Oblivious transfer method over replicated database and binary erasure channel

Abstract

The present invention discloses an oblivious transmission method under a replicated database and a binary erasure channel. The implementation process of the method includes sending a random sequence, generating an index set, and generating a request message and a reply message. The present invention utilizes the erasure characteristics of the channel and the non-collusion characteristics between databases to complete the scheme design, meet the requirements of oblivious transmission, and the transmission rate can reach the upper limit of the transmission capacity under the model.

Description

Technical Field

[0001] The present invention relates to the technical field of information theory, and in particular to a solution for the problem of two-choice oblivious transmission under two messages, two replicated databases and a binary erasure multiple access channel. Background Art

[0002] In the traditional oblivious transmission model, the database and the user are connected by a noisy channel and a noiseless channel, and the oblivious transmission can be completed by alternating the use of the two channels. In the case of dual databases, each database has a separate noiseless channel connected to the user, and the two databases use the binary erasure multiple access channel as a noise channel to connect to the user. Using the traditional two-or-one oblivious transmission scheme, in this case, only half of the upper limit of the transmission capacity can be achieved. Therefore, the design of a new transmission scheme for this model is meaningful. In view of this situation, the present invention designs a corresponding two-or-one oblivious transmission scheme. Summary of the invention

[0003] Technical problem: The technical problem to be solved by the present invention is to provide a two-choice oblivious transmission scheme for a replicated database and a binary erasure multiple access channel model. The random messages to be sent are grouped by utilizing the channel characteristics and the characteristics that there is no collusion between databases, and the composition of the request message and the composition of the reply message are designed according to the needs of the user, thereby completing the design of the scheme.

[0004] Technical solution: The technical solution adopted by the present invention is as follows:

[0005] (1) First, we consider the problem of two-choice oblivious transfer under two messages, two replicated databases, and a binary erasure multiple access channel. There are two messages stored in both databases, denoted by K0 and K1. The user wants to obtain the message K in database z , where Z∈{0,1}. At the beginning of the protocol, database 1 and database 2 send binary random sequences through the binary erasure multiple access channel. Where X1, X2∈{0,1}. The user receives a random sequence Y through the channel. n , where Y = X1 + X2∈{0,1,2}, n is the length of the random sequence, that is, the number of times the channel is used. Databases 1 and 2 will divide the two stored messages K0 and K1 into four sub-messages respectively.

[0006] (2) The user receives the random sequence Y n After that, two subscript index sets G and B are generated, where G = {i|Y i =0,2}, B = {i|Y i=1}. Define the length nβ as min{|G|,|B|}, which is the shorter length of sets G and B. Then the user randomly selects two sets of length Disjoint sets G1 and G2 of length , randomly select two sets of length The user randomly reorders the order of the four sub-messages of messages K0 and K1 in the database, and uses letters (a1, a2, a3, a4) to represent the four parts of message K0 after reordering, and (b1, b2, b3, b4) to represent the four parts of message K1 after reordering. This order is only known to the user.

[0007] (3) The user sends the following message to the two databases through the noiseless channel according to the required information:

[0008] When Z=0, the user sends request messages Q1 and Q2 to databases 1 and 2 respectively. The content of Q1 is to request sub-messages a1, b1 and a3+b2 from database 1, where the plus sign represents bitwise modulo 2 addition, i.e. bitwise XOR, and the content of Q2 is to request sub-messages a2, b2 and a4+b1 from database 2. At the same time, the user sets Equal to (G1, G2, B1, B2), and send the four sets to the two databases at the same time.

[0009] When Z=1, the user sends request messages to databases 1 and 2 respectively. The content of Q1 is to request sub-messages a1, b1 and b3+a2 from database 1, and the content of Q2 is to request sub-messages a2, b2 and b4+a1 from database 2. At the same time, the user sets Equal to (B1, B2, G1, G2), and send the four sets to the two databases at the same time.

[0010] (4) After receiving the message, databases 1 and 2 send reply messages A1 and A2 to the user through a noise-free channel.

[0011] When Q1=(a1,b1,a3+b2), the structure of A1 is: and When Q1=(a1,b1,b3+a2), its structure is: and

[0012] When Q2=(a2,b2,a4+b1), the structure of A2 is: and When Q2=(a2,b2,b4+a1), its structure is: and

[0013] in Indicates the inversion operation of X1. The plus sign is bitwise modulo 2 addition. After receiving the reply message, the user can solve all the required sub-messages (a1, a2, a3, a4) or (b1, b2, b3, b4) based on messages A1 and A2, but cannot solve any information of the other message.

[0014] Beneficial effects: The present invention proposes a two-choice oblivious transmission scheme for a dual-copy database and a binary erasure multiple access channel model, which utilizes the channel characteristics of the binary erasure multiple access channel and the random sequence sent on the channel to generate a key, and utilizes the non-collusion characteristics between databases to design a symmetric request message structure. The user requests different parts of the required message from the two databases, and the database encrypts the message with the key. This scheme ensures that the database cannot obtain the information of the user's required message from the request message. The user can only decrypt the required message through the key and cannot obtain information of other messages. Calculations show that the transmission rate under this scheme reaches the upper limit of the transmission capacity. Therefore, the present invention can reach the upper limit of the transmission capacity while ensuring the reliability and confidentiality of the transmission. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is the reply message structure of the two databases when the user demand Z is 0 or 1. DETAILED DESCRIPTION

[0016] The technical solution of the present invention is described in detail below, but the protection scope of the present invention is not limited to the implementation examples.

[0017] The present invention proposes a two-or-the-other oblivious transmission scheme for two messages, two replicated databases and a binary erasure multiple access channel.

[0018] An embodiment is given below:

[0019] (1) First, we consider the problem of two-choice oblivious transfer under two messages, two replicated databases, and a binary erasure multiple access channel. There are two messages stored in both databases, denoted by K0 and K1. The user wants to obtain the message K in database z , where Z∈{0,1}. At the beginning of the protocol, database 1 and database 2 send binary random sequences through the binary erasure multiple access channel. Where X1, X2∈{0,1}. The user receives a random sequence Y through the channel. n , where Y = X1 + X2∈{0,1,2}, n is the length of the random sequence, that is, the number of times the channel is used. Databases 1 and 2 will divide the two stored messages K0 and K1 into four sub-messages.

[0020] (2) The user receives the random sequence Y n After that, two subscript index sets G and B are generated, where G = {i|Y i =0,2}, B = {i|Y i =1}. Define the length nβ as min{|G|,|B|}, which is the shorter length of sets G and B. Then the user randomly selects two sets of length Disjoint sets G1 and G2 of length , randomly select two sets of length The user randomly reorders the order of the four sub-messages of messages K0 and K1 in the database, and uses letters (a1, a2, a3, a4) to represent the four parts of message K0 after reordering, and (b1, b2, b3, b4) to represent the four parts of message K1 after reordering. This order is only known to the user.

[0021] (3) The user sends the following message to the two databases through the noiseless channel according to the required information:

[0022] When Z=0, the user sends request messages Q1 and Q2 to databases 1 and 2 respectively. The content of Q1 is to request sub-messages a1, b1 and a3+b2 from database 1, where the plus sign represents bitwise modulo 2 addition, i.e. bitwise XOR, and the content of Q2 is to request sub-messages a2, b2 and a4+b1 from database 2. At the same time, the user sets Equal to (G1, G2, B1, B2), and send the four sets to the two databases at the same time.

[0023] When Z=1, the user sends request messages to databases 1 and 2 respectively. The content of Q1 is to request sub-messages a1, b1 and b3+a2 from database 1, where the plus sign represents bitwise modulo 2 addition, i.e. bitwise XOR. The content of Q2 is to request sub-messages a2, b2 and b4+a1 from database 2. Equal to (B1, B2, G1, G2), and send the four sets to the two databases at the same time.

[0024] (4) After receiving the message, databases 1 and 2 send reply messages A1 and A2 to the user through a noise-free channel. The structures of reply messages A1 and A2 are as follows: Figure 1 As shown. Indicates the inversion operation of X1. The plus sign indicates bitwise modulo 2 addition. We assume that the message required by the user is K0. After receiving messages A1 and A2, the user knows the sequence due to the channel characteristics. Equal to Y(G1), sequence Equal to Y(G2), sequence Equal to Y(G1) and the sequence is equal to Y(G2), so the user can solve sub-messages a1 and a2. At the same time, the answer in message A2 and By performing a modulo-2 sum, we can solve sub-message a3. Similarly, we can solve a4. At this point, all the required sub-messages are solved. The user can get K0.

Claims

1. An oblivious transmission method under a replicated database and a binary erasure channel, for the problem of two-choice oblivious transmission under two replicated databases and a binary erasure multiple access channel, characterized in that: The steps include: (1) There are two messages stored in both databases, denoted by K0 and K1. The user wants message K in database Z , where Z∈{0,1}; at the beginning of the protocol, database 1 and database 2 send binary random sequences through the binary erasure multiple access channel Where X1, X2∈{0, 1}; the user receives a random sequence Y through the channel n , where Y = X1 + X2∈{0, 1, 2}, n is the length of the random sequence, that is, the number of times the channel is used; databases 1 and 2 divide the two messages K0 and K1 stored into four sub-messages; (2) The user receives the random sequence Y n After that, it is divided into two sets G and B, where G = {i|Y i =0,2},B={i|Y i =1}; Define the length nβ as min{|G|,|B|}, which is the shorter length of sets G and B. Then the user randomly selects two values ​​of length Disjoint sets G1 and G2 of length , randomly select two sets of length disjoint sets B1 and B2; at the same time, the user randomly rearranges the order of the four sub-messages of messages K0 and K1 in the database in advance, and uses letters a1, a2, a3, a4 to represent the four parts of message K0 after reordering, and uses b1, b2, b3, b4 to represent the four parts of message K1 after reordering; this order is only known to the user; (3) The user sends message request messages Q1 and Q2 and a random sequence index set to the two databases through a noise-free channel based on the required information. and (4) After receiving the message, databases 1 and 2 send reply messages A1 and A2 to the user through a noise-free channel. After receiving the reply message, the user deciphers all the required sub-messages (a1, a2, a3, a4) or (b1, b2, b3, b4) based on messages A1 and A2, but cannot decipher any information of the other message.

2. The oblivious transmission method under a replicated database and a binary erasure channel as claimed in claim 1, characterized in that: The specific steps of step (3) are as follows: When Z=0, the user sends request messages Q1 and Q2 to databases 1 and 2 respectively. The content of Q1 is to request sub-messages a1, b1 and a3+b2 from database 1, where the plus sign represents bitwise modulo 2 addition, i.e. bitwise XOR; the content of Q2 is to request sub-messages a2, b2 and a4+b1 from database 2; at the same time, the user orders the set Equal to (G1, G2, B1, B2), and send the four sets to the two databases at the same time; When Z=1, the user sends request messages Q1 and Q2 to databases 1 and 2 respectively. The content of Q1 is to request sub-messages a1, b1 and b3+a2 from database 1; the content of Q2 is to request sub-messages a2, b2 and b4+a1 from database 2. At the same time, the user sends a request to the collection Equal to (B1, B2, G1, G2), and send the four sets to the two databases at the same time.

3. The oblivious transmission method under a replicated database and a binary erasure channel as claimed in claim 2, characterized in that: The specific steps of step (4) are as follows: Database 1 will random sequence Perform bitwise inversion, and use the inverted sequence Indicates that database 1 receives request message Q1 and set and After that, all sub-messages of the requested message K0 are combined with and The random sequence corresponding to the index in The elements in are encrypted, and all sub-messages of the requested message K1 are encrypted with the set and The random sequence corresponding to the index in The essence of encryption is to perform bitwise modulo-2 addition on the requested information and the random sequence; the encrypted message constitutes the reply message A1, and when Q1 = (a1, b1, a3 + b2), its structure is: and When Q1=(a1,b1,b3+a2), its structure is: and Database 2 receives request message Q2 and collection and After that, all sub-messages of the requested message K0 are combined with and The random sequence corresponding to the index in The elements in are encrypted, and all sub-messages of the requested message K1 are encrypted with the set and The random sequence corresponding to the index in The elements in are encrypted; the essence of encryption is to perform bitwise modulo-2 addition on the desired information and the random sequence; the encrypted message constitutes the reply message A2, and when Q2 = (a2, b2, a4 + b1), its structure is: and When Q2 = (a2, b2, b4 + a1), its structure is: and

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