Abstract: An approximate function calculation apparatus includes: a first error upper bound calculating unit which obtains an upper bound of a first error of an approximation of a function f(x) by the function gb(x) in a section [x0, b]; an expansion position calculating unit which obtains an expansion position b? that represents a maximum b at which the upper bound of the first error; a second error upper bound calculating unit which obtains an upper bound of a second error of an approximation of the function f(x) by a function gb?(x) in a section [b?, x2]; a right end position calculating unit which calculates a right end position x2? that represents a maximum x2 at which the upper bound of the second error; and a control unit which repeats processing of the respective units with a section [x2?, x1] as the section D.

Abstract: A secret decision tree test device configured to evaluate a division condition at each of a plurality of nodes of a decision tree when learning of the decision tree is performed by secret calculation, the secret decision tree test device includes a memory; and a processor configured to execute inputting a numerical attribute value vector composed of specific numerical attribute values of items of data included in a data set for learning of the decision tree, a label value vector composed of label values of the items of the data, and a group information vector indicating grouping of the items of the data into the nodes; and calculating, using the numerical attribute value vector, the label value vector, and the group information vector, first to fourth frequencies, to evaluate the division condition using the first to fourth frequencies.

Abstract: Techniques for performing secure computing of softmax functions at high speed and with high accuracy are provided. A secure softmax function calculation system that calculates a share ([[softmax (u1)]], . . . , [[softmax (uJ)]]) from a share ([[u1]], . . . , [[uJ]]) includes a subtraction means for calculating a share ([[u1?u1]], [[u2?u1]], . . . , [[uJ?uJ]]), a first secure batch mapping calculation means for calculating, [[exp (u1?u1)]], [[exp (u2?u1)]], . . . , [[exp (uJ?uJ)]], an addition means for calculating a share ( [ [ ? j = 1 J ? exp ? ( u j - u 1 ) ] ] , … , [ [ ? j = 1 J ? exp ? ( u j - u J ) ] ] , and a second secure batch mapping calculation means for calculating a share ([[softmax (u1)], . . . , [[softmax (uJ)]]).

Abstract: The secure join system includes the first and second information-processing-apparatuses respectively holding first and second data. The second information-processing-apparatus is configured to: create third and fourth vectors in which a hash-value related to a key-value of the first data in a first vector and a ciphertext of the first data corresponding to the key-value in a second vector are rearranged by permutation; and create a fifth vector having a hash-value related to a key-value of the second data. The first information-processing-apparatus is configured to: search for j in which a hash-value of an i-th element of the fifth vector matches a j-th element value of the third vector for each i and create encrypted data in which a ciphertext of a j-th element value of the fourth vector is set when j is found and a ciphertext of a dummy value is set when j is not found.

Abstract: Data search by secure computation is efficiently performed and retrieved data is safely provided. A searcher terminal acquires condition data. The searcher terminal extracts a feature from the condition data. The searcher terminal encrypts the feature of the condition data. A secure search apparatus acquires a search result indicating a ciphertext of target data corresponding to a feature of target data similar to the feature of the condition data while keeping the feature of the target data and the feature of the condition data secret. The secure search apparatus transmits the search result to an encryption apparatus and the searcher terminal. The searcher terminal acquires the ciphertext of the target data indicated by the search result. The encryption apparatus transmits a decryption key to the searcher terminal. The searcher terminal decrypts the ciphertext of the target data using the decryption key.

Abstract: Provided is a clustering apparatus capable of securely performing hierarchical clustering while concealing all of a calculation process and values in the middle.

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: A secure maximum value computation apparatus, assuming that a set X={[[x1]], [[x2]], . . . , [[xn]]}, includes an output unit 1 that outputs [[x1]] and [[1]] as a maximum secret value [[y]] and a flag [[z(x1)]], respectively, when n=1 holds, a comparison unit 2 that computes a comparison result of which is larger with respect to a predetermined order for each pair {[[xi]], [[xj]]}?X of elements of the X, a flag computation unit 3 that computes whether all comparison results related to each of the [[xi]]s are “large” for each of the [[xi]]s to set a computed value as a flag [[z(xi)]], and a maximum value computation unit 4 that uses the [[z(xi)]] to computes a maximum value [[y]].

Abstract: A secure collation system performs secure-data-collation between first and second information processing apparatuses and includes the first and second information processing apparatuses. The second information-processing-apparatus creates, when receiving a first vector having a hash value of a key value of the first information-processing-apparatus as an element, a second vector by adding a dummy hash value to the first vector and rearranging the first vector by random permutation; creates a third vector having, as elements, a hash value of a key value of the second information-processing-apparatus and a hash value of a dummy key value; and transmits the second and third vectors to the first information-processing-apparatus. The first information-processing-apparatus calculates a hash value of an element of the third vector and creates a fourth vector having the hash value as an element; and collates matched values between each element of the third vector and each element of the fourth vector.

Abstract: Provided is a technique for computing confidential values of a first plurality of pieces of data satisfying predetermined search conditions from a sequence of confidential values of N pieces of aligned data and confidential values of a query. A vector decomposition means for computing a share [[?vi]] of a vector ?vi (i=1, . . .

Abstract: A first matrix calculation means that calculates a share of a matrix E in which each row satisfies a predetermined condition using a share of a matrix X representing N pieces of data and a share of a column vector ?g representing groups obtained by grouping the N pieces of data, second matrix calculation means that calculates a share of a matrix Y and a share of a matrix U in which each row satisfies the predetermined condition, a third matrix calculation means that calculates a share of a matrix S in which each row satisfies the predetermined condition, and a first vector calculation means that calculates a share of a column vector ?z with an attribute number of an attribute having a best evaluation value among K attributes selected at random in a group to which an i-th data belongs as an i-th element are included.

Abstract: A calculation of a gradient descent method in secure computing is performed at high speed while maintaining accuracy. A secure gradient descent computation method calculates a gradient descent method while keeping a gradient and a parameter concealed. An initialization unit initializes concealed values [M], [V] of matrices M, V (S11). A gradient calculation unit determines concealed value [G] of a matrix G of a gradient g (S12). A parameter update unit calculates [M] ?1 [M]+(1??1) [G] (S13-1), calculates [V]??2 [V]+(1??2) [G]?[G] (S13-2), calculates [M{circumflex over (?)}]??{circumflex over (?)}1, t [M] (S13-3), calculates [V{circumflex over (?)}]??{circumflex over (?)}2, t [V] (S13-4), calculates [G{circumflex over (?)}]?Adam ([V{circumflex over (?)}]) (S13-5), calculates [G{circumflex over (?)}]?[G{circumflex over (?)}]?[M{circumflex over (?)}] (S13-6), and calculates [W]?[W]?[G{circumflex over (?)}] (S13-7).

Abstract: A secure computation system includes first, second, and third secure-computation-apparatuses each having a tripartite-share of a concealed input vector. The first secure-computation-apparatus converts its tripartite-share into a bipartite-share with the third secure-computation-apparatus; calculates a third vector obtained by subtracting a second permutation of a first vector and a second vector from its permutation of its bipartite-share; and transmits the third vector and the second permutation to the second secure-computation-apparatus. The third secure-computation-apparatus converts its tripartite-share into a bipartite-share with the first secure-computation-apparatus; calculates a fourth vector obtained by adding the first vector to a first permutation of its bipartite-share; transmits the fourth vector to the third secure-computation-apparatus: set the second vector as a bipartite-share with the second secure-computation-apparatus.

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: A server determines an array [[addr]] indicating a storage destination of each piece of data, generates an array of concealed values, and connects the generated array to the array [[addr]] to determine an array [[addr?]]. The server generates a sort permutation [[?1]] for the array, applies the sort permutation [[?1]] to the array [[addr?]], and converts the array [[addr?]] into an array with a sequence composed of first Z elements set to [[i]] followed by ?i elements set to [[B]]. The server generates a sort permutation [[?2]] for the converted array [[addr?]], generates dummy data, imparts the generated dummy data to the concealed data sequence, applies the sort permutations [[?1]] and [[?2]] to the data array imparted with the dummy data, and generates, as a secret hash table, a data sequence obtained by deleting the last N pieces of data from the sorted data array.

Abstract: A secret grouping apparatus which classifies a plurality of elements into one or more groups includes a processor configured to receive a target vector in which the plurality of elements are disposed so that elements belonging to a same group are continuous, a group information vector representing a last element in the group, and a classification destination vector representing a classification destination of each of the elements in the group; calculate a detection vector representing a last element of elements classified into a same classification destination in the group by using the target vector, the group information vector, and the classification destination vector; and stably sort the target vector and the detection vector with respect to the classification destination vector to create a target vector after classifying each of the elements into the classification destination and a group information vector representing a last element in a group after the classification.

Abstract: A combustion gas bleeding probe includes a gas pipe for bleeding a part of a combustion gas from a kiln, and a plurality of discharge ports each of which is provided penetrating through the gas pipe and each of which discharges a low-temperature gas in a direction that is perpendicular to a direction of flow of a bleed gas bled by the gas pipe and that is directed toward a center of the flow of the bleed gas. The discharge ports discharge the low temperature gas such that a ratio of a momentum of the low-temperature gas per discharge port to a momentum of the bleed gas satisfies 1.2 to 4.0, and a value (m-1) obtained by dividing a ratio of a wind speed of the low-temperature gas to a wind speed of the bleed gas by an inner diameter of the gas pipe satisfies 1.5 to 3.5.

Abstract: A combustion gas bleeding probe includes a gas pipe for bleeding a part of a combustion gas from a kiln, and a plurality of discharge ports each of which is provided penetrating through the gas pipe and each of which discharges a low-temperature gas in a direction that is perpendicular to a direction of flow of a bleed gas bled by the gas pipe and that is directed toward a center of the flow of the bleed gas. The discharge ports discharge the low-temperature gas such that a ratio of a momentum of the low-temperature gas per discharge port to a momentum of the bleed gas satisfies 1.2 to 4.0, and a value (m?1) obtained by dividing a ratio of a wind speed of the low-temperature gas to a wind speed of the bleed gas by an inner diameter of the gas pipe satisfies 1.5 to 3.5.

Abstract: A search key is generated (S20). A key relationship array is transmitted (S11). If an element matching the key relationship array is present, the found search key is held (S21). A key relationship index is transmitted (S22). A record read out using the key relationship index is transmitted (S12). If the record matches the search key, the found search key is held (S23). The found search key is set for an empty element of the key relationship array and is transmitted (S24). A data array is transmitted (S13). If an element matching the data array is present, the found data is held (S25). A data index is transmitted (S26). A record read out using the data index is transmitted (S14). If the record matches the search key, the found data is held (S27). Desired data is set for an empty element of the data array and is transmitted (S28).

Abstract: Provided is a technology for performing secure computation of a random number generation method using weighted probability distribution with high accuracy while keeping data secure. The technology includes: first vector computation means that computes a share ([[p?1]], . . . , [[p?L]]) from a share ([[p1]], . . . , [[pL]]) by using prefix sum; uniform random number generation means that generates a share ([[q1]], . . . , [[qS]]) of a vector (q1, . . . , qS) (where qi (i=1, . . . , S) is a uniform random number, and satisfies 0?qi?1) having a uniform random number as an element; and random number computation means that computes a share ([[r1]], . . . , [[rS]]) of a vector (r1, . . . , rS) having an output value as an element from the share ([[p?1]], . . . , [[p?L]]), a share ([[x1]], . . . , [[xL]]), and the share ([[q1]], . . . , [[qS]]) by using secure collective mapping.