Abstract: A secure sigmoid function calculation system is a system in which map? is assumed to be secure batch mapping defined by parameters (a0, . . . , ak-1) representing the domain of definition of a sigmoid function ?(x) and parameters (?(a0), . . . , ?(ak-1)) representing the range of the sigmoid function ?(x) (a0, . . . , ak-1 are real numbers that satisfy a0< . . . <ak-1) and which is configured with three or more secure sigmoid function calculation apparatuses and calculates, from a share [[x?]] of an input vector x?, a share [[y?]] of a value y? of a sigmoid function for the input vector x?, the system including a secure batch mapping calculating means that calculates the share [[y?]] by [[y?]]=map?([[x?]])=([[?(af(0))]], . . . , [[?(af(m-1)]]) (where f(i) (0?i?m?1) is j that makes aj?xi<aj+1 hold).

Abstract: Provided is a technique for performing statistical processing such as processing for obtaining parameters of logistic regression analysis faster than before. A secure statistical processing system includes a cross tabulation table computing device 2 that performs secure computation on a cross tabulation table in which frequencies are in plain texts while keeping each record concealed; and a statistical processing device 3 that performs predetermined statistical processing using the cross tabulation table in which frequencies are in plain texts. The cross tabulation table computing device 2 may include a plurality of secure computation devices 221, . . . , 22N that perform secure computation on a cross tabulation table in which frequencies are fragments subjected to secret sharing while keeping each record concealed, and a management device 21 that restores the fragments to compute the cross tabulation table in which frequencies are in plain texts.

Abstract: A secure computation technique of calculating a polynomial in a shorter calculation time is provided. A secure computation system generates concealed text [[u]] of u, which is the result of magnitude comparison between a value x and a random number r, from concealed text [[x]] by using concealed text [[r]]; generates concealed text [[c]] of a mask c from the concealed text [[x]], [[r]], and [[u]]; reconstructs the mask c from the concealed text [[c]]; calculates, for i=0, . . . , n, a coefficient bi from an order n, coefficients a0, a1, . . . , an, and the mask c; generates, for i=1, . . . , n, concealed text [[si]] of a selected value si, which is determined in accordance with the result u of magnitude comparison, from the concealed text; [[u]]; and calculates a linear combination b0+b1[[s1]]+ . . . +bn[[sn]] of the coefficient bi and the concealed text [[si]] as concealed text [[a0+a1x1+ . . . +anxn]].

Abstract: A secure joining system is a secure joining system including a plurality of secure computing apparatuses. The plurality of secure computing apparatuses include a first vector joining unit, a first permutation calculation unit, a first vector generation unit, a second vector joining unit, a first permutation application unit, a second vector generation unit, a first inverse permutation application unit, a first vector extraction unit, a second permutation application unit, a third vector generation unit, a second inverse permutation application unit, a second vector extraction unit, a modified second table generation unit, a third permutation application unit, a fourth vector generation unit, a shifting unit, a third inverse permutation application unit, a bit inversion unit, a third vector extraction unit, a modified first table generation unit, a first table joining unit, and a first table formatting unit.

Abstract: Calculation time is reduced without degrading approximation accuracy in calculation of a complicated function through secure computation. A secret batch approximation system calculates a concealed text [z] of an approximate value z for a function value y satisfying yj=f(xj) by using a concealed text [x] of a value x as input. g is defined as a polynomial for approximating each section of m sections into which the function f is divided. A parameter acquisition unit acquires a concealed text [a] of a parameter a corresponding to the value x for each integer j that is not less than 1 and not more than n, where aj is defined as a parameter pi corresponding to a section Ri including a value xj. A polynomial calculation unit calculates a polynomial g([x], [a]) by using the concealed text [x] of the value x as input based on the concealed text [a].

Abstract: Fisher's exact test is efficiently computed through secure computation. A computation range determination part determines i0, i1, x0, x1. A preliminary computation part computes f(x0), . . . , f(x1), and generates an array M=(f(x0), . . . , f(x1)). A securing part secures the array M, and generates a secure text array <M>=(<f(x0)>, . . . , <f(x1)>). A batch-reading part generates a function value secure text (<f(ai)>, <f(bi)>, <f(ci)>, <f(di)>) (i0?i?i1).

Abstract: A secure joining system is a secure joining system comprising a plurality of secure computation apparatuses; and the plurality of secure computation apparatuses are provided with vector joining parts 11n, first permutation calculating parts 12n, first permutation applying parts 13n, first vector generating parts 14n, second vector generating parts 15n, bit-flipping parts 16n, second permutation calculating parts 17n, second permutation applying parts 18n, third vector generating parts 19n, inverse permutation applying parts 110n, vector separating parts 111n, third permutation applying parts 112n, attribute value permutating parts 113n and fourth vector generating parts 114n.

Abstract: Fisher's exact test is efficiently computed through secure computation. It is assumed that a, b, c and d are frequencies of a 2×2 contingency table, [a], [b], [c] and [d] are secure texts of the respective frequencies a, b, c and d, and N is an upper bound satisfying a+b+c+dN. A reference frequency computation part computes a secure text ([a0], [b0], [c0], [d0]) of a combination of reference frequencies (a0, b0, c0, d0) which are integers satisfying a0+b0=a+b, c0+d0=c+d, a0+c0=a+c, and b0+d0=b+d. A number-of-patterns determination part determines integers h0 and h1 satisfying h0?h1. A pattern computation part computes [ai]=[a0]+i, [bi]=[b0]?i, [ci]=[c0]?i and [di]=[d0]+i for i=h0, . . . , h1, and obtains a set S={([ai], [bi], [ci], [di])}i of secure texts of combinations of frequencies (ai, bi, ci, di).

Abstract: To efficiently determine intermediate data for use with an aggregate function while keeping confidentiality, a bit decomposition unit generates a share of a bit string by bit decomposition and concatenation of key attributes. A group sort generation unit generates a share of a first permutation, which performs a stable sort of the bit string in ascending order. A bit string sorting unit generates a share of a sorted bit string obtained by sorting the bit string with the first permutation. A flag generation unit generates a share of a flag indicating a boundary between groups. A key aggregate sort generation unit generates a share of a second permutation, which performs a stable sort of the negation of the flag in ascending order. A de-duplication unit generates shares of de-duplicated key attributes. A key sorting unit generates shares of sorted key attributes by sorting the de-duplicated key attributes.

Abstract: A secure joining system is a secure joining system including a plurality of secure computing apparatuses. The plurality of secure computing apparatuses include a vector joining unit 11n, a first vector generation unit 12n, a first permutation calculation unit 13n, a first permutation application unit 14n, a second vector generation unit 15n, a third vector generation unit 16n, a second permutation calculation unit 17n, a second permutation application unit 18n, a fourth vector generation unit 19n, a fifth vector generation unit 110n, a first inverse permutation application unit 111n, a first vector separation unit 112n, a second inverse permutation application unit 113n and a second vector separation unit 114n, a third permutation application unit 115n, a fourth permutation application unit 116n, and a first joined table generation unit 117n.

Abstract: A secure strong mapping computing system is a secure joining system including a plurality of secure computing apparatuses. The plurality of secure computing apparatuses include a first vector joining unit 11n, a first permutation calculation unit 12n, a first vector generation unit 13n, a second vector joining unit 14n, a first permutation application unit 15n, a second vector generation unit 16n, a first inverse permutation application unit 17n, and a first vector extraction unit 18n.

Abstract: A concealed-decision-tree computation system includes a user apparatus and 0th to (n?1)-th server apparatuses, where n is a predetermined positive integer. The user apparatus secret-shares data D into n shares [D]j (j=0, . . . , n?1) and sends the n shares [D]j (j=0, . . . , n?1) to the 0th to (n?1)-th server apparatuses, respectively. The 0th to (n?1)-th server apparatuses use the n shares [D]j (j=0, n?1) to perform secret cooperation computation to obtain n shares [out]0, . . . , [out]n-1 of a value “out” corresponding to the data D in a predetermined decision tree and send the n shares [out]0, . . . , [out]n-1 to the user apparatus. The user apparatus uses at least k shares out of the n received shares [out]0, . . . , [out]n-1 to restore the value “out” corresponding to the data D in the predetermined decision tree, where k is a predetermined integer equal to or smaller than n.

Abstract: A secure text having an authentication code is efficiently created. A key generation part 12 generates secure texts ([x], [?], [?]) of “x”, “?” and “?” that are values satisfying x?=?. A secure text generation part 13 generates secure texts [ai] of random values “ai” for i=1, . . . , N. An authentication code generation part 14 generates authentication codes [?(ai)] by multiplying the secure texts [ai] by the secure text [?] for i=1, . . . , N. A verification value generation part 15 generates a secure text [w] of a verification value “w” using the secure texts ([x], [?], [?]), the secure text [ai] and the authentication code [?(ai)]. A verification value determination part 16 determines whether the verification value “w” is equal to zero or not.

Abstract: A secure table reference system includes a first combining part 11n for generating [v?] of v? ? Fm+nt in which d and v are combined, a difference calculation part 12n for generating [r?] of r? that has a difference between a certain element of r and an element before the certain element as an element corresponding to the certain element, a second combining part 13n for generating [r?] of r? ? Fm+nt in which r? and an m-dimensional zero are combined, a permutation calculation part 14n for generating {{?}} of a permutation ? that stably sorts v? in ascending order, a permutation application part 15n for generating [s] of s: =?(r?) obtained by applying the permutation ? to r?, a vector generation part 16n for generating [s?] of a prefix-sum s? of s, an inverse permutation application part for generating [s?] of s? obtained by applying an inverse permutation ??1 of the permutation ? to s?, and an output part 17n for generating [x] of x ? Fm consisting of (nt+1)th and subsequent elements of s?.

Abstract: An efficient share recovery technique for Shamir's secret sharing is provided. n share recovery apparatuses p0, . . . , pn?1 generate a share [r]i of a secretly shared value shared through Shamir's secret sharing, which becomes a random number r when restored. k share recovery apparatuses ?0, . . . , ?k?1 calculate a share [b]i by subtracting the share [r]i from a share [a]i. The share recovery apparatus ?k receives the shares [b]0, . . . , [b]k?1 from the share recovery apparatuses ?0, . . . , ?k?1. The share recovery apparatus ?k recovers shares [b]k, . . . , [b]k+m?1 using the shares [b]0, . . . , [b]k?1. m?1 share recovery apparatuses ?k+1, . . . , ?k+m?1 receive a share [b]j from the share recovery apparatus ?k. m share recovery apparatuses ?k, . . . , ?k+m?1 calculate the share [a]j by adding the share [r]j to the share [b]j.

Abstract: A coating is formed on a surface of a base material 11 of a furnace, and includes a base layer 12 and a sliding material layer 13 that is formed on a surface of the base layer 12 and contains an oxide ceramic and a compound having a layered crystal structure. The sliding material layer 13 causes the collided ashes to be slipped and facilitates the drop off of the adhered ashes. The base material 11 forms a heat transfer tube or a wall surface of the furnace. The coating is also applied to a coal gasification furnace, a pulverized coal fired boiler, a combustion apparatus, or a reaction apparatus containing a furnace.

Abstract: A secret share value of object data on which secure computation is to be performed is stored in a secure computation device, and a query which requests secure computation or secret share value of the query is input to the secure computation device. The secure computation device performs consistency verification of the secret share value of the object data and consistency verification of the query or the secret share value of the query, obtains a secret share value of a calculation result by performing secure computation in accordance with the query or the secret share value of the query which passed the consistency verification by using the secret share value of the object data which passed the consistency verification, and outputs the secret share value of the calculation result.

Abstract: Data is efficiently read from and written in a sequence without an access position being revealed. A secure reading and writing apparatus (1) receives a read command or a write command as input, and, when the read command is input, outputs a secret text [a[x]] which is an x-th element of a secret text sequence [a], and, when the write command is input, adds the secret text [a[x]] which is the x-th element of the secret text sequence [a], to a secret text [d]. A secure reading part (12) reads the secret text [a[x]] which is the x-th element from the secret text sequence [a]. A buffer addition part (13) adds a secret text [c] of an unreflected value c to the secret text [a[x]]. A buffer appending part (14) appends a secret text [x] and the secret text [d] to a write buffer [b].

Abstract: An agreement apparatus P(i) (where i=0, . . . , n?1) which executes a consensus protocol generates an opinion value with a signature Xij=(xi, sig_i(xi)) including an opinion value xi indicating an opinion and a signature sig_i(xi) on the opinion value xi or information different from the opinion value with the signature Xij as an opinion value with a signature X?ij=(x?ij, e?ij) and outputs the opinion value with the signature X?ij to an agreement apparatus P(j) (where j=0, . . . , n?1, i?j). The agreement apparatus P(j) accepts the opinion value with the signature X?ij and outputs the opinion value with the signature X?ij or information different from the opinion value with the signature X?ij to an agreement apparatus P(m) (where m=0, . . . , n?1, m?i, m?j) as an opinion value with a signature X?ij.

Abstract: The present invention provides a technique for performing confidential sort at a faster speed than in the prior art. A confidential sort system comprises first to Mth apparatuses. The first to Mth apparatuses obtain inverse substitution [[?0?1]] of L-bit stable sort of {?k0}. The first to Mth apparatuses perform, on i=1, . . . , N?1, a process of converting [[?i?1?1]] to hybrid substitution to obtain {?i?1?1}, a process of inversely substituting {?ki} with {?i?1?1} to obtain {?i?1?ki}, a process of obtaining inverse substitution [[??i?1]] of L-bit stable sort of [[?i?1?ki]], a process of synthesizing {?i?1?1} with [[??i?1]] to obtain [[?i?1]]:=[[?i?1?1??i?1]], and a process of converting [[?N?1?1]] to hybrid substitution to obtain {?N?1?1}. The first to Mth apparatuses inversely substitute [[?v]] with {?N?1?1} and output [[?N?1?v]].