A two-choice oblivious transmission method under a single-privacy eavesdropping channel model

Abstract

The present invention discloses a two-choice oblivious transmission scheme under a single-privacy eavesdropping channel model. The meaning of single privacy is that neither the sending end nor the receiving end will collude with the eavesdropper. The specific implementation scheme includes sending random messages, dividing the received random messages into three sets according to channel characteristics, calculating the required key length, generating keys using a double random clustering method, and using the keys for encrypted communication. The length of the key is calculated according to the channel capacity formula of the eavesdropping channel, and a key is generated using the random message in the first set to encrypt and send one bit, and the one-bit information is used to encrypt the selected bit of the receiving end. Then, two keys are generated using the random messages in the latter two sets, wherein the two keys satisfy that the receiving end can only decrypt one key, while the eavesdropper cannot decrypt both keys, and the private message of the sending end is encrypted using the two keys, and the required oblivious transmission communication can be completed by sending it to the receiving end.

Description

Technical Field

[0001] The present invention belongs to the technical field of information theory, and in particular relates to a two-choice oblivious transmission method under a single-privacy eavesdropping channel model. Background Art

[0002] In the traditional oblivious transmission model, the sender and the receiver are linked by a noisy channel and a noiseless channel. By alternating the two channels, oblivious transmission can be achieved. In the oblivious transmission problem with an eavesdropper, the eavesdropper can monitor all the information from the sender to the receiver on the noiseless channel, and can access the noisy channel to eavesdrop on the random messages sent from the sender to the receiver. This makes the traditional oblivious transmission protocol no longer able to well guarantee the privacy information of the sender and the receiver. Single privacy means that neither the sender nor the receiver will collude with the eavesdropper. In such a scenario, existing research can solve the oblivious transmission problem under the eavesdropping channel as an independent binary erasure broadcast channel. However, when the eavesdropping channel is a physically degraded binary erasure broadcast channel, although the scheme can guarantee the confidentiality of the privacy information of the sender and the receiver, the transmission capacity is low. Summary of the invention

[0003] The present invention aims to provide a two-choice oblivious transmission method under a single privacy eavesdropping channel model to solve the technical problem that the existing scheme cannot simultaneously guarantee the confidentiality of the privacy information of the sender and the receiver and the transmission capacity is also low.

[0004] In order to solve the above technical problems, the specific technical solutions of the present invention are as follows:

[0005] A two-choice oblivious transmission method under a single-privacy eavesdropping channel model comprises the following steps:

[0006] Step 1: First, for the problem of inadvertent transmission of two messages in the presence of an eavesdropper, the sender and the receiver are connected through two channels, one is a noisy channel and the other is a noiseless channel. The eavesdropper can passively eavesdrop on all the information on the noiseless channel and connect to the sender using a noisy channel. W(Y|X) is used to describe the noisy channel from the sender to the receiver, and W(Z|X) is used to describe the noisy channel from the sender to the eavesdropper; the sender has two messages, represented by K0 and K1; the receiver receives a message from the sender, represented by K C Indicates, where bit C∈{0,1} is selected; it is agreed before the start of the protocol that there is a random variable S. When S=0, the sender uses key F0 to encrypt message K0 and key F1 to encrypt message K1; if S=1, key F1 is used to encrypt message K0 and key F0 is used to encrypt message K1. This agreement is known to the sender, the receiver and the eavesdropper.

[0007] Step 2: The transmitter uses a noisy channel to pre-send a random tuple X=(X1, ..., X1) of length n to the receiver. n ), after receiving the random tuple Y = (Y1, ..., Yn), the receiving end divides it into two parts according to the channel characteristics, and stores the subscript indexes of the two parts in the sets G and B respectively;

[0008] Step 3: Use αn elements in set G to form set L α ; Through the noiseless channel, the set L α Transmitted to the sender, the sender randomly and uniformly generates a bit random variable S; the sender uses the elements in the tuple X corresponding to the subscript index contained in the set Lα to generate the key F α and auxiliary decrypted message M α , and using the key F α To encrypt a bit random variable S; the encrypted message and the auxiliary decryption message M are transmitted through a noiseless channel α After being transmitted to the receiving end, the receiving end decrypts the key F according to the key characteristics. α , and the eavesdropper cannot solve it, so only the receiver gets the value of the random variable S;

[0009] Step 4. According to the random variable S and the channel characteristics, the receiving end selects 2βn elements from the sets G and B to form sets L0 and L1 of length βn according to the designed structure; the receiving end transmits the sets L0 and L1 to the sending end using a noiseless channel, and the sending end generates keys F0 and F1 and auxiliary decryption messages M0 and M1 according to the elements in the tuple X corresponding to the subscript indexes in the sets L0 and L1; encrypts messages K0 and K1 using F0 and F1; and transmits the encrypted messages M0 and M1 to the sending end using a noiseless channel. M0 and M1 are sent to the receiving end, and the receiving end decrypts the key So we get the message K C .in Represents the modulo-two sum, i.e., message K C and The numbers in each digit (binary 0 and 1) are added and the modulo 2 is taken. It means that when the modulo 2 sum of C and S is 0, use F0 and K C Modulo 2 sum, when it is 1, use F1 and K C Modulo two and.

[0010] Furthermore, the channel model established in step 1 is as follows:

[0011]

[0012] Among them, Y0 belongs to the alphabet set Y0, Y1 belongs to the alphabet set Y1, and the alphabet set Y0 and the alphabet set Y1 do not intersect; Z0 belongs to the alphabet set Z0, Z1 belongs to the disjoint alphabet set Z1, and the alphabet set Z0 and the alphabet set Z1 do not intersect; ∈1 is the probability of the transmitted character falling into the channel W(Y1|X), 1-∈1 is the probability of the transmitted character falling into the channel W(Y0|X), among which ∈=∈1∈2+(1-∈1)∈3, ∈2 is the probability that Z belongs to Z1 given that Y belongs to Y1, and ∈3 is the probability that Z belongs to Z1 given that Y belongs to Y0.

[0013] Furthermore, the specific steps of step 2 are as follows:

[0014] After receiving the tuple Y, the receiver divides it into two sets according to the letter sets corresponding to its elements, namely G = {i|Y i ∈Y0}, B={i|Y i ∈Y1}, i=1,..n, the length of set G is (1-∈1)n, and the length of set B is ∈1n.

[0015] Furthermore, the specific steps of step 3 are as follows:

[0016] Uniformly randomly select αn elements from the set G to form a set Lα, where α can be arbitrarily small. The sender receives the set L α Then, using the set L α The tuple element corresponding to the subscript index stored in Generate key F α and auxiliary decrypted message M α The key generation method is double random clustering method, and the generated key F α The length of is αn(I(X;Y0)-∈3I(X;Z1)-(1-∈3)I(X;Z0)), where I(;) is the mutual information.

[0017] Furthermore, the composition structures of the sets L0 and L1 in step 4 are as follows:

[0018] Let βn represent the length of sets L0 and L1, where α is the set L in step 3 α The length of the set L divided by n α The ratio of the length of the total random tuple X, Represents rational numbers.

[0019] When S=0, When, from the set G\L α Uniformly randomly select βn elements from the set L C Among them, G\L α represents the set G minus the set L αThe remaining set of elements after the element in step 3 has been used. α Therefore, the set L cannot be used in this step. α elements in; select βn elements uniformly and randomly from set B and put them into set L1-C;

[0020] When S=1, When, from the set G\L α Uniformly randomly select βn elements from the set L 1-C In; uniformly randomly select βn elements from set B and put them into set L C middle;

[0021] When S=0, When, from the set G\L α Uniformly randomly select βn elements from the set L C In; uniformly randomly select ∈1n elements from set B, set G\(L C ∪L α ) uniformly randomly select (β-∈1)n elements and put them into the set L 1-C In; if Then from the set L C Uniformly select (2β-1)n elements from the set L 1-C middle;

[0022] When S=1, When, from the set G\L α Uniformly randomly select βn elements from the set L 1-C In; uniformly randomly select ∈1n elements from set B, set G\(L 1-C ∪L α ) uniformly randomly select (β-∈1)n elements and put them into the set L C In; if Then from the set L 1-C Uniformly select (2β-1)n elements from the set L C middle.

[0023] Furthermore, the lengths of the keys F0 and F1 in step 4 are selected as follows:

[0024] Using the double random clustering method, the tuple elements corresponding to L0 and L1 are The equal-length keys F0 and F1 and the auxiliary decryption messages M0 and M1 are obtained respectively. The lengths of the keys F0 and F1 are determined by the following formula:

[0025]

[0026] Where i∈{0,1}, I(;) is the mutual information, and its calculation formula is:

[0027] Where p(x, y) represents the joint probability of X and Y, p(x) represents the probability of X, and p(y) represents the probability of Y.

[0028] The two-choice oblivious transmission method under a single-privacy eavesdropping channel model of the present invention has the following advantages:

[0029] In step 3, the present invention introduces a random variable with a length of one bit, and uses a small transmission rate to transmit this one bit from the sending end to the receiving end, and it cannot be eavesdropped by an eavesdropper. The privacy information of the receiving end, i.e., the selected bit, can be encrypted through this one-bit random variable, and a corresponding oblivious transmission protocol is designed to ensure that when the sending end and the receiving end complete the two-choice oblivious transmission protocol, the privacy information of both parties will not be obtained by the eavesdropper. And because only a small part of the transmission rate is consumed in step 3 to encrypt the privacy information of the receiving end, i.e., the selected bit, most of the rate can be used to encrypt the private message transmitted by the sending end in step 4, thereby improving the transmission capacity. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a schematic diagram of the single privacy eavesdropping channel two-choice oblivious transmission model of the present invention. DETAILED DESCRIPTION

[0031] In order to better understand the purpose, structure and function of the present invention, the following further describes in detail the two-choice oblivious transmission method under a single privacy eavesdropping channel model of the present invention in conjunction with the accompanying drawings.

[0032] The present invention proposes a two-choice oblivious transmission method under a single privacy eavesdropping channel model.

[0033] An embodiment is given below:

[0034] Step 1: First, we need to solve the problem of inadvertent transmission of messages in the case of eavesdropping. Figure 1 As shown in the figure, Alice represents the sender and Bob represents the receiver. The sender and the receiver are connected through two channels, one is a noisy channel and the other is a noiseless channel. The eavesdropper can passively eavesdrop on all the information on the noiseless channel and connect to the sender using a noisy channel. Use W(Y|X) and W(Z|X) to describe the channel model from the sender to the receiver and the eavesdropper respectively. The sender has two messages, represented by K0 and K1. Bob represents the receiver. The message that the receiver wants from the sender is represented by K CRepresents, where C∈{0,1}. It is agreed before the start of the protocol that there is a random variable S. When S=0, the sender uses key F0 to encrypt message K0 and key F1 to encrypt message K1. If S=1, key F1 is used to encrypt message K0 and key F0 is used to encrypt message K1. This agreement is known to the sender, receiver and eavesdropper.

[0035] The channel model established is as follows:

[0036]

[0037] Among them, Y0 belongs to the alphabet set Y0, Y1 belongs to the alphabet set Y1, and the alphabet set Y0 and the alphabet set Y1 do not intersect; Z0 belongs to the alphabet set Z0, Z1 belongs to the disjoint alphabet set Z1, and the alphabet set Z0 and the alphabet set Z1 do not intersect; ∈1 is the probability of the transmitted character falling into the channel W(Y1|X), 1-∈1 is the probability of the transmitted character falling into the channel W(Y0|X), among which ∈=∈162+(1-∈1)∈3, ∈2 is the probability that Z belongs to Z1 given that Y belongs to Y1, and ∈3 is the probability that Z belongs to Z1 given that Y belongs to Y0.

[0038] Step 2: The transmitter uses a noisy channel to pre-send a random tuple X=(X1, ..., X1) of length n to the receiver. n ).like Figure 1 As shown, the receiving end receives a random tuple Y = (Y1, ..., Yn), and divides the random tuple Y into two parts according to the channel characteristics, and stores the subscript indexes of the two parts in sets G and B respectively, where G = {i|Yi∈Y0}, B = {i|Y i ∈Y1}, i=1,..n, the length of set G is (1-∈1)n, and the length of set B is ∈1n.

[0039] Step 3: Randomly and uniformly select αn elements from the set G to form the set L α . Through the noiseless channel, the set L α Transmitted to the sender, the sender randomly and uniformly generates a random variable S. The sender uses the elements in the tuple X corresponding to the subscript index contained in the set to generate a key F of length αn[I(X;Y0)-∈3I(X;Z1)-(1-∈3)I(X;Z0)] through a double random clustering method. α and auxiliary decrypted message M α , and use the key to encrypt a bit random variable S, and transmit the encrypted message and M through a noiseless channel α Transmitted to the receiving end. According to the key characteristics, the receiving end can decrypt the key F α , and the eavesdropper cannot solve it. Therefore, only the receiver can get the value of S.

[0040] The specific steps are to randomly select αn elements uniformly from the set G to form the set Lα, where α can be arbitrarily small; after the sender receives the set Lα, the tuple elements corresponding to the subscript indexes stored in the set Lα are used to generate the secret key Fα and the auxiliary decryption message M α , and the method for generating the secret key is the double random clustering method, and the generated secret key F α has a length of αn[I(X; Y0) - ∈3I(X; Z1) - (1 - ∈3)I(X; Z0)]. Where I(; ) is the mutual information.

[0041] Step 4: According to the random variable S and the channel characteristics, the receiver will select some of the elements from the sets G and B and form the sets L0 and L1 according to the designed structure. The composition structures of the sets L0 and L1 are as follows:

[0042] Let βn represent the lengths of the sets L0 and L1, where

[0043] When S = 0, then βn elements are randomly selected uniformly from the set G\L α and put into the set L C ; βn elements are randomly selected uniformly from the set B and put into the set L 1-C .

[0044] When S = 1, then βn elements are randomly selected uniformly from the set G\L α and put into the set L 1-C ; βn elements are randomly selected uniformly from the set B and put into the set L C .

[0045] When S = 0, then βn elements are randomly selected uniformly from the set G\L α and put into the set L C ; ∈1n elements are randomly selected uniformly from the set B, and (β - ∈1)n elements are randomly selected uniformly from the set G\(L C ∪L α ) and put into the set L 1-C . If then (2β - 1)n elements are randomly selected uniformly from the set L C and put into the set L 1-C .

[0046] When S = 1, then βn elements are randomly selected uniformly from the set G\L α and put into the set L 1-CIn; uniformly randomly select ∈1n elements from set B, set G\(L 1-C ∪L α ) uniformly randomly select (β-∈1)n elements and put them into the set L C If Then from the set L 1-C Uniformly select (2β-1)n elements from the set and put them into the set L C middle.

[0047] The receiving end transmits the sets L0 and L1 to the sending end using a noiseless channel. The sending end generates keys F0, F1 and auxiliary decryption messages M0, M1 respectively by double random clustering method according to the elements in the tuple X corresponding to the subscript index in the sets L0 and L1. The lengths of the keys F0 and F1 are selected as follows:

[0048] Using the double random clustering method, L0 and L1 can be used to obtain equal-length keys F0 and F1 respectively. The length of keys F0 and F1 is determined by the following formula:

[0049]

[0050] Where i∈{0,1}, I(;) is the mutual information, and its calculation formula is:

[0051] Where p(x, y) represents the joint probability of X and Y, p(x) represents the probability of X, and p(y) represents the probability of Y.

[0052] Encrypt the message K0, K1 with keys F0 and F1. Then use the noiseless channel to send the encrypted message The auxiliary decryption messages M0 and M1 are sent to the receiving end. The receiving end can decrypt the key So we can get the message K C .

[0053] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A two-choice oblivious transmission method under a single-privacy eavesdropping channel model, characterized in that: The following steps are involved: Step 1: First, for the problem of inadvertent transmission of messages with two choices in the presence of an eavesdropper, the sender and the receiver are connected through two channels, one is a noisy channel and the other is a noiseless channel. The eavesdropper can passively eavesdrop on all the information on the noiseless channel, but cannot change the message, and is connected to the sender through a noisy channel; W(Y|X) is used to describe the noise channel from the sender to the receiver, and W(Z|X) is used to describe the noise channel from the sender to the eavesdropper; The sender has two messages, represented by K0 and K1; the receiver receives a message from the sender, represented by K C Indicates, where bit C∈{0,1} is selected; it is agreed before the start of the protocol that there is a random variable S with a length of one bit. When S=0, the sender uses key F0 to encrypt message K0 and key F1 to encrypt message K1; if S=1, key F1 is used to encrypt message K0 and key F0 is used to encrypt message K1. This agreement is known to the sender, the receiver and the eavesdropper. Step 2: The sender uses a noisy channel to pre-send a random tuple X=(X1,…,X n ), the receiving end receives a random tuple Y=(Y1,…,Y n ), divide it into two parts according to the channel characteristics, and store the subscript indexes of the two parts in sets G and B respectively; Step 3: Use αn elements in set G to form set L α ; Through the noiseless channel, the set L α Transmitted to the sender, the sender randomly and uniformly generates a random variable S with a length of one bit; the sender uses the set L α Generate the key F from the element in tuple X corresponding to the subscript index contained in α and auxiliary decrypted message M α , and using the key F α De-encrypt the random variable S; transmit the encrypted message and the auxiliary decryption message M through the noiseless channel α After being transmitted to the receiving end, the receiving end decrypts the key F according to the key characteristics. α , and the eavesdropper cannot solve it, so only the receiver gets the value of the random variable S; Step 4. According to the random variable S and the channel characteristics, the receiving end selects 2βn elements from the sets G and B, and forms two sets L0 and L1 of length βn according to the designed structure; the receiving end transmits the sets L0 and L1 to the sending end using a noiseless channel, and the sending end generates keys F0 and F1 and auxiliary decryption messages M0 and M1 according to the elements in the tuple X corresponding to the subscript indexes in the sets L0 and L1; encrypts messages K0 and K1 using F0 and F1; and transmits the encrypted information K0 and K1 to the sending end using a noiseless channel. C ⊕F C⊕S , M0 and M1 are sent to the receiving end, and the receiving end decrypts the key F C⊕S , so we get the message K C ; where ⊕ represents the modulo-two sum, i.e., the message K C With F C⊕S Add the numbers on each digit and take the modulo 2; F C⊕S It means that when the modulo 2 sum of C and S is 0, use F0 and K C Modulo 2 sum, when it is 1, use F1 and K C Modulo two and; The composition structure of the sets L0 and L1 in step 4 is as follows: Let βn represent the length of sets L0 and L1, where α is the set L in step 3 α The length of the set L divided by n α The ratio of the length of the total random tuple X, represents rational numbers; When S=0, When, from the set G\L α Uniformly randomly select βn elements from the set L C Among them, G\L α represents the set G minus the set L α The remaining set of elements after the element in step 3 has been used. α Therefore, the set L cannot be used in this step. α elements in; select βn elements uniformly and randomly from set B and put them into set L 1-C middle; When S=1, When, from the set G\L α Uniformly randomly select βn elements from the set L 1-C In; uniformly randomly select βn elements from set B and put them into set L C middle; When S=0, When, from the set G\L α Uniformly randomly select βn elements from the set L C In; uniformly randomly select ∈1n elements from set B, set G\(L C ∪L α ) uniformly randomly select (β-∈1)n elements and put them into the set L 1-C In; if Then from the set L C Uniformly select (2β-1)n elements from the set L 1-C middle; When S=1, When, from the set G\L α Uniformly randomly select βn elements from the set L 1-C In; uniformly randomly select ∈1n elements from set B, set G\(L 1-C ∪L α ) uniformly randomly select (β-∈1)n elements and put them into the set L C In; if Then from the set L 1-C Uniformly select (2β-1)n elements from the set L C middle; The lengths of the keys F0 and F1 in step 4 are selected as follows: Using the double random clustering method, the tuple elements corresponding to L0 and L1 are The equal-length keys F0 and F1 and the auxiliary decryption messages M0 and M1 are obtained respectively. The lengths of the keys F0 and F1 are determined by the following formula: Where i∈{0,1}, I(;) is the mutual information, ∈1 is the probability that the transmitted symbol falls into the channel W(Y1|X), where ∈=∈1∈2+(1-∈1)∈3, ∈2 is the probability that Z belongs to Z1 given that Y belongs to Y1, and ∈3 is the probability that Z belongs to Z1 given that Y belongs to Y0; The calculation formula of mutual information is: Where p(x,y) represents the joint probability of X and Y, p(x) represents the probability of X, and p(y) represents the probability of Y.

2. The method for alternative oblivious transmission under the single-privacy eavesdropping channel model according to claim 1, characterized in that: The channel model established in step 1 is as follows: Among them, Y0 belongs to the alphabet set Y0, Y1 belongs to the alphabet set Y1, and the alphabet set Y0 and the alphabet set Y1 do not intersect; Z0 belongs to the alphabet set Z0, Z1 belongs to the disjoint alphabet set Z1, and the alphabet set Z0 and the alphabet set Z1 do not intersect; ∈1 is the probability of the transmitted character falling into the channel W(Y1|X), 1-∈1 is the probability of the transmitted character falling into the channel W(Y0|X), among which ∈=∈1∈2+(1-∈1)∈3, ∈2 is the probability that Z belongs to Z1 given that Y belongs to Y1, and ∈3 is the probability that Z belongs to Z1 given that Y belongs to Y0.

3. The method for alternative oblivious transmission under the single-privacy eavesdropping channel model according to claim 2 is characterized in that: Step 2 The specific steps are as follows: After receiving the tuple Y, the receiver divides it into two sets according to the letter sets corresponding to its elements, namely G = {i|Y i ∈Y0}, B={i|Y i ∈Y1}, i=1,..n, the length of set G is (1-∈1)n, and the length of set B is ∈1n.

4. The method for alternative oblivious transmission under the single-privacy eavesdropping channel model according to claim 3 is characterized in that: Step 3 The specific steps are as follows: Uniformly randomly select αn elements from the set G to form the set L α , where α can be arbitrarily small; the sender receives the set L α Then, using the set L α The tuple element corresponding to the subscript index stored in Generate key F α and auxiliary decrypted message M α The key generation method is double random clustering method, and the generated key F α The length of is αn[I(X;Y0)-∈3I(X;Z1)-(1-∈3)I(X;Z0)]; where I(;) is the mutual information.

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