1. Communication model and historical background

In 6G wireless communication, similar to the previous communication model, the main factors affecting security are channel quality and the ability of eavesdroppers to ensure the correctness and security of the receiver. The abstract communication model is as follows:

The signal system proposed by Shannon in 1949 is noiseless, and its practical application value is weak. In 1975, Wyn first introduced noise. Subsequently, secure communication mainly develops along two directions, one is the key generation model , and the other is the eavesdropping channel model . Among them, the eavesdropping channel model mainly has two aspects. One is a modular approach, including extractor-based and IO-based models (a newer field in 2022). The second is a coding-based scheme, including LDPC-based coding , polar code- based and lattice-based coding (currently a scheme that can be proven to achieve semantic security).

2. Safety indicators and perfect communication

There are two main aspects to the development of perfect communication. The first is information theory and coding, which mainly includes weak security, strong security, semantic security based on differentiated security, information theory security, and computational security. The last two are security analysis that have only been developed in recent years. The second is modern cryptography, which mainly includes semantic security and computational security based on indistinguishability. Summarizing the above security, the corresponding paper is below the theory, and the flow chart is as follows:

Alice sends a message M and forms X through the encoder. At this time, X can be eavesdropped by Eve, and the receiver forms M' through the decoder and is received by Bob, as shown in the following figure:

There are two understandings of perfect communication. One is that the mutual information between message M and message X is 0, as follows:

$I(M;X)=0$

The other is to know that the conditional entropy of message M pushed by X is equal to the entropy of M itself, as follows:

$H(M|X)=H(M)$

The Shannon circle tells us that the entropy of the key needs to be greater than or equal to the entropy of the message, as follows:

$H(K)\geq H(M)$

3. Eavesdropping channel model and security analysis

Firstly, construct the eavesdropping channel model, as follows:

M, X, Y, and Z in the above figure can all be regarded as functions of k. To achieve secure communication, the eavesdropping channel ChE needs to have more noise than the receiving channel ChB. From this, the weak security can be obtained as follows:

$\lim_{k\to \infty}\frac{I(M|Z)}{|M|}=0\quad uniformly\,M$

Strong security is defined as follows:

$\lim_{k\to\infty}I(M;Z)=0\quad uniformly\,M$

The final mutual information security does not require a uniform message M, which is defined as follows:

$max_{P_M}I(M;Z)=negl$

Before explaining semantic security, let's look at a very interesting picture, as follows:

From this, the definition of semantic security can be obtained as follows:

Using $Z_b$ messages received on behalf of the eavesdropping end, differentiated security can be defined as follows:

$max_{A,M_0,M_1}Pr[A(M_0,M_1,Z_b)=b]=\frac{1}{2}+negl$

Summarizing the above security, from strong to weak, the following flow chart can be formed:

In the figure above, DS stands for differentiated security, SS stands for semantic security, and MIS-R stands for random MIS.

4. Modular-based security solution

Alice transmits a b-bit message M, passes through the security module to form a k-bit ciphertext C, and then passes through the ECC to form an n-bit X, and then flows in two directions. One direction is to form Y through the normal channel ChR, after inversion $ECC^{-1}$ , and then through the security module, it can be restored to message M, so that Bob receives it. The second direction is to form n-bit Z through the wiretapping channel ChE, and finally form M' at the wiretapping end through some kind of operation. Form the above process into a flow chart, as follows:

Based on the above scheme, the security can be established by using the primitives of cryptography, and the correctness can be guaranteed by using the error correction code (ECC). If ChE is more noisy than ChR, combined with ECC, the following conclusions can be drawn:

$H(C|Y)=0,\tilde{H}_\infty(C|Z)=h$

If Ext belongs to $(h,\alpha)$ the extractor, according to the leftover hash lemma, the following conclusions can be drawn:

$SD((S,Ext(S,C),Z),(S,U_b,Z))\leq\alpha\quad \alpha=2^{-128}$

Attached are three commonly used extractor abbreviations:

XtX:eXtractor the Xor

ItE：Invert then Encode

HtE:Hash then Encode

Take the second ItE modular scheme as an example, as shown in the following figure:

From this the following operations can be obtained:

Due to the uncertainty of C and noise in the above, it can be used as a key on the eavesdropping channel ChE, as follows:

$\tilde{H}_\infty(C|Z)=h$

The above formula mainly reflects uncertainty. With the help of artificial noise, error correction code and MIMO technology, the following safety conditions can be realized:

$H(C|Y)=0$

$\tilde{H}_\infty(C|Z)=h$

$b\leq h+2log\alpha-2$

The information-theoretic security scheme cannot exceed the Shannon boundary. Using α to represent the security parameter, the following conclusions can be drawn:

$H(K)\leq H(M)(1-\alpha)$

Then look at a computing security communication model diagram:

Easy to get, ChB cannot be regarded as a degenerate channel of ChE

6G security communication indicators

1. Communication model and historical background

2. Safety indicators and perfect communication

3. Eavesdropping channel model and security analysis

4. Modular-based security solution

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