Abstract:
According to an aspect of an embodiment, a method comprises providing a matrix comprising m rows and n columns, each of the rows and columns comprising elements of zero and one, dividing data into n data blocks, associating each of the data blocks with each of the columns, calculating an exclusive-OR of selected data blocks in reference to one of the rows, the selected data blocks being determined by the element of one in the associated columns in the one of the rows, repeating the calculating in other rows and storing separately the calculated data resulting from the exclusive-OR of data blocks in association with the associated rows, respectively.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to an encoding apparatus and method of generating a plurality of partial information blocks used to distribute confidential information and store individual distributed information pieces, and more particularly, to an encoding apparatus and method capable of reducing the amount of arithmetic operations and the amount of each partial information block when confidential information is divided into partial information blocks and the individual information blocks are managed so that the confidential information can be stored safely and flexibly. 
     2. Description of the Related Art 
     Examples of the related art are disclosed in Japanese Unexamined Patent Application Publication Nos. 9-50236 and 2003-348065. 
     SUMMARY 
     According to an aspect of an embodiment, a method comprises providing a matrix comprising m rows and n columns, each of the rows and columns comprising elements of zero and one, dividing data into n data blocks, associating each of the data blocks with each of the columns, calculating an exclusive-OR of selected data blocks in reference to one of the rows, the selected data blocks being determined by the element of one in the associated columns in the one of the rows, repeating the calculating in other rows and storing separately the calculated data resulting from the exclusive-OR of data blocks in association with the associated rows, respectively. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of the essential part of an encoding apparatus according to a first embodiment; 
         FIG. 2  is a diagram explaining encryption of a token in accordance with the first embodiment; 
         FIG. 3  is a diagram illustrating the structure of data to be encoded in accordance with the first embodiment; 
         FIG. 4  is a diagram illustrating an encoding matrix in accordance with the first embodiment; 
         FIG. 5  is a flowchart showing the operation of the encoding apparatus according to the first embodiment; 
         FIG. 6  is a diagram illustrating RPS coding in accordance with the first embodiment; 
         FIG. 7  is a block diagram of the essential part of an encoding apparatus according to a second embodiment; 
         FIG. 8  is a flowchart of the operation of the encoding apparatus according to the second embodiment; 
         FIG. 9  is a diagram illustrating arrangement of the encoding apparatus, groupware, and computers in accordance with the second embodiment; and 
         FIG. 10  is a diagram illustrating the hardware configuration of a computer, serving as an encoding apparatus. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     In some cases, a chip called a security chip is mounted on a computer, such as a notebook computer. The security chip has a unique cryptographic key therein and automatically encrypts data to be stored into a hard disk using the cryptographic key to prevent the stored data from being stolen by a third person or being infected with a virus. It is impossible for an outsider to obtain a cryptographic key in each security chip. If data encrypted using a cryptographic key is removed, the data cannot be decrypted in another computer. 
     As described above, the security chip provides robust security to a user. Disadvantageously, if the security chip fails, an authorized user may not decrypt data. As a typical measure, a token for reconstructing a cryptographic key in a security chip is generated in an emergency. The token is a file whose data size is small and which can be stored into, for example, a universal serial bus (USB) memory. If a security chip fails, a cryptographic key in the security chip is reconstructed using a token. 
     Unfortunately, if a token for reconstructing a cryptographic key falls into the hands of a third person while a security chip provides a high degree of safety of data, the cryptographic key in the security chip is reconstructed. Therefore, for example, a token has to be divided into pieces, and after that, the pieces have to be held by a plurality of reliable persons or be distributed to a plurality of computers each including a security chip and be stored therein. 
     Specifically, according to an approach, conditions needed to reconstruct a secret key are predetermined and partial information blocks obtained by dividing the secret key are distributed to a plurality of persons. To reconstruct the secret key, the secret key is reconstructed from the partial information blocks only when the predetermined reconstruction conditions are satisfied. According to another approach, the secret key is error-correction-encoded using a Reed-Solomon code to generate a plurality of shared keys (partial information blocks) and the generated keys are distributed and stored. 
     Disadvantageously, in the above-described distributed storage of the keys, the reconstruction of the secret key requires many arithmetic operations. Further, each partial information block having the same data size as that of the original secret key may become a burden on the storage capacity of, for example, a computer that stores the partial information block. In other words, to reconstruct the secret key, it is necessary to solve high-order simultaneous congruences related to a remainder. Each partial information block has the same size as that of the original secret key and the amount of arithmetic operations is increased. The use of a Reed-Solomon code as an error correction code leads to an increase in the amount of arithmetic operations. 
     In the case where confidential information, such as a token or a key, is divided into partial information blocks and the information blocks are distributed and are stored, the original confidential information cannot be reconstructed unless all of the partial information blocks are collected and used. If only one partial information block is lacked, the confidential information cannot be reconstructed even in an emergency. Accordingly, the above-described approach is inflexible. On the other hand, if the original confidential information can be reconstructed using remarkably few partial information blocks, the safety is not ensured. Therefore, it is desirable that the number of partial information blocks obtained from confidential information and the number of partial information blocks necessary to reconstruct confidential information can be flexibly set. 
     Embodiments will now be described with reference to the drawings. A case where a token used to reconstruction of a cryptographic key in a security chip is stored will be described below. The embodiments can be applied to another case where a cryptographic key used for encryption of normal data is stored. 
     First Embodiment 
       FIG. 1  is a block diagram of the essential part of an encoding apparatus according to a first embodiment. Referring to  FIG. 1 , the encoding apparatus  100 , which is connected to a security chip  101 , outputs partial information blocks each containing information related to a token for reconstruction of a cryptographic key used by the security chip  101 . Specifically, the encoding apparatus  100  includes a token acquiring unit  102 , an encrypting unit  103 , a data generating unit  104 , a dividing unit  105 , an encoding-matrix storing unit  106 , and an exclusive-ORing unit  107 . 
     The token acquiring unit  102  acquires a token necessary to reconstruct a cryptographic key used by the security chip  101  upon encrypting and decrypting data. The token acquiring unit  102  may generate a new token in the security chip  101  or acquire a token which has previously been generated and be stored. The token is a file for reconstruction of the cryptographic key in the security chip  101  in, for example, an emergency. The token can be stored into, for example, a USB memory because the token has a relatively small size. 
     The encrypting unit  103  encrypts the token acquired by the token acquiring unit  102 . Specifically, the encrypting unit  103  encrypts the token using a temporary cryptographic key for temporary use to generate an encrypted token, as shown in  FIG. 2 . The encrypting unit  103  outputs the encrypted token together with the temporary cryptographic key to the data generating unit  104 . In this instance, the temporary cryptographic key used by the encrypting unit  103  is independent of the cryptographic key held in the security chip  101 . A new temporary cryptographic key is used each time a token is encrypted. 
     The data generating unit  104  generates data to be encoded from the temporary cryptographic key and the encrypted token. Specifically, the data generating unit  104  combines the temporary cryptographic key with the encrypted token obtained using the temporary cryptographic key to generate data to be encoded, as shown in  FIG. 3 . 
     The dividing unit  105  divides the generated data to be encoded into data blocks having the same size. At that time, the dividing unit  105  divides the data into data blocks equal in number to columns of an encoding matrix used for encoding. The dividing unit  105  may add, for example, dummy data to the data to be encoded and then divide the resultant data into data blocks in order to equalize the sizes of the data blocks. 
     The encoding-matrix storing unit  106  previously stores the encoding matrix used for encoding data to be encoded. Specifically, the encoding-matrix storing unit  106  stores an encoding matrix shown in, for example,  FIG. 4 . 
     The encoding matrix has elements of “0” and “1”. The elements “0” and “1” are arranged at random such that the orders of elements “0” and “1” in respective rows are different from one another. The number of rows of the encoding matrix corresponds to the number of partial information blocks output by the encoding apparatus  100 . The number of columns of the encoding matrix may be set to any value. The larger the number of columns of the encoding matrix, the higher the reconstruction efficiency. In the use of the encoding matrix shown in  FIG. 4 , the data to be encoded is divided into eight data blocks (i.e., eight indicates the number of columns) and fourteen partial information blocks (fourteen indicates the number of rows) are output. Further, the number of elements “1” in each row is equal to or larger than a value obtained by multiplying the number of columns by a value, which is obtained by subtracting 1 from the degree of redundancy (the ratio of the total amount of partial information blocks to the amount of data to be encoded). 
     The exclusive-ORing unit  107  reads the encoding matrix from the encoding-matrix storing unit  106  and exclusive-ORs the data blocks in accordance with the positions of the elements “1” in each row of the encoding matrix to generate a partial information block. Specifically, the exclusive-ORing unit  107  assigns a number to each data block generated by the dividing unit  105  and exclusive-ORs the data blocks having the numbers respectively corresponding to the positions of the elements “1” in each row of the encoding matrix. The exclusive-ORing unit  107  generates a partial information block that contains a header portion including elements in each row of the encoding matrix and a data portion including the exclusive-OR obtained in accordance with the row. Consequently, the exclusive-ORing unit  107  generates partial information blocks equal in number to the number of rows of the encoding matrix. 
     The above-described encoding is called random parity stream (RPS) coding. In the present embodiment, the dividing unit  105 , the encoding-matrix storing unit  106 , and the exclusive-ORing unit  107  constitute an RPS coding section. 
     A token encoding process by the encoding apparatus  100  having the above-described structure will now be described with reference to a flowchart shown in  FIG. 5 . 
     In the present embodiment, to reconstruct the cryptographic key used by the security chip  101  in the computer in an emergency, a token for reconstruction of the cryptographic key is generated. The token acquiring unit  102  acquires a token (step S 101 ) and outputs the token to the encrypting unit  103 . As described above, the token acquiring unit  102  may generate a new token in the security chip  101  and acquire the generated token. Alternatively, the token acquiring unit  102  may acquire a token previously stored outside the relevant computer. 
     The encrypting unit  103  encrypts the token output from the token acquiring unit  102  using a temporary cryptographic key. Specifically, the encrypting unit  103  generates a temporary cryptographic key for encryption of the token and encrypts the token using the temporary cryptographic key. The encrypting unit  103  outputs the encrypted token together with the temporary cryptographic key used for encryption to the data generating unit  104 . The data generating unit  104  combines the temporary cryptographic key with the encrypted token to generate data to be encoded (step S 102 ). 
     The dividing unit  105  divides the data to be encoded into data blocks equal in number to columns of an encoding matrix (step S 103 ). For example, in the use of the encoding matrix shown in  FIG. 4 , the data to be encoded is divided into eight data blocks. The data blocks are output to the exclusive-ORing unit  107 . The exclusive-ORing unit  107  reads the encoding matrix from the encoding-matrix storing unit  106  and exclusive-ORs the data blocks corresponding to the elements “1” in each row of the encoding matrix (step S 104 ). For example, as for the uppermost row of the encoding matrix in  FIG. 4 , the first, second, fifth, and seventh data blocks are exclusive-ORed. The obtained exclusive-OR contains information about the original data blocks. 
     After that the exclusive-ORing unit  107  obtains the exclusive-ORs in this manner, the exclusive-ORing unit  107  generates partial information blocks each containing the obtained exclusive-OR of the data blocks as a data portion and the row of the matrix encoding related to the exclusive-OR as a header portion, and outputs the partial information blocks (step S 105 ). Therefore, the exclusive-ORing unit  107  outputs the partial information blocks equal in number to the rows of the encoding matrix. The output partial information blocks are distributed to a plurality of reliable persons and are stored by them. Each partial information block may be stored into at least one hard disk and/or at least one removable medium, such as a flash memory. Alternatively, each partial information block may be stored into a storage connected via a network. Further, the partial information blocks may be shared between computers each having another security chip. In this case, the partial information blocks may be encrypted by the other security chip in each computer, thus further improving safety measures. 
     A concrete example of the RPS coding according to the present embodiment will now be described with reference to  FIG. 6 . In the following description, it is assumed that an encoding matrix has four columns. 
     The data generating unit  104  generates data to be encoded, the data containing a temporary cryptographic key and an encrypted token. The dividing unit  105  divides the data to be encoded. Since the dividing unit  105  divides the data into data blocks equal in number to the columns of the encoding matrix stored in the encoding-matrix storing unit  106 , the data is divided into four data blocks as shown in  FIG. 6 . 
     The data blocks are output to the exclusive-ORing unit  107 . The exclusive-ORing unit  107  exclusive-ORs the data blocks according to the encoding matrix to perform the RPS coding. For example, when the uppermost row of the encoding matrix is “1010” as shown in  FIG. 6 , the first and third data blocks are exclusive-ORed and a partial information block is generated such that “1010”, serving as a header portion, is added to the obtained exclusive-OR. When the second row from the top of the encoding matrix is “0110”, the second and third data blocks are exclusive-ORed and a partial information block is generated such that “0110”, serving as a header portion, is added to the obtained exclusive-OR. 
     As described above, in the RPS coding, the data blocks are exclusive-ORed, thus encoding the data. Advantageously, therefore, the amount of arithmetic operations is not so large and the amount of each partial information block is substantially the same as that obtained by adding the amount of a header portion to the amount of one data block, which is obtained by dividing the data to be encoded. Consequently, both of the amount of arithmetic operations and the amount of data can be reduced. Furthermore, the number of partial information blocks and the amount of data can be flexibly set by adjusting the number of columns and that of rows of the encoding matrix and the positions of the elements “1”. 
     In decoding the encoded data, i.e., to obtain the original data from the partial information blocks obtained by RPS coding, the partial information blocks of at least the same number as the columns of the encoding matrix are collected and are arranged vertically. The matrix composed of the header portions of the respective partial information blocks are transformed into a unit matrix using the Gauss elimination method. In the transformation into the unit matrix, each data portion is converted into data blocks obtained by dividing the original data to be encoded. The data blocks are combined into the original data to be encoded. Since the original data contains a temporary cryptographic key and an encrypted token, the encrypted token is decrypted using the temporary cryptographic key, thus obtaining the token for reconstruction of the cryptographic key in the security chip  101 . 
     As described above, according to the present embodiment, a token is encrypted using a temporary cryptographic key to generate data to be encoded, the data is divided into data blocks equal in number to columns of an encoding matrix, and the exclusive-OR in each row of the encoding matrix is obtained using the data blocks to encode the data, so that partial information blocks containing the encoding matrix and the exclusive-ORs are output. Therefore, the generation of the partial information blocks requires only dividing the original data to be encoded into the data blocks and exclusive-ORing the data blocks. The amount of each partial information block is substantially the same as that of each data block obtained by dividing the original data. Consequently, when confidential information is divided into partial information blocks and the partial information blocks are distributed and are managed, the amount of arithmetic operations and the amount of each partial information block can be reduced and the confidential information can be stored safely and flexibly. 
     Second Embodiment 
     According to a feature of a second embodiment, partial information blocks are distributed to a plurality of computers that use the same groupware. 
       FIG. 7  is a block diagram showing the essential part of an encoding apparatus according to the present embodiment. In  FIG. 7 , the same components as those in  FIG. 1  are designated by the same reference numerals and a description of the previously described components is omitted. Referring to  FIG. 7 , the encoding apparatus  100 , which is connected to a security chip  101 , outputs partial information blocks to groupware  300 . The partial information blocks each contain information about a token for reconstruction of a cryptographic key used by the security chip  101 . Specifically, the encoding apparatus  100  includes a token acquiring unit  102 , an encrypting unit  103 , a data generating unit  104 , an encoding-matrix generating unit  201 , a dividing unit  202 , and an exclusive-ORing unit  107 . 
     The encoding-matrix generating unit  201  generates an encoding matrix in accordance with information indicating the distribution proportions of partial information blocks for computers, the information being sent from the groupware  300 . In other words, the encoding-matrix generating unit  201  determines the number of columns of the encoding matrix according to the amount of each partial information block and also determines the number of rows of the encoding matrix according to the number of partial information blocks to be distributed. Specifically, the encoding-matrix generating unit  201  determines the amount of each data block on the basis of the amount of each partial information block indicated by information sent from the groupware  300 , divides the amount of data to be encoded by the amount of each data block to obtain the division number, and uses the division number as the number of columns of the encoding matrix. In addition, the encoding-matrix generating unit  201  uses the total number of partial information blocks, indicated by information sent from the groupware  300 , as the number of rows of the encoding matrix. After the determination of the number of columns and that of rows of the encoding matrix, the encoding-matrix generating unit  201  arranges elements “1” at random and transmits information indicating the number of columns to the dividing unit  202 . 
     When receiving the information indicating the number of columns of the encoding matrix from the encoding-matrix generating unit  201 , the dividing unit  202  divides data to be encoded, generated by the data generating unit  104 , into data blocks equal in number to the columns of the encoding matrix. 
     In the present embodiment, the encoding-matrix generating unit  201 , the dividing unit  202 , and the exclusive-ORing unit  107  constitute an RPS coding section. 
     Again referring to  FIG. 7 , the groupware  300  includes a distribution-proportion determining unit  301  and a partial-information distributing unit  302 . 
     The distribution-proportion determining unit  301  acquires share information blocks from computers  400  which use the groupware  300 . Each share information block indicates the amount of data, serving as a partial information block, storable in the corresponding computer  400 . After that, the distribution-proportion determining unit  301  determines the numbers of partial information blocks to be stored into the respective computers. Specifically, the distribution-proportion determining unit  301  determines a minimum value of the amount of storable data on the basis of the share information blocks sent from the respective computers  400  and sets the determined minimum value to the amount of each partial information block. The distribution-proportion determining unit  301  determines the number of partial information blocks to be stored in each computer  400  on the basis of the share information block sent from the computer  400 . The distribution-proportion determining unit  301  then transmits information indicating the determined numbers for the respective computers  400  to the partial-information distributing unit  302 . In addition, the distribution-proportion determining unit  301  transmits the information indicating the amount of each partial information block and information indicating the total number of partial information blocks to be distributed to the computers to the encoding-matrix generating unit  201 .  FIG. 9  shows arrangement of the encoding apparatus  100 , the groupware  300 , and the computers  400 . The encoding apparatus  100  and the groupware  300  constitute a computer  400  (# 0 ). The computer  400  (# 0 ) is connected to, for example, N computers  400  (# 1 ) to (#N). In this case, N indicates an arbitrary integer. The computers  400  (# 1 ) to (#N) each include the encoding apparatus  100  and the groupware  300 . With this arrangement, each computer can store divided data blocks sent from the other computers. 
     The partial-information distributing unit  302  distributes partial information blocks, output from the exclusive-ORing unit  107 , to the respective computers in accordance with the numbers of partial information blocks for the respective computers  400  indicated by the information transmitted from the distribution-proportion determining unit  301 . 
     A token encoding process by the encoding apparatus with the above-described structure will now be described with reference to a flowchart of  FIG. 8 . In  FIG. 8 , the same steps as those in  FIG. 5  are designated by the same reference numerals. 
     According to the present embodiment, to reconstruct a cryptographic key used by the security chip  101  in any computer in an emergency, a token for reconstruction of the cryptographic key is generated in a manner similar to the first embodiment. The token acquiring unit  102  acquires a token (step S 101 ) and outputs the token to the encrypting unit  103 . The token acquiring unit  102  may generate a new token in the security chip  101  and acquire the generated token. Alternatively, the token acquiring unit  102  may acquire a token previously stored outside the computer. 
     The encrypting unit  103  encrypts the token output from the token acquiring unit  102  using a temporary cryptographic key. Specifically, the encrypting unit  103  generates a temporary cryptographic key for encryption of the token and encrypts the token using the temporary cryptographic key. The encrypting unit  103  outputs the encrypted token together with the temporary cryptographic key used for encryption to the data generating unit  104 . The data generating unit  104  combines the temporary cryptographic key with the encrypted token to generate data to be encoded (step S 102 ). 
     In the groupware connected to the computers, the distribution-proportion determining unit  301  collects share information blocks from the respective computers, each share information block indicating the amount of data that can be stored as a partial information block in the corresponding computer. The distribution-proportion determining unit  301  then determines a minimum value of the amount of data as the amount of each partial information block on the basis of the share information blocks. The distribution-proportion determining unit  301  transmits information indicating the amount of each partial information block and information indicating the total number of partial information blocks to be stored in the respective computers to the encoding-matrix generating unit  201 . The encoding-matrix generating unit  201  generates an encoding matrix on the basis of the amount of each partial information block and the total number of partial information blocks (step S 201 ). 
     In other words, the encoding-matrix generating unit  201  determines the amount of each data block in accordance with the amount of each partial information block and divides the amount of the data to be encoded by the amount of each data block, thus obtaining the number of data blocks obtained from the data to be encoded. The number of data blocks is used as the number of columns of the encoding matrix. The encoding-matrix generating unit  201  transmits information indicating the number of columns to the dividing unit  202 . Further, the encoding-matrix generating unit  201  sets the total number of partial information blocks to the number of rows of the encoding matrix and arranges elements “1” at random to generate the encoding matrix. 
     When receiving the information indicating the number of columns of the encoding matrix, the dividing unit  202  divides the data to be encoded into data blocks equal in number to the columns of the encoding matrix (step S 202 ). The dividing unit  202  outputs the data blocks to the exclusive-ORing unit  107 . The exclusive-ORing unit  107  reads the encoding matrix from the encoding-matrix generating unit  201  and exclusive-ORs the data blocks corresponding to the elements “1” in each row of the encoding matrix (step S 104 ). 
     After that the exclusive-ORing unit  107  obtains the exclusive-ORs of the data blocks in this manner, the exclusive-ORing unit  107  generates partial information blocks each containing the obtained exclusive-OR as a data portion and the row of the matrix encoding related to the exclusive-OR as a header portion, and outputs the partial information blocks to the partial-information distributing unit  302 . Therefore, the exclusive-ORing unit  107  outputs the partial information blocks equal in number to the rows of the encoding matrix. Since the number of rows of the encoding matrix is the same number as the total number of partial information blocks determined on the basis of the share information blocks collected from the respective computers as described above, those partial information blocks are distributed to the respective computers in accordance with the share information blocks (step S 203 ). In other words, the distribution-proportion determining unit  301  determines the numbers of partial information blocks to be distributed to the respective computers on the basis of the determined amount of each partial information block and the share information blocks of the respective computers, and transmits information indicating the distribution proportions for the respective computers to the partial-information distributing unit  302 . The partial-information distributing unit  302  distributes the partial information blocks, output from the exclusive-ORing unit  107 , to the respective computers in accordance with the distribution proportions for the respective computers. And the partial-information, calculated data resulting form an exclusive-OR of data blocks in association with associated rows is stored separately. 
     As described above, according to the present embodiment, share information blocks are collected from a plurality of computers that use the same groupware and the amount of each partial information block and the distribution proportions of partial information blocks for the respective computers are determined on the basis of the share information blocks. An encoding matrix is generated in accordance with the amount of each partial information block and the total number of partial information blocks. Data to be encoded is encoded using the generated encoding matrix. Obtained partial information blocks are distributed to the respective computers in accordance with the distribution proportions determined on the basis of the share information blocks. Consequently, the encoding matrix can be flexibly generated in accordance with the amounts of storable data in the computers which use the same groupware and the partial information blocks can be distributed according to the storage capacities of the respective computers. 
     In decoding encoded data, i.e., to obtain original data from partial information blocks obtained by RPS coding, the partial information blocks of at least the same number as the columns of the encoding matrix may be collected from the computers. A description of the decoding method is omitted because the decoding method is the same as that described in the first embodiment. 
     In the above-described embodiments, the encoding apparatus is connected to the security chip  101 . The encoding apparatus according to each embodiment may be connected to a hard disk or a removable medium which stores a cryptographic key for encryption of, for example, normal data to perform RPS coding on the normal cryptographic key. 
     The processes by the encoding apparatus described in each embodiment can be realized by allowing an information processing apparatus to execute a program prepared. An example of the information processing apparatus for executing a program for realization of various processes will now be described with reference to  FIG. 10 . 
       FIG. 10  is a diagram illustrating the hardware configuration of an information processing apparatus  0 , serving as an encoding apparatus. The information processing apparatus  0  includes an input device  30  for receiving data input by a user, a monitor  31 , a random access memory (RAM)  32 , a read only memory (ROM)  33 , a reader  34  for reading a program from a recording medium which stores various programs, a network interface  35  for transmitting and receiving data to/from another information processing apparatus via a network, a central processing unit (CPU)  36 , and a magnetic disk unit, such as a hard disk drive (HDD)  37 , the components  30  to  37  connecting to a bus  38 . 
     When the information processing apparatus  0  functions as an encoding apparatus, the HDD  37  stores various programs  37   b  for providing functions similar to those of the encoding apparatuses. The CPU  36  reads the various programs  37   b  from the HDD  37  into the RAM  32  and executes the various programs  37   b , thus starting various processes  36   a  for realizing the above-described functions of the encoding apparatuses. The various processes  36   a  correspond to the token acquiring unit  102 , the encrypting unit  103 , the data generating unit  104 , the dividing unit  105 , the encoding-matrix storing unit  106 , and the exclusive-ORing unit  107  in  FIG. 1  and also correspond to the encoding-matrix generating unit  201  and the dividing unit  202  in  FIG. 7 . 
     The HDD  37  stores various data blocks  32   a  corresponding to data blocks stored in a memory unit of each of the above-described encoding apparatuses. The CPU  36  stores the various data blocks  32   a  into the HDD  37 , reads the various data blocks  32   a  from the HDD  37  into the RAM  32 , and executes data processing on the basis of the various data blocks  32   a  stored in the RAM  32 . 
     It is unnecessary to store the various programs  37   b  into the HDD  37  from the beginning. For example, the various programs  37   b  may be stored into a portable physical medium, such as a flexible disk (FD), a compact disk read only memory (CD-ROM), a digital versatile disk (DVD), a magneto-optical disk, or an IC card which is loaded into the information processing apparatus  0 , a fixed physical medium, such as a hard disk drive (HDD) disposed inside or outside the information processing apparatus, and/or another information processing apparatus (or a server) connected to the information processing apparatus  0  via a public circuit, the Internet, a local area network (LAN), or a wide area network (WAN). The information processing apparatus  0  may read the various programs  37   b  from the storing medium or apparatus and executes the programs. 
     The encoding apparatus  100  may be constructed as hardware including the token acquiring unit  102 , the encrypting unit  103 , the data generating unit  104 , the dividing unit  105 , the encoding-matrix storing unit  106 , the exclusive-ORing unit  107 , the encoding-matrix generating unit  201 , and the dividing unit  202 . 
     The above-described embodiments can be applied to a case where confidential information is divided into partial information blocks and the information blocks are managed to reduce the amount of arithmetic operations and the amount of each partial information block and store the confidential information safely and flexibly.