WO2010095662A1

WO2010095662A1 - Encoding device, decoding device, transmission system, encoding method, decoding method, program

Info

Publication number: WO2010095662A1
Application number: PCT/JP2010/052373
Authority: WO
Inventors: 俊則荒木
Original assignee: 日本電気株式会社
Priority date: 2009-02-17
Filing date: 2010-02-17
Publication date: 2010-08-26
Also published as: JPWO2010095662A1

Abstract

Disclosed is a method whereby data size is reduced when a message is encoded and transmitted through channels. Said method comprises an adjustment parameter generation means, which selects an adjustment parameter, which is a coefficient that reduces the degree to which the capacity for pieces of message information decreases and increases the degree to which data for determining improper channels increases; a message encoding means, which generates at least two pieces of message information from the message based on an encoding procedure that takes the adjustment parameter into consideration; and a means for generating data for determining improper code words, which generates a t-degree polynomial over a finite field where the t-degree polynomial contains the message, processes the t-degree polynomial such that the pieces of message information result in differing values over the finite field, and generates data for determining improper encoded messages corresponding to the pieces of message information, where the output resulting from inputting the pieces of message information into the processed t-degree polynomial is the data for determining improper encoded messages.

Description

Encoding device, decoding device, transmission system, encoding method, decoding method, program

The present invention relates to an encoding device, a decoding device, a transmission system, an encoding method, a decoding method, a program, and a recording medium, and in particular, an encoding device, a decoding device, and a transmission system that reduce the size of data that flows through each channel. The present invention relates to an encoding method, a decoding method, and a program.

There are various methods for transmitting a message via a network (see Patent Documents 1 and 2). Such a method requires (1) a function that can send a message with sufficient accuracy even if there is a slight failure in the network. In addition, various functions are added depending on the application. In particular, (2) a function for not knowing what is being sent to the eavesdropper is also important.

As shown in FIG. 8, a transmission system that implements the message transmission method having the two functions (1) and (2) described above includes a transmission device 100, a reception device 200, and these

devices

100 and 200. And a plurality of channels 300-1 = 300-n arranged therebetween. In the example shown in FIG. 8, n channels 300-1 to 300-n are arranged between the transmission device 100 and the reception device 200.

The functions (1) and (2) described above will be specifically described as follows. That is,
Function 1: Information that flows through up to t channels can be falsified, and the receiver can receive messages sent from the transmitter with an overwhelming probability even if an unauthorized person exists.
Function 2: Information that flows through up to t channels can be falsified, and even if there is an unauthorized person who can know, the unauthorized person cannot estimate any message sent by the transmitting device.
It is a function. As described above, the t channels are channels assumed as channels that can be used by an unauthorized person to falsify information, and the number of channels, t, is the number of assumed illegal channels in the following description. Call it.

The operation of the transmission system shown in FIG. 8 has two phases. That is, a transmission phase in which a message is encoded and the encoded message is transmitted through channels 300-1 to 300-n, and a reception phase in which an encoded message received from channels 300-1 to 300-n is decoded. There is.
The transmission apparatus 100 operates in the transmission phase, and the reception apparatus 200 operates in the reception phase.

In FIG. 8, as a method of encoding and transmitting a message and receiving and decoding the transmitted message, there is a method disclosed in Non-Patent Document 1.
The method shown in Non-Patent Document 1 is a method of encoding a message into n codewords, and information about the message cannot be obtained from t or less encoded messages in the transmission phase. A message encoded using a method capable of correcting the error even if there is an error in t data or less is transmitted one by one from each channel, and in the reception phase, the transmission phase is determined from the codeword of the received message. The message is restored using a decoding method corresponding to the encoding method used in FIG.
In the method of Non-Patent Document 1, when a message is selected from elements of a set with the number of elements p, data transmitted through each channel is an element of the set with the number of elements p ^{[1 / (n−3t)]} . Note that the number of elements n is the number of channels for transmitting data, and t is the number of channels that an unauthorized person can tamper with information.
The method disclosed in Non-Patent Document 1 has an advantage that the message reception failure probability is 0, but has a problem that the capacity (size) of data transmitted through the channel increases.

As a technique for solving the problem regarding the data capacity in Non-Patent Document 1, there is a method shown in Non-Patent Document 2.
The method according to Non-Patent Document 2 can be said to be a method intended to reduce the size of data flowing through a channel instead of allowing a failure of data reception with a small probability.

The operation of the message transmission system according to Non-Patent Document 2 has two phases. That is, the two phases are a transmission phase in which a message is encoded and the encoded message is transmitted through a channel, and a reception phase in which an encoded message received from the channel is decoded. The configuration of the message transmission system according to Non-Patent Document 2 will be described with reference to FIGS.

As shown in FIG. 9, the transmission device 100 in the message transmission system according to Non-Patent Document 2 includes a message encoding unit 101 and an illegal channel specifying information generation unit 102. The receiving apparatus 200 is connected to the transmitting apparatus 100 through channels 300-1 to 300-n, and includes a message decoding unit 201 and an unauthorized channel specifying unit 202.

In addition to the message s, the message encoding unit 101 shown in FIG. 9 includes an assumed number t of unauthorized channels assumed as the number of channels by which unauthorized persons tamper information, and the number n of channels set for transmitting data. Is input (step A1 in FIG. 11).
The message encoding unit 101 generates n encoded message information V1 to Vn by executing message encoding processing using the message s, the assumed illegal channel number t, and the channel number n. Then, the message information V1 to Vn is input to the channels 300-1 to 300-n and the illegal channel specifying information generation unit 102 (step A2 in FIG. 11).
The illegal channel identification information generation unit 102 shown in FIG. 9 receives information on the assumed number of illegal channels t assumed as the number of channels that an unauthorized person has tampered with information and the number of channels n set for transmitting data. Has been. Upon receiving the message information V1 to Vn from the message encoding unit 101, the unauthorized channel specifying information generating unit 102 receives the message information V1 to Vn, the number of assumed unauthorized persons t and the number of channels that have been input. n is used to generate illegal channel specifying information A1 to An corresponding to each of the message information V1 to Vn, and the generated illegal channel specifying data A1 to An are assigned to channels 300-1 to 300-n. Input (step A3 in FIG. 11).

As shown in FIG. 10, the receiving apparatus 200 includes message information V1 to Vn encoded by the message encoding unit 101, illegal channel specifying data A1 to An generated by the illegal channel specifying information generating unit 102, and The information of the assumed illegal channel number t and the channel number n input to the message encoding unit 101 is input (step B1 in FIG. 12).

The unauthorized channel specifying unit 202 of the receiving device 200 reads the message information V1 to Vn from the channels 300-1 to 300-n (Step B2 in FIG. 12), and the message information V1 to Vn and the unauthorized channel specifying data. A1 to An are used to identify message information V1 to Vn-1 or Vn that has been tampered with when transmitted through channels 300-1 to 300-n.
When tampering is detected, the unauthorized channel specifying unit 202 generates a set L whose elements are identifiers indicating the channels 300-1 to 300-n in which the tampering has been performed (step B3 in FIG. 121). The set L is input to the message decryption unit 201. If no alteration is detected, the unauthorized channel identification unit 202 inputs an empty set indicating that no alteration has been performed on the channels 300-1 to 300-n to the message decoding unit 201.

The message decoding unit 201 receives the message information V1 to Vn from the channels 300-1 to 300-n, and the channels 300-1 to 300-n-1 that are not included in the set L input from the unauthorized channel specifying unit 202. Alternatively, it is checked whether the message information V1 to Vn-1 or Vn transmitted through 300-n are all codewords of the same message. More specifically, when the set L includes, for example, channels 300-1 to 300-50, the message decoding unit 201 uses other channels, that is, channels 300-51 to 300-51 to which are not included in the set L. For example, it is checked whether the message information V51 to Vn transmitted through 300-n are all codewords of the same message (step B4 in FIG. 12).
When the message decoding unit 201 determines that the codewords are the same message, the message decoding unit 201 outputs a message obtained from the codeword (step B5 in FIG. 12). When the message decoding unit 201 determines that they are not codewords of the same message, the message decoding unit 201 outputs a symbol indicating that reception of the message information V1 to Vn has failed (step B6 in FIG. 12).

Japanese Patent Laid-Open No. 06-350528 JP 2002-530007 A

When the method according to Non-Patent Document 2 is used, if the probability of failure in receiving a message is δ, each channel 300-1 to 300-n-1 or Data transmitted through 300-n is an element of a set of approximately the number of elements p ^{[1 / (n-2t)]} + 1 / δ.
The method according to Non-Patent Document 2 is a method of encoding a message into n pieces of data as shown in FIGS. In the transmission method of Non-Patent Document 2, the following method is adopted as the encoding method. That is, in the encoding method, information about data cannot be obtained from t or less encoded data, and the original n data can be decoded even if t or less tampered data exists. In other words, encoding is performed in such a way that it can be checked whether the codewords of n−t + 1 or more messages are all codewords of the same message. The n−t + 1 number indicates the number obtained by subtracting the assumed number of illegal channels t assumed to receive information tampering from the number n of all channels and adding one to the subtracted value. In the transmission method, by adopting the encoding method, the message is encoded into n pieces of data, and these data are transmitted one by one through each channel.
In the transmission method of Non-Patent Document 2, n illegally encoded message specifying data A1 to An are generated corresponding to n pieces of data, and these illegally encoded message specifying data A1 to An are generated as described above. It is sent to each channel along with the data. The data for specifying an illegally encoded message is data for enabling detection of t or less errors in the codeword of the message even if an error due to tampering occurs in t or less data. . ,
In the reception method of Non-Patent Document 2, using the plurality of received messages and the data for specifying illegally encoded messages, the codewords of all messages are checked for errors and then determined to be error-free. Check that all of the codewords in the message are codewords of the same message, if all are codewords of the same message, decode the message from the codewords, otherwise, in some form Outputs that message reception has failed.

In the method of Non-Patent Document 2, it has been described that the data transmitted through each of the channels 300-1 to 300-n is an element of a set of about the number of elements p ^{[1 / n-2t]} + 1 / δ. Is a message codeword (message information V1 to Vn) is an element of a set having the number of elements p ^{[1 / n-2t]} , and illegal message specifying data A1 to data for detecting an error in the codeword of this message. An is an element of a set having the number of elements 1 / δ.

In the method of Non-Patent Document 2, a message is output when all message information from channels not included in the set L is the same message codeword as described above (step B5 in FIG. 12), and only one message is output. If the codeword of the wrong message passes through the error detection process using the illegally encoded message specifying data, the message reception process fails (step B6 in FIG. 12).
Therefore, in the method of Non-Patent Document 2, a set of about 1 / δ is required as a set of data for specifying illegally encoded messages so that even a single erroneous data does not pass through the detection process. .
Therefore, in the method of Non-Patent Document 2, as the capacity of the message information V1 to Vn is reduced, the capacity of the illegally encoded message specifying data A1 to An is increased, and as a result, the channels 300-1 to 300- There is a limit to reducing the amount of information transmitted through 300-n.

In the method of Non-Patent Document 2, when an element of a set having the number of elements p is sent as a message, the codeword of the message has a size of the number of elements p ^{[1 / n−2t]} . In the method of Non-Patent Document 2, the larger the number of channels n, the smaller the value of the number of elements, but the degree of decrease in the number of elements p when the number of channels increases by one decreases. For example, even if the number of channels is increased by 1, the degree of reduction in the number of elements p is limited to a degree of reduction that is a fraction of 1 / δ.

As described above, the message transmission system according to Non-Patent Document 2 has a problem that the size of data flowing through the channel is large and there is a limit in reducing the size.

It is an object of the present invention to provide a transmission method that can reduce the size of data flowing through each channel in a message transmission system.

The encoding apparatus according to the present invention is a code that outputs n message m codewords and n illegal codeword specifying data, where t is the number of assumed illegal channels and δ is an acceptable message reception failure probability. | M | represents the bit length of m, and | m | / (t + 1-s)
+ Adjustment parameter generation means for generating an adjustment parameter s that minimizes (log1 / δ) / s, and an n- (t + s + 1) degree polynomial F over a finite field in which the message is embedded A message encoding means for generating n points on the polynomial as a codeword of the message, and generating a t-order polynomial G on a finite field with the codeword of the message as an input, and the codeword of the message generated in G Each of the above is processed so as to have a different value on the finite field, and an illegal codeword specifying data generating means for generating the output when the processed value is input in correspondence with the codeword of the message as the illegal codeword specifying data And.

The decoding device according to the present invention includes a codeword of a message that is an output of the encoding device according to the present invention, illegal codeword specifying data, the number of channels n, an assumed number of illegal channels t, an adjustment parameter s, , And outputs a message, the Reed-Solomon error correction process is performed on the incorrect codeword specifying data, and these are generated from the incorrect codeword specifying data after the correction process t Perform a restoration process of the second order polynomial, process the t-order polynomial restored for the codewords of all messages in the same way as the processing performed by the encoder, and convert the processed value to the t-order polynomial. It is judged whether the input value is equal to the codeword specific data corresponding to the codeword of the message before processing, and an illegally encoded message that outputs a list of codewords of all equal messages. And a Reed-Solomon error correction process on the codewords of the messages included in the list output by the illegally encoded message specifying means, and n- (t + s + 1) It is characterized by comprising encoded message error correction means for restoring a degree polynomial and extracting and outputting a message from the polynomial by a method corresponding to a method in which the encoding device embeds a message.

The transmission system according to the present invention is the above-described encoding apparatus according to the present invention, the encoding apparatus having a process for transmitting the output thereof, and the above-described present invention having a process for receiving the output of the encoding apparatus. And a decoding device according to the above.

The encoding method according to the present invention is a code that outputs a codeword of n messages m and n illegal codeword specific data, where t is the number of assumed illegal channels and δ is an acceptable message reception failure probability. Where | m | represents the bit length of m, and | m | / (t + 1-s)
+ Generates an adjustment parameter s that minimizes (log1 / δ) / s, and generates an n- (t + s + 1) -degree polynomial F over a finite field with embedded messages. N points are generated as codewords of the message, and a t-order polynomial G on the finite field is generated using the codeword of the message as an input, and each of the codewords of the message generated in G has a different value on the finite field. The output when the processed value is input is generated as illegal codeword specifying data in correspondence with the codeword of the message.

A decoding method according to the present invention includes a codeword of a message that is an output of the encoding method according to the present invention, illegal codeword specifying data, the number of channels n, an assumed number of illegal channels t, an adjustment parameter s, , And outputs a message, the Reed-Solomon error correction process is performed on the incorrect codeword specifying data, and these are generated from the incorrect codeword specifying data after the correction process. Perform a restoration process of the second order polynomial, process the t-order polynomial restored for the codewords of all messages in the same way as the processing performed by the encoder, and convert the processed value to the t-order polynomial. It is determined whether or not the input value is equal to the codeword specific data corresponding to the codeword of the message before processing, and a list of codewords of all the messages that are equal is output. Reed-Solomon error correction processing is performed on the codeword of the message included in the message, and an n- (t + s + 1) degree polynomial is restored from the codeword of the message after the correction processing. The message is extracted and output by a method corresponding to the method in which the message is embedded.

The encoding program according to the present invention is a code that outputs codewords of n messages m and n illegal codeword specifying data, where t is the number of assumed illegal channels and δ is an acceptable message reception failure probability. Where | m | represents the bit length of m, and | m | / (t + 1-s)
+ A function to generate an adjustment parameter s that minimizes (log1 / δ) / s and an n- (t + s + 1) th order polynomial F over a finite field with embedded messages. A function for generating n points as message codewords and a t-order polynomial G on a finite field using the message codewords as input, and each of the message codewords generated in G is on a finite field And a function for generating an output corresponding to the codeword of the message as invalid codeword specific data, by processing the value so as to have different values in the computer, and causing the computer to execute. .

A decoding program according to the present invention includes a codeword of a message that is an output of the encoding device according to claim 1, illegal codeword specifying data, the number of channels n, an assumed number of illegal channels t, and an adjustment parameter s. And a message that outputs a message, the Reed-Solomon error correction process is performed on the incorrect codeword specifying data, and these are generated from the incorrect codeword specifying data after the correction process. A t-order polynomial that has been restored to the t-order polynomial that has been restored to the code word of all messages by the same method as the processing performed by the encoding device, and that has been restored to the t-order polynomial that has been restored by the t-order polynomial. To determine whether the value entered in the message is equal to the codeword specific data corresponding to the codeword of the message before processing, and to output a list of codewords of all equal messages And a Reed-Solomon error correction process on the codeword of the message included in the list output by the illegally encoded message specifying process, and the n- (t + s + 1) th order from the codeword of the corrected message A function of restoring a polynomial and extracting and outputting a message by a method corresponding to a method in which the encoding device embeds the message from the polynomial is output to the computer.

The recording medium according to the present invention is a computer-readable recording medium for recording the processing of the program according to the present invention.

According to the present invention, it is possible to reduce the size of the data that flows through each channel, on the balance between the degree that the capacity of the message information is reduced and the degree that the illegal channel specifying data is increased.

It is a block diagram which shows the structure of the transmitter in the message transmission system which concerns on embodiment of this invention. It is a block diagram which shows the structure of the receiver in the message transmission system which concerns on embodiment of this invention. It is a block diagram which shows the structure of the computer used when building the message transmission system which concerns on embodiment of this invention on software. It is a flowchart which shows operation | movement of the transmitter in the message transmission system which concerns on embodiment of this invention. It is a flowchart which shows operation | movement of the receiver in the message transmission system which concerns on embodiment of this invention. It is a block diagram which shows concretely the structure of the unauthorized channel specific information generation part in the transmitter of the message transmission system which concerns on embodiment of this invention. It is a block diagram which shows concretely the structure of the unauthorized channel specific | specification part in the receiver of the message transmission system which concerns on embodiment of this invention. It is a block diagram which shows the structure of a general message transmission system. It is a block diagram which shows the structure of the transmitter which concerns on a nonpatent literature 2. It is a block diagram which shows the structure of the receiver which concerns on a nonpatent literature 2. 10 is a flowchart illustrating an operation of a transmission device according to Non-Patent Document 2. 10 is a flowchart showing an operation of the receiving device according to Non-Patent Document 2.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. The embodiments described below are preferred embodiments of the present invention, and thus various technically preferable limitations are given. However, the scope of the present invention is particularly limited in the following description. As long as there is no description of the effect, it is not restricted to these aspects.

The embodiment of the present invention is a scheme intended to reduce the size of data flowing through a channel, instead of allowing a failure to receive data with a small probability, for transmitting message information V1 to Vn. The following is a specific example of a method related to a case where the relationship between the number of all channels n and the number of assumed illegal channels t, which is the number of channels assumed to cause tampering on the channel, satisfies n ≧ 3t + 1. explain.

First, the basic principle in the embodiment of the present invention will be described. In the following description, the number of all channels for transmitting the message information V1 to Vn is expressed as n, and the assumed number of illegal channels assumed that tampering or the like may occur on the channel is expressed as t. Further, a transmission message (a message composed of two or more message information V1 to Vn) is expressed as m, and an acceptable message reception failure probability is expressed as δ. In the following description, the term “tamper” refers not only to the case where an unauthorized person intentionally falsifies, but also due to some factor in the process in which the message information V1 to Vn is transmitted on the channels 300-1 to 300-n. This includes cases where the message information V1 to Vv has been altered to an illegal one. Further, the assumed number of illegal channels t means the upper limit of the number of assumed illegal channels that are assumed to be falsified on the channels 300-1 to 300-n.

In the message transmission system according to the present embodiment, in the transmission phase in which the encoded message information V1 to Vn is transmitted through two or more channels 300-1 to 300-n, the degree to which the capacity of the message information V1 to Vn decreases is small. In addition, the adjustment parameter s, which is a coefficient that increases the degree of increase in the unauthorized channel specifying data A1 to An, is selected, and the message information V1 to Vn is transmitted from the message m based on the encoding method that takes into account the selected adjustment parameter s. Is generated and transmitted.
In the encoding method, information on the message m cannot be obtained from t or less encoded message information V1 to Vn-1 or Vn, and t + s or less encoded message information V1 to Vn-1 or Vn. Even if the message is falsified, the message m composed of n pieces of message information V1 to Vn can be decoded, and s or less errors among the code words (message information V1 to Vn) of nt or more messages Code words (message information V1 to Vn) of n messages that can be corrected, and the n message information V1 to Vn are transmitted. Further, the encoding method may generate code words (messages) of the n messages even if there are errors in t message information V1 to Vn-1 or Vn when generating the message information V1 to Vn. Among the information V1 to Vn), n pieces of illegally encoded message specifying data capable of detecting t errors or less are generated, and the n pieces of illegally encoded message specifying data A1 to An are transmitted.

In order to execute the encoding method in the message transmission system according to the embodiment of the present invention, the transmission apparatus 400 includes an adjustment parameter generation unit 401, a message encoding unit 402, and illegal channel identification information generation as shown in FIG. Part 403.
In the following description, it is assumed that the assumed number of illegal channels assumed that information may be falsified on channels 300-1 to 300-n is t, and the allowable message reception failure rate is δ. For m codewords of message m, when m is represented as | m |, | m | represents the bit length of m.

The adjustment parameter generation unit 401 receives the message m, the assumed number of illegal channels t, the number n of channels, and the allowable message reception failure rate δ, and the degree of reduction in the capacity of the message information V1 to Vn is small. In addition, the adjustment parameter s, which is a coefficient that increases the degree of increase in the illegal channel specifying data A1 to An, is selected, and the selected adjustment parameter s is output to the message encoding unit 402.

A method by which the adjustment parameter generation unit 401 selects the adjustment parameter s will be described. The adjustment parameter generation unit 401 selects the following equation as an example.
The following equation is expressed as follows.
| M | / (n−2t + 1−s) + log (1 / δ) / s
In the above expression, | m | means the bit length of the message m selected from the elements of the set having the number p of elements. n is the total number of channels for transmitting the message information V1 to Vn. t is an assumed number of illegal channels assumed that tampering or the like may occur on the channel. δ is an acceptable message reception failure rate.
In other words, the adjustment parameter generation unit 401 receives the message m, the assumed number of illegal channels t, the number of channels n, and the allowable message reception failure rate δ, and | m | / (n−2t + 1) The adjustment parameter s that minimizes −s) + log (1 / δ) / s is selected, and the selected adjustment parameter s is output to the message encoding unit 402.
In the present embodiment, the above formula is used when selecting the adjustment parameter s. However, the degree to which the capacity of the message information V1 to Vn decreases is small and the degree to which the illegal channel specifying data A1 to An increases. Any expression other than the above expression may be used as long as the adjustment parameter s, which is a coefficient that increases, can be selected.

The message encoding unit 402 receives the information of the message m, the number of all channels n, the assumed number of illegal channels t, and the adjustment parameter s, and based on the encoding method considering the adjustment parameter s. The message information V1 to Vn is generated from the message m, and these message information V1 to Vn are transmitted to the channels 300-1 to 300-n and the illegal channel specifying information generating unit 403.

As the encoding method, the method shown in Non-Patent Document 3 can be cited. The encoding method according to Non-Patent Document 3 is called the (a, b, c) threshold encoding method. This encoding method encodes message m into distributed information in which c messages are distributed. Among them, the secret information regarding the distribution of the message m into c pieces can be completely restored based on any a or more pieces of shared information, but the information about the secret information can be completely restored based on up to ab pieces of shared information. It has the characteristic that it cannot be obtained. Therefore, even if up to ab shared information is stolen, the secret information is not leaked, and the secret information can be restored even if up to ca shared information is destroyed. In addition, in the encoding method shown in Non-Patent Document 3, a codeword that is distributedly encoded based on the (a, b, c) threshold method is used for Reed-Solomon error correction processing, and a + 2y or more. In the codeword, y or less errors can be corrected.

In the present embodiment, the value of the adjustment parameter s is used as the y, and a, b, and c, which are the threshold values of Non-Patent Document 3, are replaced with the number of all channels n, the number of assumed illegal channels t, and the adjustment parameter s. Thus, encoding is performed using the (a, b, c) threshold method of Non-Patent Document 3.
That is, the message encoding unit 402 uses the input parameters, ie, the number n of all channels, the number t of assumed illegal channels, and the adjustment parameter s, so that a = n− (t + s), b = t + 1−s, The message m is embedded in a finite field by using the (n− (t + s) t + 1−s, n) threshold method instead of c = n, and the (n− (t + s + 1)) degree polynomial F on the finite field is embedded. And the points on the generated polynomial F are generated as n pieces of message information V1 to Vn which are message codewords. The message encoding unit 402 transmits the generated n pieces of message information V1 to Vn to the channels 300-1 to 300-n and the illegal channel specifying information generating unit 403.

By using the (a, b, c) threshold method according to Non-Patent Document 3, when the data that encodes the message m is message information V1 to Vn, the message information V1 to Vn is used as input and t on a finite field is input. An order polynomial G is generated, the generated t-order polynomial G is processed so that the message information V1 to Vn have different values on a finite field, and the message information is converted into the processed t-order polynomial G. By using the output when V1 to Vn are input as the illegally encoded message specifying data A1 to An, t or less errors in the n pieces of message information V1 to Vn are corrected by the Reed-Solomon error correction process. It is known that detection and correction are possible (Non-Patent Document 4).
Further, the t-order polynomial G can be restored based on the data for specifying the illegally encoded message A1 to An, and by checking the consistency with the values when the message information V1 to Vn is input to the t-order polynomial G. It is known that tampering of up to t message information V1 to Vn can be detected (Non-patent Document 2).

The illegal channel specifying information generating unit 403 in this embodiment receives the message information V1 to Vn from the message encoding unit 402, the assumed illegal channel number t, and the channel number n, and receives a finite field in which the message m is embedded. The above t-order polynomial G is generated, the t-order polynomial G is processed so that the message information V1 to Vn have different values on the finite field, and the message information V1 is converted into the t-order polynomial after the processing. Outputs when .about.Vn are inputted are illegally encoded message specifying data A1 to An, and the illegally encoded message specifying data A1 to An are generated in correspondence with the message information V1 to Vn. The illegally encoded message specifying data A1 corresponds to the message information V1. Similarly, the illegally encoded message specifying data An corresponds to the message information Vn.
The illegal channel specifying information generating unit 403 outputs the generated illegal encoded message specifying data A1 to An to the channels 300-1 to 300-n.

The message transmission system according to the embodiment of the present invention receives message information from the channels 300-1 to 300-n in the reception phase for decoding the message information V1 to Vn received from two or more channels 300-1 to 300-n. Each message information is received by receiving V1 to Vn and the corresponding illegally encoded message specifying data A1 to An and using the message information V1 to Vn and the illegally encoded message specifying data A1 to An. It is determined whether or not V1 to Vn are falsified illegal message information, error correction processing is performed on the message information that is not determined to be illegal message information, and the message is decoded from the corrected message information To do.

The receiving device 500 for executing the reception phase in the message transmission system according to the embodiment of the present invention includes an encoded message error correction unit 501 and an illegal channel specifying unit 502 as shown in FIG.

The illegal channel specifying unit 502 receives illegal encoded message specifying data A1 to An and message information V1 to Vn from the channels 300-1 to 300-n in addition to the assumed illegal channel number t and channel number n. Then, error correction processing is performed on the received illegally encoded message specifying data A1 to An, and the incorrect channel specifying information generating unit 403 generates based on the incorrect encoded message specifying data after the correction processing. The t-order polynomial G is restored, and the t-order polynomial G restored for all the message information V1 to Vn is processed by the same method as the processing performed by the unauthorized channel specifying information generation unit 403, The values obtained by inputting the message information V1 to Vn to the t-order polynomial are not corresponding to the message information V1 to Vn before processing. It is determined whether it is equal to the correct encoded message specifying data A1 to An, and a list of all equal encoded message specifying data A1 to An-2 or An that are equal is output as a set L.

The encoded message error correction unit 501 receives the set L from the illegal channel specifying unit 502 in addition to the assumed illegal channel number t and the channel number n, and message information V1 to Vn from the channels 300-1 to 300-n. And error correction processing is performed on the message information V1 to Vn-1 or Vn corresponding to the illegally encoded message specifying data A1 to An-1 or An not included in the set L, and the message information after the correction processing is performed. The n- (t + s + 1) degree polynomial F generated by the message encoding unit 402 based on the above is restored, and from this polynomial F, the message encoding unit 402 corresponds to a method of embedding message information V1 to Vn in a finite field. The message is extracted and output by this method.

Next, using the message transmission system according to the embodiment of the present invention, a method for encoding a message into message information and a method for decoding the message based on the encoded message information transmitted through the channel are executed. The case where it does is demonstrated.

First, the case where the method of encoding the message m into message information is executed will be described.
The adjustment parameter generation unit 401 receives the message m, the assumed illegal channel number t, the channel number n, and the allowable message reception failure rate δ (step C1 in FIG. 4), and the capacity of the message information V1 to Vn. The adjustment parameter s, which is a coefficient that increases the degree of increase of the unauthorized channel specifying data A1 to An, is selected (step C2 in FIG. 4), and the selected adjustment parameter s is encoded with the message. Output to the unit 402.

The message encoding unit 402 uses the input parameters of all the channel number n, the assumed illegal channel number t, and the adjustment parameter s, so that a = n− (t + s), b = t + 1−s, c = N, by using the (n- (t + s) t + 1-s, n) threshold method, the message m is embedded in a finite field, and the (n- (t + s + 1)) degree polynomial F over the finite field is generated Then, the generated points on the polynomial F are generated as n pieces of message information V1 to Vn which are message codewords (step C3 in FIG. 4), and the generated n pieces of message information V1 to Vn are transmitted to the channel 300. −1 to 300-n and the unauthorized channel identification information generation unit 403.

The illegal channel specifying information generating unit 403 in this embodiment receives the message information V1 to Vn from the message encoding unit 402, the assumed illegal channel number t, and the channel number n, and receives a finite field in which the message m is embedded. The above t-order polynomial G is generated, the t-order polynomial G is processed so that the message information V1 to Vn have different values on the finite field, and the message information V1 is converted into the t-order polynomial after the processing. Outputs when .about.Vn are input are illegally encoded message specifying data A1 to An, and the illegally encoded message specifying data A1 to An are generated in correspondence with the message information V1 to Vn (step C4 in FIG. 4). ) To output the illegally encoded message specifying data V1 to Vn to the channels 300-1 to 300-n.

Next, a case where a method for decoding a message based on message information encoded and transmitted through a channel will be described.

The unauthorized channel identifying unit 502 receives the unauthorized encoded message identifying data A1 to An and the message information V1 to Vn from the channels 300-1 to 300-n in addition to the assumed unauthorized channel number t and the channel number n ( Steps D1 and D2) of FIG. 5 perform error correction processing on the received illegally encoded message specifying data A1 to An, and based on the incorrect encoded message specifying data after the correction processing, the illegal channel The same method as the processing performed by the unauthorized channel specifying information generating unit 403 is performed on the t order polynomial G recovered by performing restoration processing of the t order polynomial G generated by the specific information generating unit 403 and restoring all the message information V1 to Vn. The value obtained by inputting the message information V1 to Vn into the t-order polynomial after processing is the message information before processing. It is determined whether or not the data V1 to Vn corresponding to the illegally encoded message specifying data A1 to An is equal, and a list of all equal message information V1 to Vn is output as a set L (step D3 in FIG. 5).

The encoded message error correction unit 501 receives the set L from the illegal channel specifying unit 502 in addition to the assumed illegal channel number t and the channel number n, and message information V1 to Vn from the channels 300-1 to 300-n. And performs error correction processing on the message information V1 to Vn-1 or Vn corresponding to the illegally encoded message specifying data A1 to An-1 or An not included in the set L (step D4 in FIG. 5). Then, the n- (t + s + 1) degree polynomial F generated by the message encoding unit 402 based on the message information after the correction processing is restored, and from this polynomial F, the message encoding unit 402 converts the message information V1 to Vn to finite A message is extracted and output by a method corresponding to the method embedded in the body (step D5 in FIG. 5).

As described above, according to the embodiment of the present invention, by adjusting the message encoding method using the adjustment parameter s, for example, up to s pieces of erroneous data are errors due to illegally encoded message specifying data. Even if the detection process is passed, it is possible to correct s or less errors in the codeword of the message. Therefore, the reception of the message is successful as long as at least s + 1 erroneous data does not pass through the error detection process using the illegally encoded message specifying data.
Therefore, the data transmitted through each channel can be reduced in the case where the size of the codeword of the message is hardly reduced when the number of channels is increased.

In other words, assuming that the probability that one erroneous data passes through the error detection process is ρ, if simply evaluated, the probability that s + 1 data passes through the error detection process is about ρ ^[s] . In other words, if the allowable probability is δ and δ = ρ ^[s] , the size of each illegally encoded message specifying data is 1 / ρ = 1 / (δ ^{[1 / s]} ). Compared with the method of Non-Patent Document 3, the bit length is 1 / s.

At this time, since the adjustment parameter s is selected so that | m | / (t + 1−s) + (log (1 / δ) / s is minimized, the number of channels is large in the method described in Non-Patent Document 2. Thus, it can be seen that it is efficient when the data transmitted through each channel does not decrease so much when the number of channels increases by one.

The case where n channels are used has been described above. However, if the means for realizing the channels can transmit a plurality of data generated by the transmission device separately, the n channels are used. There is no need to provide it. The assumed number of illegal channels represents the maximum number that allows tampering and eavesdropping on n sets of information generated by the transmission device. The adjustment parameter s may be input with a value calculated beforehand.

The assumed number of illegal channels means the upper limit number of assumed illegal channels. According to the message transmission system of this embodiment, the number of encoded message information up to the assumed number of channels has been altered. The encoded message information can be specified.

First, it is not necessary to transmit the distributed message information, and then transmit the illegal channel specifying information, and it may be sent at a time after all the information is generated. The adjustment parameter s is transmitted from each channel. By doing in this way, even if the value of y transmitted using less than half of the number of channels is falsified, the correct y value can be reliably received by taking a majority vote. Such a method is also used in the embodiment of the present invention.

In the above description, the transmission apparatus 400 shown in FIG. 1 and the reception apparatus 500 shown in FIG. 2 in the message transmission system according to the embodiment of the present invention are constructed as hardware, but the present invention is not limited to this. The adjustment parameter generation unit 401, the message encoding unit 402, and the illegal channel identification information generation unit 403 of the transmission apparatus 400 illustrated in FIG. 1 may be configured on software by causing a computer to execute an encoding program. It is. Furthermore, the encoded message error correcting unit 501 and the illegal channel specifying unit 502 of the receiving apparatus 500 shown in FIG. 2 may be constructed on software by causing a computer to execute a decoding program. The encoding program and the decoding program are recorded on a recording medium and are subject to commercial transactions.
An example of the computer is shown in FIG.

In FIG. 3, the processing device 10 executes predetermined processing according to a program. The input device 20 is an input device used for inputting commands and information to the processing device 10. The output device 30 is an output device for monitoring the processing result of the processing device 10.

The processing device 10 includes a CPU (Central Processing Unit) 11, a main storage unit 12, a recording medium 13, a data storage unit 14, a memory control interface unit 15, and an I / O interface unit 16. Are connected to each other.

The CPU 11 is a processor that executes a program. The main storage unit 12 temporarily stores information necessary for the processing of the CPU 11. The recording medium 13 stores a program for the CPU 11 to execute. The data storage unit 14 stores secret information and access structure data. The memory control interface unit 15 is an interface device that controls writing and reading of data in the main storage unit 12, the recording medium 13, or the data storage unit 14. I
The / O interface unit 16 is an interface device that controls data input / output with the input device 20 and the output device 30. Using this interface device, data is transmitted and received using the channel 300. The recording medium 13 is a magnetic disk, a semiconductor memory, an optical disk, or other recording medium.

Next, the message transmission system according to the embodiment of the present invention will be described in more detail based on a specific example.

In the following description, a case where n ≧ 3t + 1 holds between the number of channels n and the assumed number of illegal channels t will be described as an example. In addition, when p is a prime power, it may be a prime number itself. At this time, the finite field GF (p ^[N] ) represents an Nth-order extension field of the finite field with respect to the power p of the prime number.

The adjustment parameter generation unit 401 of the transmission apparatus 400 in the message transmission system according to the embodiment of the present invention has a value that minimizes | m | / (n−2t + 1−s) + log (1 / δ) / s for the message m. The adjustment parameter s is selected, and the adjustment parameter s is input to the message encoding unit 402. Further, the adjustment parameter generation unit 401 transmits the adjustment parameter s to the receiving device 500 through the channels 300-1 to 300-n.

The transmitter 100 is inputted with information of a message m, an assumed number of unauthorized persons t, an adjustment parameter s, and the number of all channels n. The message m, which is an element of GF (p ^[n-2ts-s] ), has (m, 0,... M ^[n-2ts-s-1] ) as a sequence of the elements of GF (p). It can be expressed as follows.

The message encoding unit 402 of the transmitting apparatus 400 has coefficients (m, 0,... M ^[n−2t−s] from the constant term on GF (p) to the n−2t−s−1 order term. ^−1] ) is randomly generated as an n− (t + s + 1) degree polynomial. This polynomial is denoted as fm (x). However, x is 1 to n. In this case, n corresponds to the total number of channels n.

Note that the message encoding unit 402 embeds the message m in a coefficient, but the message m embedding method may be any method as long as the message can be extracted from a polynomial. For example, a method of embedding the message m at n-2ts points on the polynomial may be used.

The message encoding unit 101 calculates fm (1), fm (2),..., Fm (n), and a pair Vi = (i, Vi) (i = 1) of the calculation result and the input i. , 2,..., N, Vi = fm (i)) are output to the channel 300-i as encoded message information V1 to Vn, respectively.

In the message transmission system according to the embodiment of the present invention, the message information (V1, Vn) Vi generated as described above is based on the existing (a, b, c) threshold method described in Non-Patent Document 3. This corresponds to the secret information that is distributed and encoded. Also, the message information encoded at this time is an element of the data set GF (p), but the number of erroneous values corresponding to the adjustment parameter s is included in the n−t + s encoded message information V1 to Vn. Even if included, the error can be corrected by Reed-Solomon error correction processing.

FIG. 6 is a block diagram showing more specifically the configuration of the unauthorized channel specifying information generating unit 403 shown in FIG. As illustrated in FIG. 6, the unauthorized channel identification information generation unit 403 includes an encoded message information conversion unit 601, an RS information source generation unit 602, and an RS codeword generation unit 603.

The encoded message information conversion unit 601 obtains message information V1 to Vn (Vi = (i, Vi)) that are output from the message encoding unit 402, and the message m for q satisfying q ≧ n × p. Xi = p × (i−1) + Vi (i = 1, 2,..., N) is calculated on the finite field GF (q) in which is embedded, and the calculation result is output to the RS codeword generation unit 603 To do.

The RS information source generation unit 602 generates random data e0, e1,..., Et on the finite field GF (q), and outputs the generated data to the RS codeword generation unit 603.

The RS codeword generation unit 603 includes xi (i = 1, 2,..., N) output from the encoded message information conversion unit 601 and e0, e1,... Output from the RS information source generation unit 602. · to acquire and et, Ai = e0 + e1 × xi + e2 × xi 2 + ··· + et × xi t (i = 1,2, ···, n) was calculated on the finite body GF (q), The data Ai is output to the channel 300-i (i = 1, 2,..., N) as illegally encoded message specifying data A1 to An.

On the other hand, the assumed number of unauthorized persons t and the number of channels n are input to the receiving apparatus 500 shown in FIG. In addition, the receiver 500 receives message information V1 to Vn (Vi = (i, V) from the channels 300-1, 300-2,..., 300-n.
i)), illegally encoded message specifying data A1 to An (Ai (i = 1, 2,..., n)), and adjustment parameter s are input.

The acquired message information A1, A2,..., An is a Reed-Solomon error correction code using the outputs e0, e1,. It is a code word.

Since n ≧ 3t + 1 from the premise, t errors included in the illegally encoded message specifying data A1 to An (Ai) are corrected, and the original information sources e0, e1,. It is possible. The t number corresponds to the assumed number t of illegal channels.

The unauthorized channel identifying unit 502 of the receiving device 500 receives the unauthorized encoded message identifying data A1 to An (Ai) and the message information V1 to Vn (Vi = (i, Vi)).

The illegal channel specifying unit 502 includes an RS error correction unit 701 and an illegal channel set output unit 702 as shown in FIG.

The RS error correction unit 701 executes Reed-Solomon error correction processing using the illegally encoded message specifying data A1 to An (Ai) and the message information V1 to Vn (Vi = (i, Vi)). As a result, the same original information sources e0, e1,..., Et as those generated by the RS information source generation unit 602 of the unauthorized channel specifying information generation unit 403 are restored, and the restored information sources are output to the unauthorized channel set. Output to the unit 502. At this time, an existing method may be used as the Reed-Solomon error correction process. An example of existing Reed-Solomon error correction processing is the Bale Kamp method.

Upon receiving the illegally encoded message specifying data A1 to An (Ai) and the message information V1 to Vn (Vi = (i, Vi)), the illegal channel set output unit 702 uses the acquired data. xi = p × (i-1 ) + Vi (i = 1,2, ···, n) to calculate the, Ai = e0 + e1 × xi + e2 × xi 2 + ··· + et × xi t is not satisfied assumed cheating channels t1 A set L that lists .about.tn-2 or tn is sent to the encoded message error correction unit 501. Note that ^∧ used in the equation of FIG. 6 means 冪 multiplication.

The encoded message error correction unit 501 acquires the set L from the illegal channel specifying unit 702, and message information V1 to Vn-2 corresponding to the assumed illegal channels t1 to tn-2 or tn not included in the set L. Alternatively, Reed-Solomon error correction processing is executed for Vn, and message information V1 to Vn-2 or Vn embedded in the encoded message after error correction is output.

As described above, in the transmission device 400, the message encoding unit 402 uses the (n−t + s, t + 1−s, n) threshold method to encode n pieces of encoded message information V1 to Vn (Vi (i = 1, 2). ,..., N)) are generated. The illegal channel identification information generation unit 403 uses the n pieces of encoded message information V1 to Vn (Vi) generated by the message encoding unit 402 and the t-order polynomial to generate each encoded message information V1 to Vn (Vi). ) To generate illegal channel specifying information A1 to An (Ai (i = 1, 2,..., N)).

On the other hand, the unauthorized channel specifying unit 502 of the receiving device 500 receives the message information V1 to Vn (Vi (i = 1, 2,..., N)) and the corresponding illegally encoded message specifying data A1 to An. Then, a Reed-Solomon error correction process is performed, and a set L that lists the actually assumed falsified channels t1 to tn-2 or tn is output.

The encoded message error correction unit 501 performs the Reed-Solomon error correction process on the encoded message information V1 to Vn (Vi) in which no error is detected in the Reed-Solomon error correction process by the unauthorized channel specifying unit 502, The message m embedded in the encoded message information V1 to Vn after the correction process is output.

A value xi (i = 1, 2,..., N) uniquely derived from each message information V1 to Vn (Vi (i = 1, 2,..., N)) is converted into a random t-order polynomial. The values obtained by substitution are used as the illegally encoded message specifying data A1 to An (Ai) for the message information V1 to Vn (Vi). At that time, when generating xi from the message information Vi and i so that xi ≠ xj is satisfied if Vi ≠ Vj for any message information Vi, Vj, for q satisfying q ≦ n × p, Xi = p × (i−1) + Vi (i = 1, 2,..., N) is calculated on the finite field GF (q).

In the present embodiment where the size of the encoded message information is p, the size of the set combining the sizes of the message information V1 to Vn and the sizes of the illegally encoded message specifying data A1 to Ant is p × q. This process may be performed by any method as long as the message information V1 to Vn are input to the t-order polynomial so as to be processed to have different values on the finite field used by the t-order polynomial. .

First, the probability that unauthorized message information V1 to Vn-2 or Vn is not detected by the unauthorized channel specifying unit 502 is approximately 1 / q. However, up to s pieces of invalid message information V1 to Vn-2 or Vn are corrected by the Reed-Solomon error correction process. That is, the probability that correct message information V1 to Vn-2 or Vn can be received is approximately 1-1 / q ^s . Therefore, the probability of failing to receive the message information V1 to Vn-2 or Vn is δ, and when the message information V1 to Vn-2 or Vn is selected from the set of the number of elements p, it is transmitted through the channels 300-1 to 300-n. The data to be processed are elements of a set of approximately the number of elements p ^{[1 / (n−2t−s)} + [1 / δ] ^{[1 / s]} .

When the method described in Non-Patent Document 2 is used, data transmitted through each channel is an element of a set of approximately the number of elements p ^{[1 / (n-2t)]} + 1 / δ. Here, by appropriately selecting p and δ, the size of data transmitted through each channel of the present embodiment is reduced as compared with the method described in Non-Patent Document 2.

In this embodiment, Reed-Solomon error correction processing is used as a method for correcting an error in data for specifying an illegally encoded message. However, other methods may be used as long as the error can be reliably corrected. Good.

As described above, when the number of channels is n, the assumed number of assumed illegal channels is t, and the allowable message reception failure probability is δ, when transmitting the message m, | m | An adjustment parameter s that minimizes | m | / (t + 1−s) + (log (1 / δ) / s as a length is generated, and the number of encoded messages is t or less. Even if there is no information about the message from the information and there is no t + s encoded message information, n message information can be decoded, and n−t or more message information (message codewords) Can decode n message information (message codeword) from 2t + 1 or more message information (message codeword) so that s or less errors can be corrected. Even when there are 3t + 1 or more message codewords and t or less errors, the identification of a plurality of illegally encoded messages that can detect t or less errors among the codewords of the plurality of messages described above A message is generated by using a message codeword and illegally encoded message specifying data for a transmission device that generates and transmits data for use, a codeword of the received message, and an illegally encoded message specifying data corresponding thereto. A receiving device that determines whether each of the codewords is fraudulent, performs error correction processing on the codeword of the message that has been determined to be fraudulent, and decodes the message from the codeword of the corrected message is used As a result, even if n channels are used and information flowing through t channels is tampered with, the message can be efficiently and accurately transmitted. A transmission system capable of transmitting a signal can be provided.

It should be noted that the program for the CPU to execute the processing shown in the flowcharts of the drawings constitutes a program according to the present invention. As a recording medium for recording the program, a semiconductor storage unit, an optical and / or magnetic storage unit, or the like can be used. By using such a program and a recording medium in a system having a configuration different from that of each of the above-described embodiments and causing the CPU to execute the program, substantially the same effect as the present invention can be obtained.

As described above, the present invention has been specifically described based on the preferred embodiments, but the present invention is not limited to the above-described ones, and it is needless to say that various modifications can be made without departing from the scope of the present invention.

This application claims priority based on Japanese Patent Application No. 2009-034468 filed on Feb. 17, 2009, the entire disclosure of which is incorporated herein.

According to the present invention, it is possible to contribute to reducing the volume of data transmitted through the channel.

100, 400 Transmitting device 101 Message encoding unit 102 Illegal channel specifying

information generating unit

200, 500 Receiving device 201 Message restoring unit 202 Illegal channel specifying unit 300-1 to 300-n Channel 401 Adjustment parameter generating unit 402 Message encoding unit 403 Unauthorized channel identification information generation unit 501 Encoded message error correction unit 502 Unauthorized channel identification unit 601 Encoded message information conversion unit 602 RS information source generation unit 603 RS codeword generation unit 701 RS error correction unit 702 Unauthorized channel set output unit

Claims

An encoding device that encodes a message into n message information and outputs the n message information to a channel,
In order to identify the channel in which the amount of message information is reduced and the message information is fraudulent, with the assumed number of illegal channels t, the acceptable message reception failure probability δ, and the number of channels n as inputs. Adjustment parameter generation means for selecting an adjustment parameter that is a coefficient that increases the degree of increase in the unauthorized channel specifying data of
Two or more messages are received from the message on the basis of an encoding scheme that receives the information of the message m, the number of all channels n, the assumed number of illegal channels t, and the adjustment parameter s. Message encoding means for generating information;
The message information from the message encoding means, the assumed number of illegal channels t, and the number of channels n are input, and a t-order polynomial G on a finite field in which the message is embedded is generated. Processing is performed so that the message information has a different value on a finite field, and the output when the message information is input to the t-order polynomial after the processing is used as data for specifying an illegally encoded message, and the illegally encoded message An encoding apparatus comprising: illegal codeword specifying data generating means for generating specifying data in association with the message information.
A decoding device that receives message information output from an encoding device and data for specifying an illegally encoded message, and decodes the message based on the encoded message information,
In addition to the assumed illegal channel number t and channel number n, the illegally encoded message specifying data and message information are received from the channel, and error correction processing is performed on the received illegally encoded message specifying data, Based on the data for specifying the illegally encoded message after the correction process, the encoding device performs a restoration process on the t-order polynomial G generated by the encoding device, and converts the t-order polynomial G restored for all message information into the encoding device. The processing is performed in the same manner as the processing performed, and it is determined whether the value obtained by inputting the message information in the t-order polynomial after processing is equal to the data for specifying the illegally encoded message corresponding to the message information before processing. An illegal channel specifying means for outputting a list of all illegally encoded message specifying data as a set,
In addition to the assumed illegal channel number t and channel number n, the set is received from the illegal channel specifying means, message information is received from the channel, and data for specifying an illegally encoded message not included in the set L is supported. Error correction processing is performed on the message information to be corrected, and the n- (t + s + 1) degree polynomial F generated by the encoding device is restored based on the message information after the correction processing. From this polynomial F, the encoding device transmits message information And a coded message error correcting means for extracting and outputting a message by a method corresponding to a method of embedding the code in a finite field.
A transmission system comprising a combination of the encoding device according to claim 1 and the decoding device according to claim 2.
An encoding method for encoding a message into n message information and outputting the n message information to a channel,
In order to identify the channel in which the amount of message information is reduced and the message information is fraudulent, with the assumed number of illegal channels t, the acceptable message reception failure probability δ, and the number of channels n as inputs. Select an adjustment parameter that is a coefficient that increases the degree of increase in the unauthorized channel identification data for
Two or more messages are received from the message on the basis of an encoding scheme that receives the information of the message m, the number of all channels n, the assumed number of illegal channels t, and the adjustment parameter s. Generate information,
The encoded message information, the assumed number of illegal channels t, and the number of channels n are input, and a t-order polynomial G on a finite field in which the message is embedded is generated. Processing is performed so that the information has a different value on the finite field, and the output when the message information is input to the t-order polynomial after the processing is used as the data for specifying the illegally encoded message. An encoding method, wherein data is generated in correspondence with the message information.
A decoding method for receiving message information encoded by an encoding device and data for specifying an illegally encoded message corresponding to the information, and decoding a message based on the encoded message information,
In addition to the assumed illegal channel number t and channel number n, the illegally encoded message specifying data and message information are received from the channel, and error correction processing is performed on the received illegally encoded message specifying data, Based on the data for specifying the illegally encoded message after the correction process, the encoding device performs a restoration process on the t-order polynomial G generated by the encoding device, and converts the t-order polynomial G restored for all message information into the encoding device. The processing is performed in the same manner as the processing performed, and it is determined whether the value obtained by inputting the message information in the t-order polynomial after processing is equal to the data for specifying the illegally encoded message corresponding to the message information before processing. Output a list of all illegally encoded message identification data as a set,
In addition to the assumed illegal channel number t and channel number n, the set is received, message information is received from the channel, and error correction is performed on message information corresponding to illegally encoded message specifying data not included in the set L. The n- (t + s + 1) degree polynomial F generated by the encoding device is restored based on the message information after correction processing, and the encoding device embeds the message information in a finite field from this polynomial F A decoding method, wherein a message is extracted and output by a method corresponding to the method.
An encoding program for performing control to encode a message into n message information and output the n message information to a channel,
On the computer,
In order to identify the channel in which the amount of message information is reduced and the message information is fraudulent, with the assumed number of illegal channels t, the acceptable message reception failure probability δ, and the number of channels n as inputs. A function for selecting an adjustment parameter, which is a coefficient that increases the degree of increase in illegal channel identification data of
Two or more messages are received from the message on the basis of an encoding scheme that receives the information of the message m, the number of all channels n, the assumed number of illegal channels t, and the adjustment parameter s. The ability to generate information,
The encoded message information, the assumed number of illegal channels t, and the number of channels n are input, and a t-order polynomial G on a finite field in which the message is embedded is generated. Processing is performed so that the information has a different value on the finite field, and the output when the message information is input to the t-order polynomial after the processing is used as the data for specifying the illegally encoded message. An encoding program for executing a function of generating data in association with the message information.
A decoding program that receives message information encoded by an encoding device and data for specifying an illegally encoded message corresponding to the information, and performs control for decoding the message based on the encoded message information. ,
On the computer,
In addition to the assumed illegal channel number t and channel number n, the illegally encoded message specifying data and message information are received from the channel, and error correction processing is performed on the received illegally encoded message specifying data, Based on the data for specifying the illegally encoded message after the correction process, the encoding device performs a restoration process on the t-order polynomial G generated by the encoding device, and converts the t-order polynomial G restored for all message information into the encoding device. The processing is performed in the same manner as the processing performed, and it is determined whether the value obtained by inputting the message information in the t-order polynomial after processing is equal to the data for specifying the illegally encoded message corresponding to the message information before processing. A function to output a list of all illegally encoded message identification data as a set,
In addition to the assumed illegal channel number t and channel number n, the set is received, message information is received from the channel, and error correction is performed on message information corresponding to illegally encoded message specifying data not included in the set L. The n- (t + s + 1) degree polynomial F generated by the encoding device is restored based on the message information after correction processing, and the encoding device embeds the message information in a finite field from this polynomial F A decoding program that executes a function of extracting and outputting a message in a method corresponding to the method.