Zhang et al 2024a - Revision history

Rimni at 10:19, 17 May 2024

2024-05-17T10:19:36Z

Rimni: /* 4.5.1 Strong indivisibility analysis */

2024-05-17T10:13:51Z

‎4.5.1 Strong indivisibility analysis

Rimni at 10:12, 17 May 2024

2024-05-17T10:12:43Z

Rimni at 10:10, 17 May 2024

2024-05-17T10:10:59Z

Rimni: /* 4.1 File encryption */

2024-05-17T10:08:14Z

‎4.1 File encryption

Rimni: /* 4.3 Proof of data holdings */

2024-05-16T14:06:36Z

‎4.3 Proof of data holdings

Rimni at 14:05, 16 May 2024

2024-05-16T14:05:48Z

Rimni at 14:04, 16 May 2024

2024-05-16T14:04:30Z

Rimni at 14:04, 16 May 2024

2024-05-16T14:04:08Z

Rimni at 14:02, 16 May 2024

2024-05-16T14:02:28Z

← Older revision		Revision as of 10:19, 17 May 2024
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−	In Eq. (11), <math display="inline">\alpha</math> and <math display="inline">q</math> represent the number and length of ciphertext data blocks respectively. In practice, the size of <math display="inline">q</math> is set to 128bit. In order to ensure the security of data storage, the user usually only retains 1 block of ciphertext data, and the size of <math display="inline">\alpha</math> is 128bit. It is thus known that the storage overhead of the proposed scheme in this paper is relatively low [17].	+	In Eq. (11), <math display="inline">\alpha</math> and <math display="inline">q</math> represent the number and length of ciphertext data blocks, respectively. In practice, the size of <math display="inline">q</math> is set to 128bit. In order to ensure the security of data storage, the user usually only retains 1 block of ciphertext data, and the size of <math display="inline">\alpha</math> is 128bit. It is thus known that the storage overhead of the proposed scheme in this paper is relatively low [17].

	'''(3) Comparative analysis of computational overhead'''		'''(3) Comparative analysis of computational overhead'''

@@ Line 220: / Line 220: @@
 Suppose the stored pseudo-message data block is <math display="inline">f_1'</math> and the outsourced data block stolen by the attacker through different channels is <math>f_2',f_3',f_4',\cdots ,f_n'</math>, at this point the steps for the provider to restore the original data learning based on the outsourced data are:
-① Sorting the acquired data according to the user's replacement rule <math display="inline"> t </math> gives: <math>M=m_1\|m_2\|m_3\|\cdots\|m_n </math>;
+''Step 1'': Sorting the acquired data according to the user's replacement rule <math display="inline"> t </math> gives: <math>M=m_1\|m_2\|m_3\|\cdots\|m_n </math>;
-''Step 1'': Get the conversion key <math display="inline">K_{tr}</math>;
+''Step 2'': Get the conversion key <math display="inline">K_{tr}</math>;
-''Step 2'': Based on the conversion key, compute the original data block.
+''Step 3'': Based on the conversion key, compute the original data block.
 An attacker can decrypt the original data only if all the above three conditions are met simultaneously.
@@ Line 230: / Line 230: @@
 The security analysis of outsourced data is specifically:
-''Step 3'': Assuming that the replacement rule <math display="inline">t  </math> is compromised and the amount of outsourced data stolen by the attacker is <math display="inline"> n </math>, there are:
+① Assuming that the replacement rule <math display="inline">t  </math> is compromised and the amount of outsourced data stolen by the attacker is <math display="inline"> n </math>, there are:
 {| class="formulaSCP" style="width: 100%; text-align: left;"

@@ Line 222: / Line 222: @@
 ① Sorting the acquired data according to the user's replacement rule <math display="inline"> t </math> gives: <math>M=m_1\|m_2\|m_3\|\cdots\|m_n </math>;
-② Get the conversion key <math display="inline">K_{tr}</math>;
+''Step 1'': Get the conversion key <math display="inline">K_{tr}</math>;
-③ Based on the conversion key, compute the original data block.
+''Step 2'': Based on the conversion key, compute the original data block.
 An attacker can decrypt the original data only if all the above three conditions are met simultaneously.
@@ Line 230: / Line 230: @@
 The security analysis of outsourced data is specifically:
-① Assuming that the replacement rule <math display="inline">t  </math> is compromised and the amount of outsourced data stolen by the attacker is <math display="inline"> n </math>, there are:
+''Step 3'': Assuming that the replacement rule <math display="inline">t  </math> is compromised and the amount of outsourced data stolen by the attacker is <math display="inline"> n </math>, there are:
 {| class="formulaSCP" style="width: 100%; text-align: left;"

@@ Line 154: / Line 154: @@
 ====4.3.1 Generation of supporting information, <math>Proof-Gen(\varepsilon,k_{ind},Z)\to proof </math>====
-* After the GSP obtains the challenge information, calculate the <math display="inline"> Z </math> set.
+① After the GSP obtains the challenge information, calculate the <math display="inline"> Z </math> set.
-* Return proof information <math>proof=(\delta,\xi) </math>
+② Return proof information <math>proof=(\delta,\xi) </math>
 {| class="formulaSCP" style="width: 100%; text-align: left;"

@@ Line 84: / Line 84: @@
 Assuming the original file is <math display="inline"> F </math>, then the user can encrypt the original data file via ''Lock(F)→UF''. The steps are as follows:
-''Step 1'':  Divide the original file to generate <math display="inline"> n </math> files, i.e., <math>F=\{f_1,f_2,f_3,\cdots,f_n\}</math>;
+''Step 1'':  Divide the original file to generate <math display="inline"> n </math> files, i.e., <math>F=\{f_1,f_2,f_3,\cdots,f_n\}</math>.
-''Step 2'':  After the division is completed, randomly select the file block and convert the secret key <math display="inline">K_{tr}</math>, <math display="inline"> t </math> to indicate the replacement rule;
+''Step 2'':  After the division is completed, randomly select the file block and convert the secret key <math display="inline">K_{tr}</math>, <math display="inline"> t </math> to indicate the replacement rule.
 ''Step 3'':  With the help of H-AONT,  <math>F=\{f_1,f_2,f_3,\cdots,f_n\}</math> is converted and thus the strongly indivisible pseudo-message data block is obtained, i.e.,  <math>F^{\prime}=\{f_1^{\prime},f_2^{\prime},f_3^{\prime},\cdots,f_{n^{\prime}}^{\prime}\}</math>, where  <math>n=n+1</math>.
-''Step 4'': In generating the pseudo-message data block, the private key <math display="inline"> K </math> is randomly selected and encryption is realized by the symmetric encryption function <math display="inline">E(\cdot )</math>, i.e.,  <math display="inline">E_K (F')\to C</math> and the ciphertext set  <math>C=\{C_1,C_2,C_3,\cdots,C_{n^{\prime}}\}</math>;
+''Step 4'': In generating the pseudo-message data block, the private key <math display="inline"> K </math> is randomly selected and encryption is realized by the symmetric encryption function <math display="inline">E(\cdot )</math>, i.e.,  <math display="inline">E_K (F')\to C</math> and the ciphertext set  <math>C=\{C_1,C_2,C_3,\cdots,C_{n^{\prime}}\}</math>.
-''Step 5'': After obtaining the set of ciphertexts, divide it into sets of varying lengths, with the long set being <math display="inline">\alpha</math> and the short set being <math display="inline">\beta</math>, then there is <math display="inline">C=\alpha + \beta</math>, where <math display="inline">\vert\alpha\vert \ll \vert\beta\vert</math>;
+''Step 5'': After obtaining the set of ciphertexts, divide it into sets of varying lengths, with the long set being <math display="inline">\alpha</math> and the short set being <math display="inline">\beta</math>, then there is <math display="inline">C=\alpha + \beta</math>, where <math display="inline">\vert\alpha\vert \ll \vert\beta\vert</math>.
 ''Step 6'': Use <math display="inline">\beta</math> as an user file and upload it to a third party; <math display="inline">\alpha</math> and <math display="inline"> K </math> are saved on the user side.

@@ Line 152: / Line 152: @@
 ③ Generate challenge messages.
-====4.3.1 Generation of supporting information, <math>\Pr oof-Gen(\varepsilon,k_{ind},Z)\to proof </math>====
+====4.3.1 Generation of supporting information, <math>Proof-Gen(\varepsilon,k_{ind},Z)\to proof </math>====
 * After the GSP obtains the challenge information, calculate the <math display="inline"> Z </math> set.

@@ Line 117: / Line 117: @@
 |}
-====4.2.2 Generate labels, i.e.,  <math>TagGen(K_{\nu er},\{uf_{ij}\})\to\Phi </math>====
+====4.2.2 Generate labels,  <math>TagGen(K_{\nu er},\{uf_{ij}\})\to\Phi </math>====
 ① The third party randomly selects the corresponding authentication key <math display="inline">K_{ver}</math>.

@@ Line 100: / Line 100: @@
 In the preprocessing process, the main algorithms used are ''SliceGen''(·) and ''TagGen''(·). After the user transmits the ciphertext to the TPA, the data is sliced and the corresponding labels are generated, and the random numbers and location information are added to them, which ensures the uniqueness of the data and avoids the attacks of the server. The specific process is:
-====4.2.1 The data is processed in slices, i.e., <math>SliceGen(UF,s,t)\to\{uf_{ij}\}</math>====
+====4.2.1 The data is processed in slices, <math>SliceGen(UF,s,t)\to\{uf_{ij}\}</math>====
 * The TPA divides <math display="inline"> UF </math> into <math display="inline"> s </math> data blocks, which gives:  <math>UF=\left\{uf_i\right\}_{1\leq i\leq s\leq n^{\prime}}</math>.