JP2007150938A - Visual secret sharing scheme and visual secret sharing system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide visual secret sharing scheme and system which reduce the number of sheets of distributed OHP sheets which each participant has to have. <P>SOLUTION: As a method of distributing a secret picture, threshold (k, n) method of Shamir on an extension field GF (2"m) is used. In order to distribute the secret picture using the threshold (k, n) method of Shamir on the extension field FG (2"m), in each pixel, a degree which becomes a polynomial f(0 ... 0)=(1 ... 1) at the time of a black pixel (p=1), and a polynomial f(0 ... 0)=(0 ... 0) at the time of a white pixel (p=0), generates a k-primary random polynomial f(x). In order to distribute using the threshold (k, n) method of the Shamir on an extension field GF(2"m) to the secret picture of m sheets, in the chromatic of each pixel p_1,...,p_m, it sets, a degree which becomes a polynomial f(0 ... 0)=(p_1 ... p_m) generates a k-primary random polynomial f(x). <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a visual decoding type secret sharing method and a visual decoding type secret sharing system, and more particularly to a visual decoding type secret sharing method in which a secret image is distributed to two or more distributed OHP sheets using Shamir's threshold method.

  The visual decryption secret sharing method is one of secret sharing methods, and more precisely, is a (k, n) threshold-visual decryption secret sharing method. The (k, n) threshold-visual decryption secret sharing method distributes the secret image to be distributed to n distributed OHP sheets, and arbitrarily k (= <n) images from the n distributed OHP sheets. The original secret image appears by overlapping the distributed OHP sheets. However, the original secret image cannot be restored from any k-1 or less distributed OHP sheets.

  In the conventionally known (k, n) threshold-visual decoding secret sharing method, as disclosed in Non-Patent Document 1 below, the black and white reversal function of a copier is used to completely restore the original secret image. There is a completely reconstructed (k, n) threshold-visual decryption type secret sharing method that can be reconstructed.

S. Cimato, A. D. Santis, A. L. Ferrara, B. Masucci, Ideal contrast visual cryptography schemes with reversing, Information Processing Letters, vol. 93, Issue 4, 2005, pp. 199-206.

  In Non-Patent Document 1 described above, the number of dispersed OHP sheets that each participant must have is 2 ^ {k-1}. That is, as the number of participants k (= <n) to be distributed increases, the number of distributed OHP sheets that each participant must have increases as an exponential function.

  Further, even when two or more secret images are owned, when two or more secret images are distributed, the secret images must be distributed for each one, which is inefficient.

  Therefore, an object of the present invention is to provide a visual decryption type secret sharing method that reduces the number of distributed OHP sheets that each participant must have.

  It is another object of the present invention to provide a visual decryption secret sharing method that reduces the amount of computation when reconstructing a distributed OHP sheet.

  It is another object of the present invention to provide a visual decoding type secret sharing method capable of efficiently distributing two or more secret images simultaneously.

  In order to solve the above problems, the present invention employs means for solving the problems having the following characteristics.

  The invention according to one aspect of the method for distributing a secret image according to the present invention uses the Shamir (k, n) threshold method on the extension field GF (2 ^ m), and the secret of the l (el) pixel to be distributed. The secret is generated by reconfiguring the image (I) by a distributed generation mechanism to generate a distributed generation phase for generating n distributed OHP sheet groups and an arbitrary k or more distributed OHP sheet groups (S) generated. And a restoration phase in which the image (I) appears after restoration.

The distributed generation phase is:
For the color p_j of each pixel (j) of the secret image (I) using the Shamir's (k, n) threshold method, the dispersion generation mechanism has an order such that f_j (0) = p_j is k−1. Generating a random polynomial f_j (x) less than or equal to:
Calculating the share V_ {j, i} = f_j (i) of the participant (i) from i = 1 to n (> = k) by the distributed generation mechanism;
The distributed generation mechanism makes the share V_ {j, i} of the participant (i) V_ {j, i} = [v_ {j, i, 1}, ..., v_ {j, i, m}] converting to a binary representation vector displaying m-order 0 or 1;
The distributed generation mechanism calculates the color of the pixel (j) of the tth distributed OHP sheet from the l binary representation vectors V_ {1, i}, ..., V_ {l, i} of the participant (i). , V_ {j, i, t} is white if 0, black if 1 or black if v_ {j, i, t} is 0, white if 1 Sheet S_ {i, 1} = (v_ {1, i, 1} ... v_ {l, i, 1}), ..., S_ {i, m} = (v_ {1, i, m} ... generating v_ {l, i, m}),
Sending m pieces of dispersed OHP sheets S_ {i, 1},..., S_ {i, m} generated by the distributed generation mechanism to the participant (i).

The restoration phase is:
Among the n participants who reconstructed, from the k participants, the m distributed OHP sheets S_ {i, 1}, ..., S_ {i, m} of each participant (i) Collecting steps,
Lagrange the distributed OHP sheets S_ {1,1}, ..., S_ {1, m}, ..., S_ {k, 1}, ..., S_ {k, m} collected by the reconstructor And a step of restoring the secret image by reversing and superimposing the dispersed OHP sheet using the interpolation formula.

  Here, the extension field GF (2 ^ m) is an extension of the Galois field GF (2) whose set element is 2, and is a Galois field with 2 ^ m (2 to the power of m) element . A Galois field is a set in which the elements of the set are finite and the four arithmetic operations are closed. The extension field is described in the IEICE editor, Satoshi Kurosawa and Waka Ogata, author, “Basic Mathematics of Modern Cryptography”, Section 4.5, Extension Field GF (2 ^ m), Corona.

  On the other hand, Shamir's (k, n) threshold method uses secret information S to be distributed using a random polynomial f (x) of order k-1 such that the polynomial f (0) = S. The secret information S is obtained by generating n shares, which are points on the polynomial, and algebraically solving the generated n shares using k (= <n) shares.

  When Shamir's (k, n) threshold method on the extension field GF (2 ^ m) is used for one secret image, for each pixel of the secret image I, the polynomial f ([ 0 ... 0]) = ([1 ... 1]), a degree such that the polynomial f ([0 .. 0]) = ([0 ... 0]) when the pixel is a white pixel Generates a k-1 random polynomial f (x). When Shamir's (k, n) threshold method on the extension field GF (2 ^ m) is used for N secret images, for each pixel color p_1, ..., p_N of N secret images, A random polynomial f (x) having an order of (k−1) th order such that the polynomial f ([0 ... 0]) = ([p_1 ... p_N]) is generated.

The invention according to one aspect of the system for distributing secret images according to the present invention,
A distributed generation phase for generating a group of n distributed OHP sheets by a distributed generation mechanism, and an arbitrary k or more distributed OHP sheet groups (i) By reconstructing S), a visual decoding type secret sharing method configured by a restoration phase in which the secret image (I) appears after restoration is used.

In the distributed generation phase,
For the color p_j of each pixel (j) of the secret image (I) using the Shamir's (k, n) threshold method, the order of the k-1th order is f_j (0) = p_j. A polynomial generating means for generating the following random polynomial f_j (x);
A polynomial calculation means for calculating the share V_ {j, i} = f_j (i) of the participant (i) from i = 1 to n (> = k), and
The distributed generation mechanism determines the share V_ {j, i} of the participant (i) as V_ {j, i} = [v_ {j, i, 1}, ..., v_ {j, i, m}] A binary representation vector conversion means for converting to a binary representation vector displaying the next 0 or 1;
The distributed generation mechanism changes the color of the pixel (j) of the tth distributed OHP sheet from the l binary representation vectors V_ {1, i}, ..., V_ {l, i} of the participant (i) to v_ Participant (i) m distributed OHP sheets S_ as white if {j, i, t} is 0, black if 1, black if v_ {j, i, t} is 0, white if 1 {i, 1} = (v_ {1, i, 1} ... v_ {l, i, 1}), ..., S_ {i, m} = (v_ {1, i, m} .. v_ {l, i, m}) for generating a distributed OHP sheet,
.., S_ {i, m} generated by the distributed generation mechanism is transmitted to the participant (i).

In the restoration phase,
Among the n participants who reconstructed, from the k participants, the m distributed OHP sheets S_ {i, 1}, ..., S_ {i, m} of each participant (i) Collecting means to collect,
Lagrange the distributed OHP sheets S_ {1,1}, ..., S_ {1, m}, ..., S_ {k, 1}, ..., S_ {k, m} collected by the reconstructor There is a restoration means for restoring the secret image by the black and white inversion and superposition of the distributed OHP sheet using the above interpolation formula.

  According to the present invention, the number of distributed OHP sheets that each participant must have is obtained by distributing the secret image using Shamir's (k, n) threshold method on the extension field GF (2 ^ m). Can be reduced.

  According to the present invention, in the Shamir (k, n) threshold method, the polynomial f ([0 ... 0]) = ([0 ... 0]) or ([1 ... 1]) and By doing so, it is possible to reduce the amount of calculation when reconfiguring the distributed OHP sheet.

  Furthermore, according to the present invention, in the Shamir's (k, n) threshold method, N images can be simultaneously obtained by setting the polynomial f ([0 ... 0]) = ([p_1 ... p_N]). It can be dispersed efficiently.

  Hereinafter, an embodiment of a visual decryption type secret sharing method using Shamir's (k, n) threshold method on the extension field GF (2 ^ m) according to the present invention will be described in detail. However, 2 ^ m> n.

  In the present invention, the Shamir (k, n) threshold method on the extension field GF (2 ^ m) is used as a method for distributing the secret image. In order to distribute the secret image using Shamir's (k, n) threshold method on the extension field GF (2 ^ m), for each pixel, the polynomial f (0... When black pixel (p = 1). 0) = (1 ... 1), and the order of polynomial f (0 ... 0) = (0 ... 0) for white pixels (p = 0) is k-1 order Generate a random polynomial f (x). In order to distribute the m secret images using the Shamir (k, n) threshold method on the extension field GF (2 ^ m), the polynomial f (in the colors p_1, ..., p_m of each pixel A random polynomial f (x) of order k-1 order such that 0 ... 0) = (p_1 ... p_m) is generated.

  Hereinafter, a first embodiment of the visual decoding type secret sharing method according to the present invention will be described. In particular, how the effect of the present invention for reducing the amount of calculation when restoring a secret image is obtained. This will be described in detail. Here, the visual decryption secret sharing method includes three phases: a preparation phase, a distributed generation phase, and a restoration phase. Hereinafter, each phase will be described in order.

1. Preparation phase Assume n participants, threshold k, and expanded field GF (2 ^ m). The secret image I has l (el) pixels.

2. Distributed Generation Phase The distributed generation mechanism used in the distributed generation phase is described in FIG. Specifically, the distributed generation mechanism includes a polynomial generation unit, a polynomial calculation unit, a binary expression vector conversion unit, a distributed OHP sheet generation unit, and a transmission unit that function in the distribution generation phase. Specifically, the restoration mechanism includes a collection unit and a restoration unit that function in the restoration phase. The polynomial generation unit has a secret image input unit, and the polynomial calculation unit has a distributed OHP sheet number input unit. The operations of the polynomial generation unit, polynomial calculation unit, binary expression vector conversion unit, and distributed OHP sheet generation unit are as described below in the distributed generation mechanism as the distributed OHP sheet generation unit. .

  The polynomial generating unit uses a Shamir's (k, n) threshold method to generate f_j (0) = p_j for the color p_j of each pixel (j) of the secret image (I). Generate a random polynomial f_j (x) of degree k-1 or less. The polynomial calculation unit calculates the share V_ {j, i} = f_j (i) of the participant (i) from the distribution generation mechanism i = 1 to n (> = k). In the binary representation vector conversion unit, the distributed generation mechanism changes the share V_ {j, i} of the participant (i) to V_ {j, i} = [v_ {j, i, 1}, ..., v_ {j , i, m}] is converted to a binary representation vector representing m-th order 0 or 1. The distributed OHP sheet generation unit generates a distribution OHP sheet of the t-th distributed OHP sheet from the l binary representation vectors V_ {1, i}, ..., V_ {l, i} of the participant (i). Participant (i) with pixel (j) as white if v_ {j, i, t} is 0, black if 1, black if v_ {j, i, t} is 0, white if 1 M distributed OHP sheets S_ {i, 1} = (v_ {1, i, 1} ... v_ {l, i, 1}), ..., S_ {i, m} = (v_ { 1, i, m} ... generates v_ {l, i, m}). The transmission means sends m distributed OHP sheets S_ {i, 1},..., S_ {i, m} generated by the distributed generation mechanism to the participant (i).

  The collection unit includes m distributed OHP sheets S_ {i, 1}, ..., S_ {each of the participants (i) from k participants among the n participants whose reconstructors are n members. collect i, m}. The restoration unit includes distributed OHP sheets S_ {1,1}, ..., S_ {1, m}, ..., S_ {k, 1}, ..., S_ {k collected by the reconstructor. , m} using Lagrange's interpolation formula to restore the secret image by black-and-white reversal and superposition of the distributed OHP sheet.

  FIG. 2 shows a sample of the secret image (I) to be distributed and generated.

(2-1). The distributed generator using the distributed generation mechanism, for each pixel (j) of the secret image (I),
Polynomial f_j ([0 ... 0]) = ([1 ... 1]) when pixel (j) is a black pixel (p_j = 1)
Random extension field GF (2 ^ m) such that polynomial f_j ([0 ... 0]) = ([0 ... 0]) when pixel (j) is a white pixel (p_j = 0) The above k-1 degree polynomial f_j (x) is generated.

  The polynomial f_j (x) is expressed as the following formula (1).

f_j (x) = x ^ {k-1} a_1 + x ^ {k-2} a_2 + ... + x a_ {k-1} + [b_1 ... b_m] ... (1)
Where a_1, ..., a_ {k-1} are random coefficients on the extension field GF (2 ^ m), and [b_1 ... b_m] is [0 ... 0] or [1 ... 1].

(2-2). The distributed generator using the distributed generation mechanism, for participant i, from i = 1 to n, and for each pixel (j) from j = 1 to l, The share V_ {j, i} of the participant i is calculated on the extension field GF (2 ^ m) from the polynomial f_j (x) generated in the item 1) according to the following formula (2).

V_ {j, i} = f_j (i) = [v_ {j, i, 1} ... v_ {j, i, m}] ... (2)
Since the share V_ {j, i} of participant i is an element of the extension field GF (2 ^ m), v_ {j, i, m} is 0 or 1, where 0 is white and 1 is black ( 0 may be black and 1 may be white), v_ {i_j, 1} is the color of pixel (j) of the first distributed OHP sheet of participant i, and v_ {i_j, m} is m of participant i Generate m distributed OHP sheets S_ {i, 1}, ..., S_ {i, m} of participant i as the color of pixel (j) of the first distributed OHP sheet according to the following equation (3) To do. In the following formula (3), there are a total of m formulas such as S_ {i, 1},..., S_ {i, m}.

S_ {i, 1} = (v_ {1, i, 1} ... v_ {l, i, 1}), ...
..., S_ {i, m} = (v_ {1, i, m} ... v_ {l, i, m}) ... (3 )
As a specific example, when the participants are n = 5, the threshold is k = 4, and the expansion field GF (2 ^ 4) is used, a sample of four distributed OHP sheets that generate a share of five participants is shown in the figure. 3 shows.

(2-3) The distributed generator gives m distributed OHP sheets S_ {i, 1},..., S_ {i, m} to participant i from i = 1 to n.

3. Restore phase
(3-1). The number of reconfigurators is k among the m distributed OHP sheets S_ {i, 1}, ..., S_ {i, m} of n participants i Collect OHP sheets.

(3-2) The reconstructor collected the distributed OHP sheets S_ {1,1}, ..., S_ {1, m}, ..., S_ {k, 1}, .. collected in 3-1. ., S_ {k, m} to restore secret image I using Lagrange's interpolation formula.

  Here, Lagrange's interpolation formula can simplify the algebraic solution of polynomials, and a polynomial passing through a plurality of discrete data is determined simply by giving a plurality of discrete data. Lagrange's interpolation formula is described in Mitsuko Miyaji and Hiroaki Kikuchi, “IT Text Information Security”, Section 7.1 Secret Sharing Method, Ohm.

  The restoration of the secret image using the Lagrange interpolation formula on the extension field GF (2 ^ m) is performed according to the following formula (4).

[I_1 ... I_m] = f ([0 ... 0]) = lambda_1 ([0 ... 0]) * [S_ {1,1} ... S_ {1, m}] + .. + lambda_k ([0 ... 0]) * [S_ {k, 1} ... S_ {k, m}] = [c_1 ... c_m] ... (4)
Note that lambda_1 ([0 ... 0]), ..., lambda_k ([0 ... 0]) is a Lagrange coefficient on the extension field GF (2 ^ m), and S_ {1,1}. .. S_ {1, m}, ..., S_ {k, 1} ... S_ {k, m} is a distributed OHP sheet with k participants each, c_1, ... , c_m are the sums of S_ {1,1}, ..., S_ {k, m} computed on the Galois field GF (2), where I_1, ..., I_m It is an image restored by the expressions c_1, ..., c_m. Among the m expressions c_1, ..., c_m, select c_t with the least number of terms to be added.

  The calculation using the superposition of the dispersed OHP sheet and the black and white inversion (of the dispersed OHP sheet) by the formula I_t = c_t on Galois field GF (2) is A XOR B = NOT (NOT (A) OR B) OR NOT ( A OR NOT (B)).

  Here, XOR (exclusive OR) indicates addition on Galois field GF (2), OR (OR) indicates superposition of distributed OHP sheets, and NOT (negative) indicates black-and-white inversion of distributed OHP sheets. Show.

  An image I_t that is the same as the secret image I is obtained by an operation using black-and-white reversal and superposition of the dispersion OHP sheet along the expression I_t = c_t on the Galois field GF (2).

As a concrete example, the dispersion OHP sheets of Participant 1, Participant 2, Participant 3 and Participant 4 out of 5 participants are collected and distributed by Lagrange's interpolation formula on expansion field GF (2 ^ 4) Fig. 4 shows a method for restoring a secret image using OHP sheet superposition and black-and-white reversal. As shown in FIG. 4, there are nine items of c ₂ and c ₃ that add the fewest items, so if I select ₂ or c ₃ and restore I ₂ , the redistributed OHP sheet can be reconstructed. The amount of calculation can be reduced. The example was to restore the I ₂ by selecting FIG 4, c ₂ is shown.

  Hereinafter, a second embodiment of the visual decoding type secret sharing method according to the present invention will be described, and in particular, how the effect of the present invention that two or more secret images can be efficiently distributed simultaneously is obtained. This will be described in detail. Here, the visual decryption secret sharing method includes three phases: a preparation phase, a distributed generation phase, and a restoration phase. Hereinafter, each phase will be described in order.

1. Preparation phase Assume n participants, threshold k, and expanded field GF (2 ^ m). There are N (= <m) secret images I_1,..., I_N, and each secret image has l pixels that satisfy the following formula (5). In the following formula (5), there are a total of N formulas such as I_1,..., I_N.

I_1 = (p_ {1,1} ... p_ {1, l}), ...
..., I_N = (p_ {N, 1} ... p_ {N, l}) ... (5)
Here, p_ {N, l} is 0 or 1, 0 corresponds to a white pixel, and 1 corresponds to a black pixel.

2. Distributed Generation Phase The distributed generator performs distributed generation of N secret images I_N using the distributed generation mechanism, as in the first embodiment. When N <m, prepare exactly m secret images by setting I_ {N + 1} = I_1, ..., I_j = I_ {jN}, ..., I_m = I_ {mN} .

(2-1). The distributed generator generates a random extension field for each pixel p_ {1,1}, ..., p_ {m, l} of m secret images I_1, ... I_m. Generate k-1th order polynomials f_1 (x), ..., f_l (x) on GF (2 ^ m).

  The polynomials f_1 (x),..., F_l (x) are expressed as the following formula (6). In the following formula (6), there are a total of l formulas such as f_1 (x),..., F_l (x).

f_1 (x) = x ^ {k-1} a_ {1,1} + x ^ {k-2} a_ {1,2} + ... + x a_ {1, (k-1)} + [ p_ {1,1} ... p_ {m, 1}], ...
..., f_l (x) = x ^ {k-1} a_ {l, 1} + x ^ {k-2} a_ {l, 2} + ... + x a_ {l, (k-1 )} + [p_ {1, l} ... p_ {m, l}]
(6)
Here, a_ {1,1}, ..., a_ {l, (k-1)} are random coefficients on the extension field GF (2 ^ m).

(2-2) The variance generator uses the polynomials f_1 (x), ..., f_l (x) generated in 2-1 to share the participant i V_ {1, i}, ..., V_ { l, i} is calculated on GF (2 ^ m) from i = 1 to n so as to satisfy the following formula (7). In the following formula (7), there are a total of l formulas such as f_1 (x),..., F_l (x).

V_ {1, i} = f_1 (i) = [u_ {1, i, 1} ... u_ {1, i, N}], ...
..., V_ {l, i} = f_l (i) = [u_ {l, i, 1} ... u_ {l, i, N}] ... ... (7)
(2-3). The distributed generator uses the share i of participant i V_ {1, i}, ..., V_ {l, i} and follows formula (8) from i = 1 to n. Generate m distributed OHP sheets S_ {i, 1},..., S_ {i, m} of participant i. In the following formula (8), there are a total of m formulas such as S_ {i, 1},..., S_ {i, m}.

S_ {i, 1} = (u_ {1, i, 1} ... u_ {l, i, 1}), ...
..., S_ {i, m} = (u_ {1, i, m} ... u_ {l, i, m}) ... (8)
Here, u_ {l, i, N} is 0 or 1, and 0 corresponds to a white pixel and 1 corresponds to a black pixel.

  Let S_ {i, 1} be the first distributed OHP sheet for participant i, and S_ {i, m} be the mth distributed OHP sheet for participant i.

(2-4) The distributed generator gives m distributed OHP sheets S_ {i, 1},..., S_ {i, m} to the participants i from i = 1 to n, respectively.

3. Restore phase
(3-1). The reconstructor collects k distributed OHP sheets S_ {i, 1}, ..., S_ {i, m} of participant i for k people.

(3-2) The reconstructor collected the distributed OHP sheets S_ {1,1}, ..., S_ {1, m}, ..., S_ {k, 1}, .. collected in 3-1. ., S_ {k, m} using Lagrange's interpolation formula, m secret images I_m are restored.

  Restoration of the m secret images I_m using the Lagrange interpolation formula on the extension field GF (2 ^ m) is performed according to the following equation (9).

[I_1 ... I_m] = f ([0 ... 0]) = lambda_1 ([0 ... 0]) * [S_ {1,1} ... S_ {1, m}] + .. + lambda_k ([0 ... 0]) * [S_ {k, 1} ... S_ {k, m}] = [c_1 ... c_m] ... (9)
Where lambda_1 ([0 ... 0]), ..., lambda_k ([0 ... 0]) is the Lagrange coefficient on the extension field GF (2 ^ m) and S_ {1,1} ... S_ {1, m}, ..., S_ {k, 1} ... S_ {k, m} is a distributed OHP sheet with k participants each, c_1,. ., c_m is the sum of some of S_ {1,1}, ..., S_ {k, m} computed on Galois field GF (2), and I_1, ..., I_m is The images are restored by the expressions c_1, ..., c_m, respectively.

  For each secret image I_j (1 = <j = <N), if I_j = I_ {j + N} = ... = I_ {j + tN}, then c_j, c_ {j + N}, ... , c_ {j + tN}, select c_ {j '} with the least number of terms to be added.

  The calculation using the superposition of the dispersed OHP sheet and the black and white inversion (of the dispersed OHP sheet) by the formula I_j = c_ {j ′} on the Galois field GF (2) is performed in the same manner as in the first embodiment.

  N secret images I_1,..., I_N are obtained by calculation using black and white reversal and superposition of the distributed OHP sheet along the formula I_j = c_ {j ′}.

  The subject of the invention also includes a program for causing a computer to execute each step in the above-described visual decryption type secret sharing method. This program may be the program itself, or this program is stored in a computer-readable recording medium. It may be what has been done.

  In the present invention, as the recording medium, a memory necessary for processing by the microcomputer, such as a ROM itself, may be a program medium, or a program as an external storage device (not shown). It may be a program medium provided with a reading device and readable by inserting a recording medium therein. In any case, the stored program may be configured to be accessed and executed by the microcomputer, or in any case, the program is read out, and the read program is stored in the program storage area of the microcomputer. The program may be loaded and executed by the program. It is assumed that this loading program is stored in the main device in advance.

  Here, the program medium is a recording medium configured to be separable from the main body, such as a tape system such as a magnetic tape or a cassette tape, a magnetic disk such as an FD (flexible disk) or HD (hard disk), or a CD-ROM / Supports fixed programs including optical disks such as MO / MD / DVD, card systems such as IC cards (including memory cards) / optical cards, and semiconductor memories such as mask ROM, EPROM, EEPROM, flash ROM, etc. It may be a medium.

  Further, in the present invention, since the system configuration is connectable to a communication network including the Internet, the medium may be a medium that dynamically carries the program so as to download the program from the communication network. When the program is downloaded from the communication network in this way, the download program may be stored in the apparatus main body in advance or may be installed from another recording medium.

  Furthermore, in the present invention, the program itself may be a process executed by a microcomputer, or may be acquired by accessing a communication network including the Internet, or may be acquired. You may send out from.

  Further, each of the above-described embodiments is merely an example of a preferred embodiment of the present invention, and the present invention can be implemented with various modifications without departing from the gist thereof.

It is a block diagram of the dispersion | distribution production | generation mechanism of the visual decoding type | formula secret sharing method. It is a sample figure of the secret image used as dispersion | distribution production | generation object in the visual decoding type | formula secret sharing method. In the distributed generation phase of the visual decryption secret sharing method, 4 participants generated shares of 5 participants when the participants were n = 5, the threshold was k = 4, and the extension field GF (2 ^ 4). It is a sample figure of a dispersion | distribution OHP sheet | seat. In the restoration phase of the visual decryption secret sharing method, when participants are n = 5, threshold is k = 4, and extended field GF (GF2 ^ 4), participant 1 out of 5 participants Method for collecting secret OHP sheets of participant 2, participant 3, and participant 4 and reconstructing secret images using superposition of black and white reversal using the Lagrange interpolation formula on expansion GF (2 ^ 4) FIG.

Claims (12)

A distributed generation phase for generating n distributed OHP sheet groups by a distributed generation mechanism for a secret image (I) of l (el) pixels to be distributed;
In the visual decryption type secret sharing method configured by the reconstruction phase in which the secret image (I) appears by reconstructing the generated k or more distributed OHP sheet groups (S),
The distributed generation phase is:
For the color p_j of each pixel (j) of the secret image (I) using the Shamir's (k, n) threshold method, the dispersion generation mechanism has an order such that f_j (0) = p_j is k−1. Generating a random polynomial f_j (x) less than or equal to:
Calculating the share V_ {j, i} = f_j (i) of the participant (i) from i = 1 to n (> = k) by the distributed generation mechanism;
The distributed generation mechanism makes the share V_ {j, i} of the participant (i) V_ {j, i} = [v_ {j, i, 1}, ..., v_ {j, i, m}] converting to a binary representation vector displaying m-order 0 or 1;
The distributed generation mechanism calculates the color of the pixel (j) of the tth distributed OHP sheet from the l binary representation vectors V_ {1, i}, ..., V_ {l, i} of the participant (i). , V_ {j, i, t} is white if 0, black if 1 or black if v_ {j, i, t} is 0, white if 1 Sheet S_ {i, 1} = (v_ {1, i, 1} ... v_ {l, i, 1}), ..., S_ {i, m} = (v_ {1, i, m} ... generating v_ {l, i, m}),
Sending m distributed OHP sheets S_ {i, 1}, ..., S_ {i, m} generated by the distributed generation mechanism to the participant (i),
The restoration phase is:
Among the n participants who reconstructed, from the k participants, the m distributed OHP sheets S_ {i, 1}, ..., S_ {i, m} of each participant (i) Collecting steps,
Lagrange the distributed OHP sheets S_ {1,1}, ..., S_ {1, m}, ..., S_ {k, 1}, ..., S_ {k, m} collected by the reconstructor A visual decoding type secret sharing method comprising the step of restoring a secret image by black and white reversal and superposition of a distributed OHP sheet using the interpolation formula of Shamir's (k, n) threshold method is a (k, n) threshold method on the extension field GF (2 ^ m),
The share V_i of the participant (i) obtained by the secret sharing method using the (k, n) threshold method is an element of the extension field GF (2 ^ m),
In order to reduce the number of distributed OHP sheets that the participant (i) must have, the share V_i is m-th order V_i = ([v_ {i, 1} ... v_ {i, m}]) 2. The visual decoding type secret sharing method according to claim 1, wherein the method is converted into a binary expression vector that displays 0 or 1 of. In the restoration phase,
For each pixel (j) of the secret image (I), the polynomial f_j ([0 ... 0] on the extension field (2 ^ m) when the pixel (j) is black (p_j = 1) ) = [1 ... 1], and the polynomial f_j ([0 ... 0]) = [0 .0] on the extension field (2 ^ m) when the pixel (j) is white (p_j = 0). .. 0] to generate the polynomial f_j (x) on the extension field (2 ^ m) such that the secret image (I) is restored in m ways,
2. The method of restoring a secret image I_t that can most efficiently be restored by reducing the amount of computation for reconstructing a distributed OHP sheet among the m ways of restoration of the secret image (I). Or the visual decryption type secret sharing method according to 2. In the distribution phase,
Using N l (el) pixel secret images I_1, ..., I_N, if N <m, (mN) images I_ {N + 1}, ..., I_m In the case of an image, using m images I_1, ..., I_N, I_ {N + 1}, ..., I_m, the color p_ {1,1}, ... of each pixel of the image , p_ {l, m}, polynomial f_1 ([0 ... 0]) = [p_ {1,1} ... p_ {m, 1}] over the extension field GF (2 ^ m) , ..., f_l ([0 ... 0]) = [p_ {1, l} ... p_ {m, l}] j = 1 on the extension field GF (2 ^ m) 4. The visual decoding-type secret sharing method according to claim 1, wherein N secret images are efficiently distributed simultaneously by generating a polynomial f_j (x) from j to j = l. .   Using N l (el) pixel secret images I_1, ..., I_N, if N <m, then (mN) images are I_ {N + 1} = I_1, ..., I_j The visual amount according to any one of claims 1 to 4, wherein a calculation amount of reconstruction of a distributed OHP sheet can be reduced by setting = I_ {jN}, ..., I_m = I_ {mN}. Decryption type secret sharing method. A distributed generation phase for generating n distributed OHP sheet groups by a distributed generation mechanism for a secret image (I) of l (el) pixels to be distributed;
A visual decoding method using a visual decoding type secret sharing method composed of a reconstruction phase in which the secret image (I) appears by reconstructing the generated k or more distributed OHP sheet groups (S). A decryption secret sharing system,
In the distributed generation phase,
For the color p_j of each pixel (j) of the secret image (I) using the Shamir's (k, n) threshold method, the order of the k-1th order is f_j (0) = p_j. A polynomial generating means for generating the following random polynomial f_j (x);
A polynomial calculation means for calculating the share V_ {j, i} = f_j (i) of the participant (i) from i = 1 to n (> = k), and
The distributed generation mechanism determines the share V_ {j, i} of the participant (i) as V_ {j, i} = [v_ {j, i, 1}, ..., v_ {j, i, m}] A binary representation vector conversion means for converting to a binary representation vector displaying the next 0 or 1;
The distributed generation mechanism changes the color of the pixel (j) of the tth distributed OHP sheet from the l binary representation vectors V_ {1, i}, ..., V_ {l, i} of the participant (i) to v_ Participant (i) m distributed OHP sheets S_ as white if {j, i, t} is 0, black if 1, black if v_ {j, i, t} is 0, white if 1 {i, 1} = (v_ {1, i, 1} ... v_ {l, i, 1}), ..., S_ {i, m} = (v_ {1, i, m} .. v_ {l, i, m}) for generating a distributed OHP sheet,
Transmission means for sending m distributed OHP sheets S_ {i, 1}, ..., S_ {i, m} generated by the distributed generation mechanism to the participant (i),
In the restoration phase,
Among the n participants who reconstructed, from the k participants, the m distributed OHP sheets S_ {i, 1}, ..., S_ {i, m} of each participant (i) Collecting means to collect,
Lagrange the distributed OHP sheets S_ {1,1}, ..., S_ {1, m}, ..., S_ {k, 1}, ..., S_ {k, m} collected by the reconstructor A visual decoding type secret sharing system, comprising: a restoration means for restoring a secret image by black and white inversion and superposition of a distributed OHP sheet using the interpolation formula of In the visual decryption secret sharing system,
Shamir's (k, n) threshold method is a (k, n) threshold method on the extension field GF (2 ^ m),
The share V_i of the participant (i) obtained by the secret sharing method using the (k, n) threshold method is an element of the extension field GF (2 ^ m),
In order to reduce the number of distributed OHP sheets that the participant (i) must have, the share V_i is V_i = ([v_ {i, 1} ... v_ {i, m}]) m 7. The visual decryption secret sharing system according to claim 6, wherein the visual decryption secret sharing system is converted into a binary representation vector representing the next 0 or 1. In the restoration phase,
For each pixel (j) of the secret image (I), the polynomial f_j ([0 ... 0] on the extension field (2 ^ m) when the pixel (j) is black (p_j = 1) ) = [1 ... 1], and the polynomial f_j ([0 ... 0]) = [0 .0] on the extension field (2 ^ m) when the pixel (j) is white (p_j = 0). .. 0], the m number of reconstructions of the secret image (I) is performed by generating the polynomial f_j (x) over the extension field (2 ^ m) such that
The method of restoring the secret image I_t that can reduce the amount of computation of reconstruction of the distributed OHP sheet most effectively and can be restored most efficiently is selected from the m methods of restoration of the secret image (I). 8. The visual decryption secret sharing system according to 6 or 7.   In the dispersion phase, using N l-pixel secret images I_1, ..., I_N, when N <m, (mN) images I_ {N + 1}, ... , I_m is an arbitrary image, and m images I_1, ..., I_N, I_ {N + 1}, ..., I_m are used to specify the color p_ {1,1 }, ..., p_ {l, m}, the polynomial f_1 ([0 ... 0]) = [p_ {1,1} ... p_ {on the extension field GF (2 ^ m) m, 1}], ..., f_l ([0 ... 0]) = [p_ {1, l} ... p_ {m, l}] extension GF (2 ^ m) 9. The vision according to claim 6, wherein N secret images are efficiently distributed simultaneously by generating a polynomial f_j (x) from j = 1 to j = l above. Decryption type secret sharing system.   Using N l (el) pixel secret images I_1, ..., I_N, if N <m, then (mN) images are I_ {N + 1} = I_1, ..., I_j 10. The visual decoding according to any one of claims 6 to 9, wherein the calculation amount of reconstruction of a distributed OHP sheet can be reduced by setting = I_ {jN}, ..., I_m = I_ {mN} Type secret sharing system. On the computer,
A distributed generation phase for generating a group of n distributed OHP sheets by a distributed generation mechanism, and an arbitrary k or more distributed OHP sheet groups (i) A program for executing a visual decoding type secret sharing method constituted by a reconstruction phase in which the secret image (I) appears by reconstructing by reconstructing S),
For the color p_j of each pixel (j) of the secret image (I) using the Shamir's (k, n) threshold method, the dispersion generation mechanism has an order such that f_j (0) = p_j is k−1. Generating a random polynomial f_j (x) less than or equal to:
Calculating the share V_ {j, i} = f_j (i) of the participant (i) from i = 1 to n (> = k) by the distributed generation mechanism;
The distributed generation mechanism makes the share V_ {j, i} of the participant (i) V_ {j, i} = [v_ {j, i, 1}, ..., v_ {j, i, m}] converting to a binary representation vector displaying m-order 0 or 1;
The distributed generation mechanism calculates the color of the pixel (j) of the tth distributed OHP sheet from the l binary representation vectors V_ {1, i}, ..., V_ {l, i} of the participant (i). , V_ {j, i, t} is white if 0, black if 1 or black if v_ {j, i, t} is 0, white if 1 Sheet S_ {i, 1} = (v_ {1, i, 1} ... v_ {l, i, 1}), ..., S_ {i, m} = (v_ {1, i, m} ... generating v_ {l, i, m}),
Sending m distributed OHP sheets S_ {i, 1}, ..., S_ {i, m} generated by the distributed generation mechanism to the participant (i);
Among the n participants who reconstructed, from the k participants, the m distributed OHP sheets S_ {i, 1}, ..., S_ {i, m} of each participant (i) Collecting steps,
Lagrange the distributed OHP sheets S_ {1,1}, ..., S_ {1, m}, ..., S_ {k, 1}, ..., S_ {k, m} collected by the reconstructor A program characterized by executing a step of restoring a secret image by black and white reversal and superposition of a distributed OHP sheet using the interpolation formula of. A computer-readable information recording medium (including a compact disk, a flexible disk, a hard disk, a magneto-optical disk, a digital video disk, a magnetic tape, or a semiconductor memory), wherein the program according to claim 11 is recorded. .

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