Abstract: According to one embodiment, a decompressing apparatus includes an input unit, a calculating unit, a first selecting unit, and a decompressing unit. The input unit inputs additional data, which is obtained based on trace expression data in which an element in a subgroup of a multiplicative group of a finite field is trace-expressed and affine expression data in which the trace expression data is affine-expressed, and the trace expression data. The calculating unit calculates a plurality of solutions of simultaneous equations derived by the trace expression data. The first selecting unit selects any of a plurality of items of affine expression data in which the element is affine-expressed based on the additional data, the affine expression data being found from the solutions. The decompressing unit decompresses the selected affine expression data to the element.

Abstract: According to one embodiment, a representation converting unit converts a set of n elements (h0, h1, . . . , hn?1) (hi: a member of a finite field Fp?m, 0?i?n?1) that is a projective representation of a member g of an n-th degree algebraic torus Tn(Fp?m) (n: positive integer, p: prime number, m: positive integer) into a limited projected representation expressed by a set of n elements (h?0, h?1, . . . , h?n?1) (h?i: a member of the finite field Fp?m, 0?i?n?1) in which at least one element out of the n elements is a zero element 0 or an identity element 1. An arithmetic unit omits part of Fp?m operation that is arithmetic operation in the finite field Fp?m based on a fact that an element in the set of n elements (h?0, h?1, . . . , h?n?1) represented by the limited projective representation is a zero element “0” or an identity element “1” when performing Fp?mn operation that is arithmetic operation of a finite field Fp?mn in combination with the Fp?m operation.

Abstract: A digital watermark detection apparatus detects a watermark value from a motion image in which a topological invariant is embedded as the watermark value. The digital watermark detection apparatus includes a watermark component extracting unit which extracts each watermark component from the motion image; an average value computing unit which computes an average value of component values of pixels included in the watermark component; an identified watermark component determination unit which determines whether or not the watermark component is an identified watermark component to be utilized in identifying an arrangement unit of a plurality of watermark components based on the average value; a watermark component identifying unit which identifies the watermark component except for the identified watermark component; and a watermark value computing unit which computes the watermark value based on the identified watermark component and the watermark components except for the identified watermark component.

Abstract: In a computing device that calculates a square of an element in a finite field, a vector representation of the element in the finite field is accepted. The vector representation includes a plurality of elements. The computing device performs a multiplication operation on a base field using the accepted elements, and obtains a multiplication value. The multiplication operation is determined by a condition under which the element in the finite field is placed in an algebraic torus. The computing device performs an addition and subtraction operation using the obtained multiplication value and the accepted elements, and obtains a calculation result of the square of the element. The addition and subtraction operation is determined by the condition. The computing device then outputs the calculation result.

Abstract: A compressing unit compresses an element on an algebraic torus into affine representation according to a compression map. A determining unit determines whether a target element on the algebraic torus to be compressed is an exceptional point representing an element on the algebraic torus that cannot be compressed by the compression map. The compressing unit generates, when it is determined that the target element is the exceptional point, a processing result including exceptional information indicating that the target element is the exceptional point, and generates, when it is determined that the target element is not the exceptional point, a processing result including affine representation obtained by compressing the target element according to the compression map.

Abstract: A parameter generating device includes an input receiving unit that receives a degree n of an algebraic torus T including a group G in which a cryptosystem used in a torus-compressed public key cryptosystem is defined, a size W of a finite field F, and a size S of the group G, an extension-degree determining unit that determines an extension degree m of a finite field Fpm in which the algebraic torus T is defined, a first prime-number search unit that searches for a prime number p, a second prime-number search unit that searches for a prime number q, a test unit that checks whether a multiplication value nm is divisible by the prime number q, a security determining unit that determines that the cryptosystem is secure based on the multiplication value nm, and an output unit that outputs parameters when it is determined that the cryptosystem is secure.

Abstract: An input unit inputs encrypted data that elements of a subgroup and expressed in an affine representation. A transforming unit transforms the inputted encrypted data into projective representation data expressed in a projective representation. A plain data calculating unit subjects the projective representation data to a decrypting process previously defined by a cryptosystem, thereby calculating plain data expressed in the projective representation.

Abstract: When converting an affine representation representing a 2r-th degree algebraic torus T2r(Fq) (r is a prime number, and q is an integer) to a projective representation representing a quadratic algebraic torus T2(Fq?r), a representation converting apparatus acquires member (c0,c1, . . . ,cr?2), (ci is a member of a finite field Fq, where 0?i?r?2) of a 2r-th degree algebraic torus T2r(Fq) represented by the affine representation. The apparatus performs a multiplication operation on the acquired member. The multiplication operation is determined by a condition under which a member of a quadratic algebraic torus T2(Fq?r) is included in the 2r-th degree algebraic torus T2r(Fq), a modulus and a base of a quadratic extension, and a modulus and a base of an r-th degree extension. The representation converting apparatus then performs an addition and subtraction operation determined by the condition, the moduli, and the bases.

Abstract: An encryption processing unit executes an arithmetic operation decided in advance and outputs an arithmetic result as an element on an algebraic torus. A compressing unit outputs, when the arithmetic result is an exceptional point representing an element on the algebraic torus that cannot be compressed by a compression map for compressing an element on the algebraic torus into affine representation, a compression result obtained by compressing the arithmetic result according to the compression map and outputs, when the arithmetic result is the exceptional point, an element belonging to a specific set decided in advance that does not overlap a set to which a compression result obtained by compressing the arithmetic result, which is not the exceptional point, belongs.

Abstract: A decrypting apparatus that decrypts encrypted data that has been encrypted first data containing plain data, the encrypted data being represented by using an affine representation F_{p?m}×F_{p?m}?*(where p: a prime number; m: a natural number; and ?: exponentiation) obtains encrypted data represented in a vector format and a secret key corresponding to a public key and judges whether a vector component contained in the encrypted data is the affine representation F_{p?m}×F_{p?m}?*. Further, based on the result of the judging process, the decrypting apparatus maps the vector component onto each of the members of an algebraic torus by forming a decompression map and decrypts the encrypted data mapped onto each of the members of the algebraic torus, by using the secret key, therefore obtains the plain data.

Abstract: A digital watermark embedding apparatus includes a watermark providing unit configured to provide a digital watermark, an obtaining unit configured to obtain an image component from a plurality of frames of video contents based on image data of the plurality of frames, the image component affecting an error occurring at a time of detecting an image pattern of the digital watermark, a generating unit configured to generate a first image pattern and a second image pattern in converse relation, using the image pattern of the digital watermark and the image component, and an overlapping unit configured to overlap the first image pattern and the second image pattern the frames on the frames, respectively, to eliminate or reduce the image component.

Abstract: A pirate user detecting apparatus includes an extracting unit that extracts, from a digital content, a part or all of a collusion-secure code embedded in correspondence with each of users and that makes it possible to trace pirate users who have made a collusion attack; a calculating unit that calculates a correlation value for each of bits between the part or all of the extracted collusion-secure code and a code assigned to a corresponding one of the users, and calculates a total score of the correlation values for each of the users; a first specifying unit that specifies a threshold value for judging whether each of the users is a pirate user, based on a code length of the extracted collusion-secure code; and a judging unit that judges whether each of the users is a pirate user using the specified threshold value and the calculated total score of each user.

Abstract: A device includes: a reception unit that receives video image; an extraction unit that extracts the watermark patterns from the video image; a storage unit that stores an accumulated information pieces and a number of accumulation times; a calculation unit that calculates degrees of correlation between the accumulated information pieces and the watermark patterns; an accumulation unit that accumulates the watermark patterns in one of the accumulated information pieces having the degree of correlation that is larger than a threshold value and is the largest among the calculated degrees of correlation; a selection unit that selects a top N-pieces of the accumulated information pieces stored in the storage unit having largest number of the accumulation times, where N is a positive integer; and a watermark value calculation unit that obtains a digital watermark value from the accumulated information pieces selected by the selection unit.

Abstract: An apparatus for embedding digital watermark information in an image, includes an image divider dividing the image into a plurality of partial images; and an embedder embedding in each of the partial images a digital watermark which indicates the digital watermark information. The digital watermark includes a plurality of watermark elements arranged in a sequence which is different for each of the partial images.

Abstract: A digital watermark detection apparatus detects a watermark value from a motion image in which a topological invariant is embedded as the watermark value. The digital watermark detection apparatus includes a watermark component extracting unit which extracts each watermark component from the motion image; an average value computing unit which computes an average value of component values of pixels included in the watermark component; an identified watermark component determination unit which determines whether or not the watermark component is an identified watermark component to be utilized in identifying an arrangement unit of a plurality of watermark components based on the average value; a watermark component identifying unit which identifies the watermark component except for the identified watermark component; and a watermark value computing unit which computes the watermark value based on the identified watermark component and the watermark components except for the identified watermark component.

Abstract: A digital watermark embedding apparatus includes a watermark providing unit configured to provide a digital watermark, an obtaining unit configured to obtain an image component from a plurality of frames of video contents based on image data of the plurality of frames, the image component affecting an error occurring at a time of detecting an image pattern of the digital watermark, a generating unit configured to generate a first image pattern and a second image pattern in converse relation, using the image pattern of the digital watermark and the image component, and an overlapping unit configured to overlap the first image pattern and the second image pattern the frames on the frames, respectively, to eliminate or reduce the image component.

Abstract: A digital watermark detecting apparatus includes an acquisition unit configured to acquire a plurality of base values for computation of a watermark value, which are contained, respectively, in all or some of a plurality of divided regions obtained by dividing digital contents, a computation unit configured to compute variance of the base values, and a determination unit configured to determine whether the digital watermark is contained in the digital contents, based on comparison of the computed variance with a threshold.

Abstract: A plurality of areas are specified in an original image in which a digital watermark is to be embedded. The areas are classified into embedding areas in which watermark information is to be embedded and specification areas in which another area is to be specified. A plurality of areas are again specified in the specification areas and these areas are classified as embedding areas. Watermark information is input and each watermark is generated based on the size and shape of the each embedding area, and the digital watermarks are arranged in positions indicated by the embedding areas and embedded into the original image.

Abstract: An apparatus for embedding digital watermark information in an image, includes an image divider dividing the image into a plurality of partial images; and an embedder embedding in each of the partial images a digital watermark which indicates the digital watermark information. The digital watermark includes a plurality of watermark elements arranged in a sequence which is different for each of the partial images.