JP5065795B2 - Distributed information generating apparatus, secret information restoring apparatus, shared information generating method, secret information restoring method, and program - Google Patents

Description

  The present invention relates to a shared information generating device, a secret information restoring device, a shared information generating method, a secret information restoring method, and a program having a degree of freedom in the data size of shared information.

  In recent years, with the increasing importance of information security, measures against theft and loss of information have become important issues. For this reason, the (k, n) threshold secret sharing method as shown in Non-Patent Document 1 is attracting attention as a method for simultaneously realizing confidentiality of information and avoidance of risk due to loss. Here, (k, n) threshold secret sharing means that secret information is distributed into n pieces of shared information, and if any k pieces of shared information are gathered, it can be restored.

  The technique described in Non-Patent Document 1 needs to process a k−1 order polynomial at the time of information distribution / restoration, and the amount of calculation becomes a problem when applied to an actual application. However, on the other hand, there is also a method that enables information to be distributed / restored at high speed by configuring the (k, n) threshold secret sharing method using exclusive OR (Exclusive-OR, XOR). It has been proposed (see Non-Patent Documents 2 and 3). These high-speed (k, n) threshold secret sharing methods not only simply operate at high speed, but as in the technique described in Non-Patent Document 1, complete information-theoretic security is guaranteed, and the data of the distributed information The length is equal to the data length of the secret information.

Further, as an extension method of the technique described in Non-Patent Document 1, a ramp-type threshold secret sharing method that can significantly reduce the size of shared information instead of slightly degrading the safety as shown in Non-Patent Document 4 and A so-called technique is also known.
A. Shamir, “How to Share a Secret,” Commun. ACM, vol. 22 no. 11 pp. 612-613, 1979. J. et al. Kurihara, S .; Kiyomoto, K. et al. Fukushima, T .; Tanaka, “A Fast (4, n) —Threshold Secret Sharing Scheme Using Exclusive-OR Operation and its Extension to (k, n) —Threshold Chemistry Research, Information v. 107, no. 44, Information Security, ISSN 0913-5585, ISEC 2007-4 Yoshihiro Fujii, Takaya Tochikubo, Norikazu Hosaka, Minako Tada, Takehisa Kato, “Structure of (k, n) threshold method using exclusive OR”, IEICE technical report, vol. 107, no. 44, Information Security, ISSN 0913-5585, ISEC 2007-5 Hiroshi Yamamoto, “(k, L, n) threshold secret sharing system”, IEICE Transactions, vol. J68-A, no. 9, pp. 945-952, September 1985

  However, although the techniques disclosed in Non-Patent Documents 2 and 3 described above can distribute distributed information safely and at high speed, there is no flexibility in the data size of the distributed information. There are problems such as giving a load and affecting communication traffic. Further, since the technique disclosed in Non-Patent Document 4 is based on the technique disclosed in Non-Patent Document 1, the data size of the distributed information has a relatively high degree of freedom. There is a problem that the operation is slow because a huge amount of calculation is required for the generation and distribution of.

  Accordingly, the present invention has been made in view of the above-described problems, and while being able to perform safe and high-speed processing, a dispersion that can reduce the size of the distributed information by giving a degree of freedom. An object of the present invention is to provide an information generation device, a secret information restoration device, a distributed information generation method, a secret information restoration method, and a program.

The present invention proposes the following items in order to solve the above problems.
(1) The present invention includes a secret information divider (for example, equivalent to the secret information divider 11 in FIG. 1) that divides secret information to generate partial secret information, and a predetermined number of secret information dividers generated by the secret information divider A partial shared information generator (for example, a partial shared information generator) that inputs partial secret information and a predetermined number of random numbers and generates partial shared information by an exclusive OR (XOR) operation of the predetermined number of partial secret information and the predetermined number of random numbers. 1 and a combiner (for example, equivalent to the coupler 14 in FIG. 1) that combines the generated partial share information to generate shared information. In the information generation device, the secret information divider has L more than a predetermined value n _p −1 (n _p is a prime number greater than or equal to the distribution number n) for inputting the secret information to the partial shared information generator. Dividing into partial secret information, the surplus L pieces of secret information are divided into the predetermined number of pieces. It proposes a distributed information generation apparatus characterized by input to the partial shared information generator as part of the number.

According to the present invention, a secret information divider that divides secret information to generate partial secret information, a predetermined number of partial secret information generated by the secret information divider and a predetermined number of random numbers are input, and the predetermined number of A partial shared information generator that generates partial shared information by exclusive OR (XOR) operation of partial secret information and a predetermined number of random numbers, and a combiner that generates the shared information by combining the generated partial shared information And the secret information divider divides the secret information into L pieces of partial secret information larger than the predetermined value n _p −1 input to the partial shared information generator, and the surplus L Pieces of secret information are input to the partial shared information generator as part of a predetermined number of random numbers. Therefore, if the predetermined value input to the partial shared information generator is n _p −1, the size of the generated shared information is (n _p −1) / (n _p −1 + L) of the size of the original secret information. The size of the distributed information can be reduced.

  (2) The present invention proposes a shared information generating apparatus according to (1), wherein the L is a variable composed of a positive integer smaller than a predetermined number of the random numbers. Yes.

According to the present invention, L is a variable composed of a positive integer smaller than a predetermined number of random numbers. Therefore, by controlling the value of L from the relational expression (n _p −1) / (n _p −1 + L), the size of the distributed information can be given a degree of freedom and the size can be set finely.

(3) The present invention is a secret information restoration device that restores secret information from the shared information generated by the shared information generation device according to claim 1 or 2, wherein k is a threshold value (k is the number of distributions n or less). A shared information divider (for example, equivalent to the shared information divider 21 in FIG. 3) that divides the inputted shared information to generate partial shared information, and the partial shared A first restorer (for example, corresponding to the first partial secret information restorer 22 in FIG. 3) that restores n _p −1 pieces (n _p is a prime number greater than or equal to the distributed number n) by inputting information. ), A second decompressor (for example, corresponding to the second partial secret information decompressor 23 in FIG. 3) that inputs the partial shared information and restores L partial secret information, and the first restore vessels and n _p restored by the second decompressor -1 + L number of portions connecting the secret information Coupling to generate the confidential information (e.g., corresponding to the coupler 24 of FIG. 3) proposes a secret reconstruction device characterized by comprising a, a.

According to the present invention, the shared information divider inputs the shared information, divides the input shared information to generate partial shared information, and the first restorer inputs the partial shared information and receives n _p − One partial secret information is restored, and the second restorer inputs the partial shared information and restores L partial secret information. Then, the concatenator generates the secret information by concatenating the n _p −1 + L pieces of partial secret information restored by the first restorer and the second restorer. Therefore, it is possible to restore the secret information safely and at high speed while finely setting the size of the distributed information.

(4) According to the present invention, a secret information divider that divides secret information to generate partial secret information, a predetermined number of partial secret information generated by the secret information divider and a predetermined number of random numbers are input, A partial shared information generator that generates partial shared information by an exclusive OR (XOR) operation of a number of partial secret information and a predetermined number of random numbers, and generates the shared information by combining the generated partial shared information A shared information generation method in a shared information generation apparatus comprising a combiner that performs the following operation, wherein the secret information is input to the partial shared information generator from a predetermined value n _p −1 (n _p is a prime number greater than or equal to the distributed number n) A first step (for example, corresponding to step S101 in FIG. 2) to divide the partial secret information into L pieces of partial secret information, and the surplus L pieces of secret information as part of the predetermined number of random numbers to the partial shared information generator The second step to input (eg, FIG. 2 And it corresponds to step S102), the XOR operation between the n _p -1 pieces of partial secret information and the L moiety secret information and the random number, a third step of generating partial shared information (e.g., the steps of FIG. 2 And a fourth step (for example, corresponding to step S104 in FIG. 2) for generating the shared information by linking the generated partial shared information. is suggesting.

According to the present invention, the secret information is divided into L pieces of partial secret information that are larger than the predetermined value n _p −1 input to the partial shared information generator, and the surplus L pieces of secret information are divided into a predetermined number of random numbers. As a part, it is input to the partial shared information generator. Then, partial shared information is generated by XOR operation of n _p −1 partial secret information, L partial secret information, and random numbers, and the generated partial shared information is connected to generate shared information. Therefore, if the predetermined value input to the partial shared information generator is n _p −1, the size of the generated shared information is (n _p −1) / (n _p −1 + L) of the size of the original secret information. The size of the distributed information can be reduced.

(5) The present invention is a secret information restoring method for restoring secret information from the shared information generated by the shared information generating method according to claim 4, wherein k is a threshold value (k is a positive integer less than or equal to the distributed number n) ), The first step (for example, corresponding to step S201 in FIG. 4) to divide the input shared information and generate partial shared information, and the partial shared information is input to n _p A second step (for example, corresponding to step S202 in FIG. 4) of restoring one piece (n _p is a prime number greater than or equal to the number n of shares) partial secret information, and the number of L pieces A third step (for example, corresponding to step S203 in FIG. 4) for restoring the secret information and the n _p −1 + L pieces of partial secret information restored in the second step and the third step are concatenated. The fourth step of generating information (E.g., corresponding to step S204 in FIG. 4) has proposed a secret reconstruction method characterized by comprising a, a.

According to the present invention, the shared information is input, the input shared information is divided to generate partial shared information, and the partial shared information is input to restore n _p −1 partial secret information. On the other hand, the partial shared information is input to restore L partial secret information. Then, the reconstructed n _p −1 + L pieces of partial secret information are connected to generate secret information. Therefore, it is possible to restore the secret information safely and at high speed while finely setting the size of the distributed information.

(6) According to the present invention, a secret information divider that divides secret information to generate partial secret information, a predetermined number of partial secret information generated by the secret information divider and a predetermined number of random numbers are input, A partial shared information generator that generates partial shared information by an exclusive OR (XOR) operation of a number of partial secret information and a predetermined number of random numbers, and generates the shared information by combining the generated partial shared information A shared information generating method in a shared information generating apparatus comprising a combiner, and a program for causing a computer to execute a shared information generating method, wherein the secret information is input to the partial shared information generator by a predetermined value n _p −1 (n _p is A first step (for example, corresponding to step S101 in FIG. 2) that divides the partial secret information into L more than the distributed number n (prime number equal to or greater than the number n), and the surplus L pieces of secret information are assigned to the predetermined number of random numbers. Partially distributed information generation as a part A second step of inputting (e.g., corresponding to step S102 in FIG. 2) to a by XOR operation of the n _p -1 pieces of partial secret information and the L moiety secret information and the random number, the partial shared information A third step (for example, corresponding to step S103 in FIG. 2) and a fourth step (for example, corresponding to step S104 in FIG. 2) for generating the shared information by connecting the generated partial distribution information, , A program for causing a computer to execute is proposed.

According to the present invention, the secret information is divided into L pieces of partial secret information that are larger than the predetermined value n _p −1 input to the partial shared information generator, and the surplus L pieces of secret information are divided into a predetermined number of random numbers. As a part, it is input to the partial shared information generator. Then, partial shared information is generated by XOR operation of n _p −1 partial secret information, L partial secret information, and random numbers, and the generated partial shared information is connected to generate shared information. Therefore, if the predetermined value input to the partial shared information generator is n _p −1, the size of the generated shared information is (n _p −1) / (n _p −1 + L) of the size of the original secret information. The size of the distributed information can be reduced.

(7) The present invention is a program for causing a computer to execute a secret information restoring method for restoring secret information from the shared information generated by the shared information generating method according to claim 4, wherein k threshold values (k is A first step of generating partial shared information by dividing the input shared information, and inputting the partial shared information, n _p −1 A second step of restoring partial secret information (n _p is a prime number equal to or greater than the number n of shares), a third step of restoring the L partial secret information by inputting the partial shared information, and the second step And a fourth step of generating secret information by concatenating the n _p −1 + L partial secret information restored in the third step and the third step are proposed.

According to the present invention, the shared information is input, the input shared information is divided to generate partial shared information, and the partial shared information is input to restore n _p −1 partial secret information. On the other hand, the partial shared information is input to restore L partial secret information. Then, the reconstructed n _p −1 + L pieces of partial secret information are connected to generate secret information. Therefore, it is possible to restore the secret information safely and at high speed while finely setting the size of the distributed information.

  According to the present invention, it is possible to reduce storage usage, memory capacity, and data communication volume with high-speed and safe operation by using a secure and destruction-resistant distributed data management method. There is.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
Note that the constituent elements in the present embodiment can be appropriately replaced with existing constituent elements and the like, and various variations including combinations with other existing constituent elements are possible. Therefore, the description of the present embodiment does not limit the contents of the invention described in the claims.

<Configuration of distributed information generation device>
The configuration of the shared information generation apparatus according to this embodiment will be described with reference to FIG.
As shown in FIG. 1, the shared information generating apparatus according to the present embodiment includes a secret information divider 11, random number generators 12a,..., 12n, a partial shared information generator 13, a coupler 14, The partial shared information generator 13 includes a transmitter 15 and includes a partial secret information input unit 13a and a random number input unit 13b.

The secret information divider 11 inputs secret information, and the input secret information is L more than a predetermined number (n _p −1) (n _p is a prime number greater than or equal to the distribution number n), (n _p −1 + L). The partial secret information is divided into (n _p −1) pieces of partial secret information to the partial secret information input unit 13a of the partial shared information generator 13, and L partial secret information is supplied to the partial shared information generator 13. To the random number input unit 13b. Note that L is a variable composed of a positive integer smaller than a predetermined number of random numbers. By controlling L, the size of the shared information can be given a degree of freedom and the size can be set finely.

  The random number generators 12a,..., 12n generate random numbers independent of each other and input the random numbers to the random number input unit 13b of the partial shared information generator 13. The number of random numbers generated by the random number generators 12a..., 12n and the number L of partial secret information input from the secret information divider 11 is a conventional XOR (k, n This corresponds to the number of random numbers in the threshold dispersion method (see Non-Patent Document 3, for example).

The partial shared information generator 13 performs an exclusive OR (XOR) of n _p −1 partial secret information input from the partial secret information input unit 13a and random numbers input from the random number input unit 13b or L partial secret information. ) Perform an operation to generate partial distribution information. The coupler 14 concatenates the partial shared information generated in the partial shared information generator 13 to generate shared information, and the transmitter 15 converts the shared information generated in the connected unit 14 into a predetermined number n (n is A positive integer) sent to the administrator.

<Processing of distributed information generation apparatus>
The process of the shared information generation device according to this embodiment will be described with reference to FIG.

(Step S101)
The secret information K is divided into (n _p −1 + L) pieces of partial secret information K _q (n _p is a prime number greater than or equal to the variance n). In Equation 1, “||” indicates a combination of bit strings.

(Step S102)
Of the partial secret information K _q , (n _p −1) pieces of partial secret information are input to the partial secret information input unit 13a of the partial shared information generator 13, and the remaining L partial secret information are generated as partial shared information. This is input to the random number input unit 13b of the device 13.

(Step S103)
(N _p −1) pieces of partial secret information K ₁ ,..., K _np−1 and random number input units 12 a,... _{Inputted to} the partial secret information input unit 13 a of the partial shared information generator 13. XOR operation with random number R ^t _l input to 12n and L pieces of partial secret information K _np ,..., K _{np + L−1} (appropriate display changes to R ^t _l according to the random number input unit) Thus, partial distribution information S _{(i, m)} is generated as follows.

(Step S104)
The partial shared information S _{(i, 0)} ,..., S _{(i, np−2)} is connected to generate the shared information S _i and securely distributed to the manager P _i .

Therefore, according to the shared information generating apparatus according to the present embodiment, the size of the generated shared information is (n _p −1) / (n _p −1 + L) times the size of the original secret information, The size can be reduced. Further, since L is a variable, by controlling the value of L from the above relational expression (n _p −1) / (n _p −1 + L), the size of the distributed information is given a degree of freedom. The size can be set finely.

Here, the secret information needs to be equally divided into (n _p −1 + L) pieces. However, n _p is a prime number satisfying n _p ≧ n with respect to the dispersion number n. Therefore, when the desired distribution number n is a composite number, a prime number n _p satisfying n _p > n is used, and n of n _p pieces of distribution information that can be generated by the above-described processing is used. The (k, n) threshold method (ramp type (k, n) threshold method) in which the size of the shared information is reduced is realized.

<Configuration of secret information restoration device>
The configuration of the secret information restoration apparatus according to this embodiment will be described with reference to FIG.
As shown in FIG. 3, the secret information restoration apparatus according to the present embodiment includes a distributed information divider 21, a first partial secret information restorer 22, a second partial secret information restorer 23, and a coupler 24. It consists of and.

The shared information divider 21 receives k pieces of shared information (k is a positive integer equal to or smaller than the number n of distributed numbers), divides the information into partial shared information, and the first partial secret information restoring unit 22 and the second To the partial secret information restoring unit 23. The first partial secret information decompressor 22 performs an exclusive OR (XOR) operation on the input partial shared information, erases the random number, and (n _p −1) (n _p is the number of distributed n or more) Partial secret information) is output to the coupler 24. The second partial secret information restoring unit 23 combines the input partial secret information, and performs an exclusive OR (XOR) operation on the normal (n _p −1) pieces of partial secret information and the normal random number. Are deleted, and L partial secret information is output to the coupler 24. The coupler 24 concatenates the (n _p −1) pieces of partial secret information and L pieces of partial secret information in total (n _p −1 + L) pieces of partial secret information to restore the secret information.

<Processing of secret information restoration device>
The process of the shared information generation device according to this embodiment will be described with reference to FIG.

(Step S201)
Each _shared information S _i0 ,..., S _ik−1 is divided into partial shared information. (K is a positive integer having a variance n or less, n _p is a prime number having a variance n or more)

(Steps S202 and S203)
In the first partial secret information decompressor 22, (n _p −1) pieces of partial secret information K ₁ , K ₂ ,..., K _np−1 are restored, and in the second partial secret information restorer 23 L partial secret information K _np ,..., K _{np−1 + L} is restored.

(Step S204)
All the partial secret information is connected, and the original secret information K is restored.

  Therefore, according to the secret information restoration apparatus according to the present embodiment, the secret information can be restored safely and at high speed while finely setting the size of the shared information. In addition, since the size of the distributed information can be given a degree of freedom, the capacity of storage and memory can be reduced and the communication infrastructure can be used effectively.

<Example>
Hereinafter, as an example, a distribution / restoration method of the threshold secret sharing method (ramp-type threshold method) using XOR with the size of the shared information configured as L = 2 and based on the (3, 5) threshold method is shown. . Prior to the description, symbols used in the description are defined as in Equation 6.

Table 1 shows an example of the configuration of the dispersion information of the ramp-type threshold method based on the (3, 5) threshold method, with n _p = n = 5, k = 3, and L = 2. In Table 1, this is realized by substituting the random number R ₀ ¹ R ₁ ¹ in the conventional (3, 5) threshold method with partial secret information K ₄ and K ₅ . As a result, the size of each piece of shared information is reduced to 2/3 of the secret information.

In the partial shared information generating device, each partial shared information is generated according to Table 1. At this time, for example, when all partial secret information is restored from S ₀ , S ₁ , S ₂ , the first secret information restorer 22 and the second secret information restorer 23 perform the following combinations of XOR operations: When executed, partial secret information is restored. First, the following is a normal partial secret information restoration operation.

  Furthermore, L = 2 pieces of partial secret information constituting the partial shared information by replacing with random numbers are restored by the following calculation.

最終的に復元された部分秘密情報は以下のように連結されて秘密情報として出力される。

The finally restored partial secret information is connected as follows and output as secret information.

  The processing of the shared information generating device and the secret information restoring device is recorded on a computer-readable recording medium, and the program recorded on the recording medium is read and executed by the shared information generating device and the secret information restoring device. The shared information generating apparatus and secret information restoring apparatus of the present invention can be realized. The computer system here includes an OS and hardware such as peripheral devices.

  Further, the “computer system” includes a homepage providing environment (or display environment) if a WWW (World Wide Web) system is used. The program may be transmitted from a computer system storing the program in a storage device or the like to another computer system via a transmission medium or by a transmission wave in the transmission medium. Here, the “transmission medium” for transmitting the program refers to a medium having a function of transmitting information, such as a network (communication network) such as the Internet or a communication line (communication line) such as a telephone line.

  The program may be for realizing a part of the functions described above. Furthermore, what can implement | achieve the function mentioned above in combination with the program already recorded on the computer system, and what is called a difference file (difference program) may be sufficient.

  The embodiments of the present invention have been described in detail with reference to the drawings. However, the specific configuration is not limited to the embodiments, and includes designs and the like that do not depart from the gist of the present invention.

It is a block diagram of the distributed information generation apparatus which concerns on this embodiment. It is a processing flow of the distributed information generation apparatus which concerns on this embodiment. It is a block diagram of the secret information decompression | restoration apparatus which concerns on this embodiment. It is a processing flow of the secret information decompression | restoration apparatus which concerns on this embodiment.

Explanation of symbols

DESCRIPTION OF SYMBOLS 11 ... Secret information splitter, 12a, ..., 12n ... Random number generator, 13 ... Partially distributed information generator, 13a ... Partial secret information input part, 13b ... Random number input part , 14 ... coupler, 15 ... transmitter, 21 ... distributed information divider, 22 ... first partial secret information decompressor, 23 ... second partial secret information decompressor, 24 ... connector,

Claims (7)

A secret information divider that divides secret information to generate partial secret information, a predetermined number of partial secret information generated by the secret information divider and a predetermined number of random numbers are input, and the predetermined number of partial secret information and A partial shared information generator that generates partial shared information by exclusive OR (XOR) operation with a predetermined number of random numbers, and a combiner that combines the generated partial shared information and generates shared information A distributed information generation device,
The secret information divider divides the secret information into L pieces of partial secret information which is L more than a predetermined value n _p −1 (n _p is a prime number greater than or equal to the variance n) input to the partial shared information generator;
The shared information generating apparatus, wherein the surplus L pieces of secret information are input to the partial shared information generator as part of the predetermined number of random numbers.   The shared information generating apparatus according to claim 1, wherein L is a variable composed of a positive integer smaller than a predetermined number of the random numbers. A secret information restoring device for restoring secret information from the shared information generated by the shared information generating device according to claim 1 or 2,
A disperse information divider that inputs threshold information k (k is a positive integer equal to or less than the dispersal number n) and divides the input disperse information to generate partial disperse information;
A first restorer that inputs the partial shared information and restores n _p −1 (n _p is a prime number greater than or equal to the distributed number n) pieces of partial secret information;
A second decompressor that inputs the partial shared information and restores L partial secret information;
A concatenator that generates secret information by concatenating n _p −1 + L partial secret information reconstructed by the first reconstructor and the second reconstructor;
A secret information restoring apparatus comprising: A secret information divider that divides secret information to generate partial secret information, a predetermined number of partial secret information generated by the secret information divider and a predetermined number of random numbers are input, the predetermined number of partial secret information and a predetermined number A partial shared information generator for generating partial shared information by exclusive OR (XOR) operation with a random number of numbers, and a combiner for generating shared information by combining the generated partial shared information A shared information generation method in a shared information generation apparatus,
A first step of dividing secret information into L pieces of partial secret information which is greater than a predetermined value n _p −1 (n _p is a prime number equal to or greater than the distribution number n) which is input to the partial shared information generator;
A second step of inputting surplus L pieces of secret information as a part of the predetermined number of random numbers to the partial shared information generator;
A third step of generating partial shared information by an XOR operation of the n _p −1 partial secret information, the L partial secret information, and a random number;
A fourth step of generating the shared information by concatenating the generated partial shared information;
A distributed information generation method comprising: A secret information restoring method for restoring secret information from the shared information generated by the shared information generating method of claim 4,
A first step of inputting threshold information k (k is a positive integer equal to or less than the number of distributions n), dividing the input distribution information and generating partial distribution information;
A second step of inputting the partial shared information to restore n _p −1 partial secret information (n _p is a prime number greater than or equal to the distributed number n);
A third step of inputting the partial shared information and restoring L partial secret information;
A fourth step of generating secret information by concatenating n _p −1 + L partial secret information restored in the second step and the third step;
A method for restoring secret information, comprising: A secret information divider that divides secret information to generate partial secret information, a predetermined number of partial secret information generated by the secret information divider and a predetermined number of random numbers are input, the predetermined number of partial secret information and a predetermined number A partial shared information generator for generating partial shared information by exclusive OR (XOR) operation with a random number of numbers, and a combiner for generating shared information by combining the generated partial shared information A program for causing a computer to execute a shared information generation method in the shared information generation apparatus,
A first step of dividing secret information into L pieces of partial secret information which is greater than a predetermined value n _p −1 (n _p is a prime number equal to or greater than the distribution number n) which is input to the partial shared information generator;
A second step of inputting surplus L pieces of secret information as a part of the predetermined number of random numbers to the partial shared information generator;
A third step of generating partial shared information by an XOR operation of the n _p −1 partial secret information, the L partial secret information, and a random number;
A fourth step of generating the shared information by concatenating the generated partial shared information;
A program that causes a computer to execute. A program for causing a computer to execute a secret information restoring method for restoring secret information from the shared information generated by the shared information generating method of claim 4,
A first step of inputting threshold information k (k is a positive integer equal to or less than the number of distributions n), dividing the input distribution information and generating partial distribution information;
A second step of inputting the partial shared information to restore n _p −1 partial secret information (n _p is a prime number greater than or equal to the distributed number n);
A third step of inputting the partial shared information and restoring L partial secret information;
A fourth step of generating secret information by concatenating the n _p −1 + L partial secret information restored in the step 2 and the third step;
A program that causes a computer to execute.

Images