output of 0, otherwise f2(. o) output 1 if bINot belonging to BK+1The column vector of (2), then the function f is executed3(. h), which functions as: judgment of
Figure FDA0003538667950000023
If the column vector belongs to B, then f3(. o) output 1, otherwise f3(. cndot.) is 0;
the quantum learning mathematical model is as follows:
modeling the decoding criterion as flow 3), an argument of {0, 1}nThe boolean function f, satisfies the following:
f：{0，1}n→{0，1}
defining c as a Boolean function set; quantum learning on c is defined as a series of unitary transformations U1,Uf，U2，Uf，U3，Uf…, wherein UiIs a unitary matrix, U, independent of a set of Boolean functionsfThen represents a quantum circuit, defined as:
Figure FDA0003538667950000024
where x ∈ {0, 1}n，y∈{0，1}；
The identification process of the attacker code word is essentially a Boolean function c, and the corresponding quantum circuit is defined as UfModeling the codeword identification process of an attacker as:
Figure FDA0003538667950000025
where | x > represents the control qubit, | y > represents the target qubit; by using the model to carry out quantum accelerated learning, the uncertain behavior of the attacker is accurately captured.
2. The method of claim 1, wherein the pilot signal is configured to: the pilot signal of the mth active uplink transmitter on the ith subcarrier during the kth OFDM symbol is
Figure FDA0003538667950000031
Where ρ isL,mFor its pilot transmission power, phik,mAnd pilot frequency phase in the kth OFDM symbol time is represented, and the subcarrier activation modes on different frequency points follow the coding mode of the non-random superposition coding technology.
3. The method for secure nonrandom superposition coding based on quantum learning in wireless communication according to claim 1, wherein in step 2,
and (3) encoding criterion: one nxc binary codebook C ═ bi,j]Referred to as a non-random superposition coding matrix, if and only if the following properties are satisfied:
for any two sets of vectors
Figure FDA0003538667950000032
There is an ith row i e {1,2
Figure FDA0003538667950000033
If yes, L is an artificially set variable, and C is the size of the codebook;
first, C is uniformly divided into K' sub-codebooks, denoted as CiI is more than or equal to 1 and less than or equal to K', and then the activation mode of the subcarrier adopted by the ith uplink transmitter is represented as bi∈CiIf the subcarrier activation mode adopted by the attacker is c, then the superposition phenomenon generated by the signals generated by the K "+ 1 nodes is characterized as follows:
b1∨…∨bK”＝bS,K”,bS,K”∨c＝bI
and is
m1+…+mK”＝mS,K”，mS,K”+c＝mI
Wherein, bS,K,mS,KRepresents the mutual superposition of independent subcarrier activation patterns generated by K' nodes; c is a subcarrier activation mode adopted by an attacker, and satisfies the following conditions:
Figure FDA0003538667950000034
bI,mIit is the only two codes that the receiver can finally obtain; all column vectors bS,KForm a code matrix BK，bS,KIs BKA certain column of vectors; for the same reason, for BKAny column vector codeword in the above can be uniquely decomposed into a set of codewords bi,1≤i≤K。
4. The method according to claim 1, wherein the specific process of step 2) is as follows:
judgment bIAnd D, judging whether all elements in D are 1, if yes, indicating that full-band attack occurs, and outputting a code word bI(ii) a Otherwise, executing the next operation;
judgment bIWhether or not it is BKIf not, partial frequency band attack occurs, and code word b is outputIIf yes, continuing to execute the next operation;
if m is presentI＝mS,KKnowing that the attacker currently keeps the silent state, the code word b is outputS,KOtherwise, judging that partial frequency band attack currently occurs, and outputting a code word bI。
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