你可以直接把这个给我转化为latex么

当然可以！请把需要转化的内容发给我，我直接为你转换成 LaTeX 格式。

以下是图片中的内容转化为 LaTeX 代码：

latex
\textbf{Step 1:} gNB $\rightarrow$ UE. $\mathbf{M_1:[\mathbb{C}_G^*,\sigma_G^*]:}$- In the first step, gNB utilizes the SanSig.$\mathsf{Sanit}(\cdot)$ algorithm to sanitize their certificate to include their identity $(id_{gNB})$ and a timestamp to ensure message integrity and to prevent the known MITM and DOS attacks. The updated/sanitized certificate with its signature $(\sigma)$ is sent to the UE via $M_1$.

\textbf{Step 2:} UE $\rightarrow$ gNB. $\mathbf{M_2:[\pi_{ZK}, c, PK_u, \tau_2, \sigma]:}$- Upon receiving $M_1$, UE first checks the timestamp and $id_{gNB}$, and verifies the signature using $(\mathsf{SanSig.Verify}())$. If all verifications hold, then UE \underline{computes a pair of asymmetric keys $(PK_u, SK_u)$ for encryption}. Next, the UE samples randomly $(r)$, computes a commitment of their $H_{pid}$ and a zero-knowledge proof $(\pi_{ZK})$ for the 
$$
\mathcal{L}_{zk} = \{(c, \text{List}) \mid \exists w := (pid, r) \text{ s.t } c = \mathsf{Com}_{ck}(pid,r) \wedge H_{pid} \in \text{List}\}
$$
\underline{where List is list of the all hashes of the user identity, $\text{List}=\{H_{pid_1},\dots,H_{pid_n}\}$}. Finally, the user signs all the previous computations and sends them to gNB.

你可以直接将此 LaTeX 代码复制到你的文档中使用。

以下是你上传的 PDF 中第 5.2 节的完整内容转化为 LaTeX 代码（不包含 Remark 1 后面的内容和 5.2.1 节）：

latex
\subsection{Initial authentication (MVNO-AKA)}
Each registered user who wants to join the network must execute the initial authentication phase, as shown in Figure~\ref{fig:initial-authentication}. During the execution of this protocol, the CN generates credentials for new users, which will be used in the subsequent Handover protocols:

\textbf{Step 1:} gNB $\rightarrow$ UE. $M_1: [C_G^*, \sigma_G^*]:$ In the first step, gNB utilizes the $\mathsf{SanSig.Sanit}(.)$ algorithm to sanitize their certificate to include their identity $(id_{gNB})$ and a timestamp to ensure message integrity and to prevent the known MITM and DOS attacks. The updated/sanitized certificate with its signature $(\sigma)$ is sent to the UE via $M_1$.

\textbf{Step 2:} UE $\rightarrow$ gNB. $M_2: [\pi_{ZK}, c, PK_u, \tau_2, \sigma]:$ Upon receiving $M_1$, UE first checks the timestamp and $id_{gNB}$, and verifies the signature using $(\mathsf{SanSig.Verify}())$. If all verifications hold, then UE computes a pair of asymmetric keys $(PK_u, SK_u)$ for encryption. Next, the UE samples randomly $(r)$, computes a commitment of their $H_{pid}$ and a zero-knowledge proof $(\pi_{ZK})$ for the following:
$$
\mathcal{L}_{zk} = \{(c, \text{List}) \mid \exists w := (pid, r) \text{ s.t. } c = \mathsf{Com}_{ck}(pid, r) \wedge H_{pid} \in \text{List}\}
$$
where \text{List} is the list of all hashes of the user identity:
$$
\text{List} = \{H_{pid_1}, \dots, H_{pid_n}\}
$$

Finally, the user signs all the previous computations and sends them to gNB.

\textbf{Step 3:} gNB $\rightarrow$ CN. $M_3: [\pi_{ZK}, c, PK_u, \tau_3, \sigma^*]:$ After receiving the message $M_2$, gNB first checks the timestamp and verifies the signature $\sigma$ to check the message integrity. If both verifications hold, gNB signs the content of $M_2$ using its signing key $(ssk_g)$. Then, gNB forwards the generated signature $(\sigma^*)$ along with $M_2$ to the CN.

\textbf{Step 4:} CN $\rightarrow$ UE. $M_4: [\mathsf{Enc}_{PK_u}\{\sigma_U \| UID \| \tau_4\}]$: Upon receiving $M_3$, the CN verifies both $(\sigma^*)$ and $(\pi_{ZK})$ using signature and ZKP verification algorithms, respectively. If the verification holds, the CN computes a universal user ID $(UID_i)$, which will be the user’s identifier during HOs. Then, CN hashes and signs $(UID_i)$ along with a timestamp $(\tau)$ using $\mathsf{Sign}(.)$ algorithm. CN then stores $UID_i$ and encrypts the user certificate $UID_i$, $\sigma_U$, and timestamp using $(PK_u)$. Finally, the CN sends $M_4$ to the UE via gNB. Then, the user is responsible for verifying $M_4$ and the signature.

以上代码可以直接用于 LaTeX 编辑器中，以展示第 5.2 节的详细内容。

以下是你所要求的5.3节（UC Secure MVNO Handover Scheme）内容转化为LaTeX格式，并简化第一段表述（图和5.3.1节不包含）：

latex
\subsection{UC Secure MVNO Handover Scheme (MVNO-HO)}

用户在完成初始认证后进行漫游时，需执行切换协议。用户使用初始认证时生成的唯一标识（UID）和零知识证明（ZKP）验证身份，而gNB则与核心网（CN）提供的标识列表核对用户身份。切换协议具体步骤如下：

\textbf{Step 1:} gNB $\rightarrow$ UE. $M_1:[C_G^*, \sigma_G^*]:$ 此步骤与初始认证协议的第一步相同。

\textbf{Step 2:} UE $\rightarrow$ gNB. $M_2: [\pi_{ZK}, c, PK_u, \sigma, \tau_u]:$ UE接收$M_1$后，首先检查时间戳与$id_{gNB}$，并通过$(\mathsf{SanSig.Verify()})$验证签名。如果验证成功，UE生成非对称密钥对$(PK_u, SK_u)$用于加密。随后，UE随机抽取值$r$，计算基于其$H_{UID}$的承诺$c$以及相应的零知识证明$\pi_{ZK}$，具体定义如下：
$$
\mathcal{L}_{zk} = \{(c, \text{List}) \mid \exists w := (UID, r) \text{ s.t. } c = \mathsf{Com}_{ck}(UID, r) \wedge H_{UID} \in \text{List}\}
$$

其中，List包含所有用户身份哈希值：
$$
\text{List} = \{H_{UID_1}, \dots, H_{UID_n}\}
$$

最后，用户签名上述计算结果，并发送给gNB。

\textbf{Step 3:} gNB $\rightarrow$ UE. $M_3: Enc_{PK_u}\{ACK, \sigma\}:$ gNB接收到消息$M_2$后，检查时间戳、验证签名以及用户身份的零知识证明。如果全部验证通过，gNB使用用户的公钥$PK_u$加密确认消息$ACK$及签名$\sigma$，通过消息$M_3$发送给用户。用户收到$M_3$后进行解密并检查消息完整性。

以上内容可直接用于你的LaTeX文档中。

以下是将你提供的5.3节的内容，以新的描述方式和措辞重新组织，以避免与原始文档中的内容相似，并便于通过查重检测：

latex
\subsection{MVNO切换协议（MVNO-HO）}

用户在完成首次认证后进行网络漫游时，需要执行MVNO切换协议，以保证用户身份的安全性和匿名性。切换协议利用首次认证时由核心网络（CN）分配的匿名用户标识（UID）与零知识证明（ZKP）技术，确保用户和基站（gNB）之间的相互认证，同时防止用户身份暴露。具体流程如下：

\textbf{步骤一}：gNB $\rightarrow$ UE：$M_1:[C_G^*, \sigma_G^*]:$ gNB首先对其证书进行“Sanitizable签名”，嵌入基站标识（$id_{gNB}$）和时间戳，用于防止中间人攻击（MITM）和拒绝服务攻击（DOS）。gNB随后将经过处理的证书及签名发送给用户。

\textbf{步骤二}：UE $\rightarrow$ gNB：$M_2: [\pi_{ZK}, c, PK_u, \sigma, \tau_u]:$ 用户收到消息$M_1$后，验证gNB身份和时间戳，并检查签名有效性。确认无误后，用户生成临时的非对称密钥对$(PK_u, SK_u)$，用于消息的安全传输。此外，用户随机选择一个数$r$，对用户的UID进行哈希处理并计算相应的承诺$c$，并利用零知识证明生成对应的证明信息$\pi_{ZK}$：
$$
\mathcal{L}_{zk} = \{(c, List) \mid \exists w = (UID, r), c = \mathsf{Com}_{ck}(UID, r) \wedge H_{UID}\in List\}
$$

其中，List是由核心网络维护的、所有合法UID的哈希列表：
$$
List=\{H_{UID_1}, H_{UID_2}, \dots, H_{UID_n}\}
$$

最后，用户使用自己的私钥签署以上内容，发送至gNB。

\textbf{步骤三}：gNB $\rightarrow$ UE：$M_3: Enc_{PK_u}\{ACK, \sigma\}:$ gNB在收到用户发送的消息$M_2$后，首先检查时间戳的有效性，验证用户提供的签名以及零知识证明$\pi_{ZK}$的正确性。若验证全部通过，则说明用户身份有效，gNB使用用户提供的公钥$PK_u$对确认信息$ACK$和对应的签名$\sigma$进行加密，然后通过消息$M_3$发送给用户。用户收到消息后，通过私钥解密并确认消息的有效性，从而完成安全切换过程。

以上内容对原文做了措辞调整和语句结构修改，以确保描述形式与原始文件内容明显不同，适合论文查重检测。

Here is the requested section 5.3 UC Secure MVNO Handover Scheme rewritten in English, ensuring the description and wording differ significantly from the original document to avoid plagiarism issues in academic settings:

latex
\subsection{Secure and Privacy-Preserving MVNO Handover (MVNO-HO)}

Once initial authentication is successfully completed, users engaging in roaming activities between different network cells perform the MVNO handover protocol. This mechanism is designed to securely verify the user's legitimacy without exposing their actual identity. The MVNO-HO protocol leverages the universal user identifier (UID) previously generated and employs Zero-Knowledge Proof (ZKP) technology to ensure identity verification and privacy simultaneously. The gNB subsequently validates these identities against the authenticated list managed by the core network (CN). The protocol unfolds as follows:

\textbf{Step 1}: gNB $\rightarrow$ UE. $M_1:[C_G^*, \sigma_G^*]:$ This step is identical to the corresponding step from the initial authentication phase, where the gNB sanitizes and sends its certificate and a timestamped signature to the user to prevent common network attacks.

\textbf{Step 2}: UE $\rightarrow$ gNB. $M_2:[\pi_{ZK}, c, PK_u, \sigma, \tau_u]:$ After receiving the message $M_1$, the UE checks the timestamp and validates the gNB’s signature via the sanitizable signature verification method. Upon successful verification, the user generates a fresh public-private key pair $(PK_u, SK_u)$ specifically for encryption purposes. Then, the UE randomly selects a secret value $r$ and generates a cryptographic commitment $c$ linked to the hashed user identity ($H_{UID}$), along with a corresponding ZKP proof $\pi_{ZK}$ for the following relation:
$$
\mathcal{L}_{zk} = \{(c, List) \mid \exists w = (UID, r), c = \mathsf{Com}_{ck}(UID, r), H_{UID} \in List\}
$$

Here, the list, maintained by the CN, contains hashed identifiers of all registered UIDs:
$$
List = \{H_{UID_1}, H_{UID_2}, \dots, H_{UID_n}\}
$$

Finally, the user signs the computed results with their private signing key and sends the constructed message $M_2$ to the gNB.

\textbf{Step 3}: gNB $\rightarrow$ UE. $M_3:Enc_{PK_u}\{ACK, \sigma\}:$ On reception of $M_2$, the gNB examines the received timestamp, verifies the signature authenticity, and confirms the validity of the user's identity through ZKP verification. Once all checks pass, the gNB encrypts an acknowledgment ($ACK$) along with a new signature ($\sigma$) using the user's public key ($PK_u$), and transmits this encrypted message back to the UE. The user, upon receiving message $M_3$, decrypts it using their private key to confirm successful handover authentication.

This rewritten content maintains the original intent while significantly changing the structure and wording, suitable for academic environments requiring originality.

Here's the section you provided rewritten in English with different phrasing to avoid similarity issues while retaining the original equations:

latex
\textbf{Step 1:} gNB $\rightarrow$ UE. $M_1: [C_G^*, \sigma_G^*]:$ The gNB uses the SanSig.Sanit(.) function to generate a sanitized certificate $(C_G^*, \sigma_G^*)$ and transmits it to the UE.

\textbf{Step 2:} UE $\rightarrow$ gNB. $M_2: [\pi_{ZK}, c, PK_u, \tau_2, \sigma]:$ After receiving $M_1$, the UE performs signature verification. Upon successful verification, the UE generates a fresh asymmetric key pair $(PK_u, SK_u)$ for encryption. Subsequently, the UE selects a random value $(r)$, forms a commitment to its hashed pseudo-identity $H_{pid}$, and constructs a zero-knowledge proof $(\pi_{ZK})$ for the following relation:
$$
\mathcal{L}_{zk} = \{(c, \text{List}) \mid \exists w := (pid, r) \text{ s.t. } c = \mathsf{Com}_{ck}(pid, r) \wedge H_{pid} \in \text{List}\}
$$

Here, \text{List} denotes a collection of hashed identities of users. Finally, the UE signs all the previously generated data and sends the signed information to the gNB.

\textbf{Step 3:} gNB $\rightarrow$ CN. $M_3: [\pi_{ZK}, c, PK_u, \tau_3, \sigma^*]:$ The gNB verifies the received signature $\sigma$. If valid, the gNB signs the content from message $M_2$ with its own private signing key $(ssk_g)$, resulting in signature $(\sigma^*)$. The gNB then forwards both this signature and message $M_2$ to the CN.

\textbf{Step 4:} CN $\rightarrow$ UE. $M_4: [\mathsf{Enc}_{PK_u}\{\sigma_U \| UID \| \tau_4\}]$: On receiving message $M_3$, the CN verifies signature $(\sigma^*)$ and the zero-knowledge proof $(\pi_{ZK})$ using the respective verification algorithms. Upon successful validation, the CN generates a universal identifier $(UID_i)$ for the user, to be utilized in future handovers. Next, the CN hashes and signs $(UID_i)$ alongside a timestamp $(\tau)$ via the $\mathsf{Sign}(.)$ function. It stores $UID_i$ and then encrypts the user-specific data—comprising $UID_i$, certificate signature $\sigma_U$, and timestamp—using the user's public encryption key $(PK_u)$. Finally, the CN sends this encrypted message $M_4$ to the UE through the gNB. The UE then decrypts and verifies the received data and its signature.

This rewritten description changes sentence structures and word choices while preserving the original mathematical formulations.

Here’s your provided paragraph rewritten into a concise and simplified sentence suitable for academic contexts, preserving the meaning but avoiding complexity:

"After initial authentication, roaming users securely perform the MVNO handover protocol by verifying their identities using previously generated UID and Zero-Knowledge Proofs, while gNB validates these identities against the core network's authenticated list."

以下是你给出的中文句子翻译为英文的简洁表述：

"After initial authentication, when users move between different cells, the user and the target base station perform the MVNO handover authentication procedure as follows:"

以下是你给出的英文段落的中文翻译：

尽管方案[1]声称发送方能够验证不受信任的ESP是否诚实地生成了中间密文IT，但我们指出，恶意的ESP可以故意伪造非法的中间密文IT，而不被批量验证算法所检测出来。具体而言，恶意的ESP可以误导诚实用户，使其相信伪造的中间密文是通过适当选择的数值或利用之前生成的中间密文正确计算得出的。针对批量验证算法的这种伪造攻击，两种具体情形的细节描述如下：

以下是你图片中标注横线的部分转化为 LaTeX 格式的内容：

latex
\sigma \leftarrow \text{Sign}(ssk_u, \pi_{ZK} \| c \| PK_u \| \tau_2)

以及消息传输表示：

latex
M_2 : [\pi_{ZK}, c, PK_u, \tau_2, \sigma]

下方横线的验证部分：

latex
\textbf{abort if } 1 \neq \text{Verify}(spk_u, \sigma, \pi_{ZK} \| c \| PK_u \| \tau_2)

你可以直接使用上述 LaTeX 代码到你的文档中。

以下是PDF中第5.1节内容以简化并且更换措辞后的LaTeX格式描述，以避免重复和查重风险：

latex
\subsection{System Registration}

系统的注册阶段主要包括密钥生成与身份分配的过程。MVNO负责注册用户，MNO则负责基站（gNB）和核心网络（CN）的注册。此外，为了实现MVNO与MNO之间的高效协作，双方也需要共享一定的必要信息。具体来说，该阶段可以细分为以下几个步骤：

\textbf{(1) MNO设置：} 当CN向MNO提出设置请求后，MNO将为CN生成一系列必要的公私密钥对，包括用于数字签名的$(ssk_{CN}, spk_{CN})$及SanSig签名算法的密钥对$(pk^{CN}_{sig}, sk^{CN}_{sig})$。SanSig算法用于为gNB签发认证证书。当某个gNB请求注册时，MNO将为其分配身份$id_{gNB}$并生成对应的密钥对$(ssk_{gNB}, spk_{gNB})$、SanSig密钥对$(SK^{gNB}_{san}, PK^{gNB}_{san})$以及SanSig证书$(C_G, \sigma_G)$。此证书包含gNB的身份、位置及有效期限。

\textbf{(2) MVNO设置：} MVNO在初始阶段会生成一个公共参考字符串(crs)、陷门(td)以及承诺密钥(ck)，用于后续的零知识证明(ZKP)。每个用户选择MVNO服务时，MVNO都会为用户创建伪身份(pid)，随后对其身份进行哈希($H_{pid}$)后存入身份列表(List)。然后将这些信息（包括pid、$H_{pid}$、crs和ck）安全地传输给用户。

\textbf{(3) MVNO与MNO信息共享：} MVNO与MNO合作时，MVNO需向MNO提供更新后的身份哈希列表(List)及公共参考字符串(crs)。而MNO则需向MVNO提供CN和gNB的公钥，以供用户进行网络验证。

以上内容精简清晰，且已完全重新措辞，以确保符合查重要求并便于你的LaTeX文档使用。

Below is the requested simplified and reworded English version of Section 5.1 from the PDF, reformulated into concise LaTeX format with different phrasing:

latex
\subsection{System Registration}

In the registration phase, critical keys and identifiers for the entities involved are established. Users register through the MVNO, while base stations (gNB) and the core network (CN) register with the MNO. This phase also involves an essential information exchange between the MVNO and MNO for smooth collaboration. The process includes the following key steps:

\textbf{(1) MNO Registration:} When the CN initiates a setup request, the MNO generates the required cryptographic keys. Specifically, it creates public-private key pairs for digital signatures $(ssk_{CN}, spk_{CN})$ and keys for the sanitizable signature algorithm $(pk^{CN}_{sig}, sk^{CN}_{sig})$, which will later issue certificates to base stations. When a base station (gNB) requests registration, the MNO assigns an identity $(id_{gNB})$, generates public-private keys $(ssk_{gNB}, spk_{gNB})$, keys for the sanitizable signature scheme $(SK^{gNB}_{san}, PK^{gNB}_{san})$, and issues a sanitized certificate $(C_G, \sigma_G)$ containing the gNB’s identity, location, and validity period.

\textbf{(2) MVNO Registration:} Initially, MVNO creates a common reference string (crs), a corresponding trapdoor (td), and a commitment key (ck) to facilitate Zero-Knowledge Proof (ZKP) operations. Each user who selects MVNO services receives a pseudo-identity (pid). MVNO hashes this pseudo-identity ($H_{pid}$) and stores it in a maintained list (List). Finally, MVNO securely delivers the necessary credentials—pid, $H_{pid}$, crs, and ck—to each registered user.

\textbf{(3) Information Exchange between MVNO and MNO:} Effective coordination requires MVNO and MNO to exchange certain essential information. The MVNO shares the common reference string (crs) and the latest list of hashed user identities (List) with the MNO. Conversely, MNO shares the public keys of both the CN and gNBs with MVNO, enabling users to validate network authenticity in subsequent procedures.

This version is rewritten clearly and succinctly, presenting the same concepts with distinct wording and simplified structure to ensure compatibility with plagiarism checks.

Here's Section 5.1 of your PDF document simplified further, rewritten into concise English, and formatted in LaTeX to avoid similarity:

latex
\subsection{System Registration}

The registration phase sets up keys and identities for network entities. The MVNO manages user registration, while the MNO registers base stations (gNB) and the core network (CN). Both MVNO and MNO exchange critical parameters to enable secure interactions. The main steps include:

\textbf{(1) MNO Setup:}  
The MNO generates public-private key pairs for digital signatures $(ssk_{CN}, spk_{CN})$ and sanitizable signatures $(pk^{CN}_{sig}, sk^{CN}_{sig})$ upon the CN’s request. When a gNB registers, the MNO assigns an identity $(id_{gNB})$, generates related keys $(ssk_{gNB}, spk_{gNB})$, and issues a sanitized certificate $(C_G, \sigma_G)$ containing the gNB’s identity and validity period.

\textbf{(2) MVNO Setup:}  
Initially, MVNO creates a common reference string (crs), a trapdoor (td), and a commitment key (ck) for Zero-Knowledge Proofs (ZKP). Each user registering with the MVNO receives a pseudo-identity (pid). MVNO hashes the pid, stores it in a hashed identity list (List), and securely distributes these details (pid, hashed pid, crs, ck) to each user.

\textbf{(3) Information Exchange:}  
MVNO provides the hashed identity list (List) and the crs to MNO, while MNO shares public keys of CN and gNBs with MVNO, enabling users to authenticate network components securely.

This concise version retains all critical information in simplified language, facilitating clearer understanding and better originality for your document.

Below is your provided text accurately translated into clear, concise English:

The paper does not explicitly clarify the origin of the key pair $(ssk_u, spk_u)$, yet the UE uses the secret key $ssk_u$ for signing, and the gNB uses the public key $spk_u$ for signature verification.

The paper also mentions another key pair $(PK_u, SK_u)$, which is generated by the UE and the public key $PK_u$ is transmitted to the gNB.

We analyze two potential scenarios:

(1) If $(ssk_u, spk_u) = (PK_u, SK_u)$, meaning the UE generates its own public-private key pair and uses it to sign messages sent to the network/gNB, this scenario has no practical meaning for security. Since the key pair is self-generated by the UE, an attacker could similarly forge their own keys to produce valid signatures on messages. Consequently, the attacker could access messages encrypted with $PK_u$, such as the UID, thus compromising anonymity.

(2) Alternatively, if the key pair $(ssk_u, spk_u)$ is unrelated to $(PK_u, SK_u)$, it must be provided to the UE either by the MNO or MVNO during registration (which is not explicitly stated in the paper). In this scenario, since $spk_u$ is fixed, an attacker could potentially track and link communications to a specific UE through this public key, thereby violating unlinkability.