Abstract: An encryption device includes one or more hardware processors functioning as the following units. A unit acquires, as a public key, n-variable indeterminate equations X having coefficients with a predetermined degree of a univariate polynomial ring Fp[t] on a finite field Fp. A unit embeds a plaintext m into coefficients of n-variable plaintext polynomial factors m having coefficients with a predetermined degree of the Fp[t]. A unit generates an n-variable plaintext polynomial M by multiplying the n-variable plaintext polynomial factors mi whose number is one or more. A unit randomly generates n-variable polynomials sk (k=1, 2), n-variable polynomials rk, and noise polynomial ek, each having coefficients with a predetermined degree of the Fp[t]. A unit generates a ciphertext ck by executing an operation including at least one of adding, subtracting, and multiplying the sk, the rk, the ek, and the X to, from, or by the M.

Abstract: An encryption device includes hardware processors to: acquire a public key including an identification polynomial f(t) and a multivariable indeterminate equation X having elements of a ring Fp[t]/g(t) as coefficients; disperse and embed a message m as coefficients of plaintext polynomial factors mi having, as coefficients, polynomials with a limited degree among the elements of the ring; generate a plaintext polynomial M by multiplying the plaintext polynomial factors mi; randomly generate a random polynomial r having as a coefficient an element of the ring; randomly generate a noise polynomial e having as coefficients polynomials with a limited degree among the elements of the ring; and generate a ciphertext by encryption processing of performing an operation including adding, subtracting, or multiplying the identification polynomial f(t), the random polynomial r, the noise polynomial e, and the multivariable indeterminate equation X to, from, or by the plaintext polynomial M.

Abstract: An encryption device includes hardware processors to: acquire a public key including an identification polynomial f(t) and a multivariable indeterminate equation X having elements of a ring Fp[t]/g(t) as coefficients; disperse and embed a message m as coefficients of plaintext polynomial factors mi having, as coefficients, polynomials with a limited degree among the elements of the ring; generate a plaintext polynomial M by multiplying the plaintext polynomial factors mi; randomly generate a random polynomial r having as a coefficient an element of the ring; randomly generate a noise polynomial e having as coefficients polynomials with a limited degree among the elements of the ring; and generate a ciphertext by encryption processing of performing an operation including adding, subtracting, or multiplying the identification polynomial f(t), the random polynomial r, the noise polynomial e, and the multivariable indeterminate equation X to, from, or by the plaintext polynomial M.

Abstract: In a symmetric encryption apparatus according to an embodiment, a storage unit stores a symmetric key formed from a plurality of elements of a first polynomial ring. A plaintext acceptance unit accepts input of plaintext information. A plaintext polynomial generation unit generates a plaintext polynomial by embedding the plaintext information whose input has been accepted in at least one of terms of a polynomial in a subspace of the first polynomial ring. A mask polynomial generation unit generates a mask polynomial having the symmetric key as a solution based on a second commutative ring defined over the first polynomial ring. An encryption unit generates a ciphertext using the plaintext polynomial and the mask polynomial.

Abstract: In a symmetric encryption apparatus according to an embodiment, a storage unit stores a symmetric key formed from a plurality of elements of a first polynomial ring. A plaintext acceptance unit accepts input of plaintext information. A plaintext polynomial generation unit generates a plaintext polynomial by embedding the plaintext information whose input has been accepted in at least one of terms of a polynomial in a subspace of the first polynomial ring. A mask polynomial generation unit generates a mask polynomial having the symmetric key as a solution based on a second commutative ring defined over the first polynomial ring. An encryption unit generates a ciphertext using the plaintext polynomial and the mask polynomial.

Abstract: According to an embodiment, a pairing computation apparatus receives two points on a predetermined elliptic curve defined on a finite field, and outputs a pairing value that is an element on an extension field of the finite field. The apparatus includes a Miller function computation unit and a final exponentiation unit. The Miller function computation unit is configured to compute a Miller function based on a predetermined pairing method. The final exponentiation unit is configured to perform computation including raising the element on the extension field to the power of a value determined on the basis of a loop parameter of the Miller function.

Abstract: A digital signature generation apparatus includes memory to store finite field Fq and section D(ux(s, t), uy(s, t), s, t) as secret key, section being one of surfaces of three-dimensional manifold A(x, y, s, t) which is expressed by x-coordinate, y-coordinate, parameter s, and parameter t and is defined on finite field Fq, x-coordinate and y-coordinate of section being expressed by functions of parameter s and parameter t, calculates hash value of message m, generates hash value polynomial by embedding hash value in 1-variable polynomial h(t) defined on finite field Fq, and generates digital signature Ds(Ux(t), Uy(t), t) which is curve on section, the x-coordinate and y-coordinate of curve being expressed by functions of parameter t, by substituting hash value polynomial in parameter s of section.

Abstract: A digital signature generation apparatus includes memory to store finite field Fq and section D(ux(s, t), uy(s, t), s, t) as secret key, section being one of surfaces of three-dimensional manifold A(x, y, s, t) which is expressed by x-coordinate, y-coordinate, parameter s, and parameter t and is defined on finite field Fq, x-coordinate and y-coordinate of section being expressed by functions of parameter s and parameter t, calculates hash value of message m, generates hash value polynomial by embedding hash value in 1-variable polynomial h(t) defined on finite field Fq, and generates digital signature Ds(Ux(t), Uy(t), t) which is curve on section, the x-coordinate and y-coordinate of curve being expressed by functions of parameter t, by substituting hash value polynomial in parameter s of section.

Abstract: A digital signature generation apparatus includes memory to store finite field Fq and section D(ux(s, t), uy(s, t), s, t) as secret key, section being one of surfaces of three-dimensional manifold A(x, y, s, t) which is expressed by x-coordinate, y-coordinate, parameter s, and parameter t and is defined on finite field Fq, x-coordinate and y-coordinate of section being expressed by functions of parameter s and parameter t, calculates hash value of message m, generates hash value polynomial by embedding hash value in 1-variable polynomial h(t) defined on finite field Fq, and generates digital signature Ds(Ux(t), Uy(t), t) which is curve on section, the x-coordinate and y-coordinate of curve being expressed by functions of parameter t, by substituting hash value polynomial in parameter s of section.

Abstract: A decryption apparatus includes a section assignment unit which assigns a section D to a plurality of encrypted texts Fi(x,y,t) (i=1, . . . , k), a one-variable polynomial arithmetic unit which subtracts L pairs of polynomials he(t) and hw(t) after the assignment, and a greatest common divisor arithmetic unit which obtains the greatest common divisor ?(t) of L polynomials gj(t)(=he(t)?hw(t)) (j=1, . . . , L) as a result of the subtraction.

Abstract: A digital content editing apparatus that edits a content having license information defining a grant for a reusing operation or a multiple content including a plurality of the contents includes: a reuse license processor that obtains a constraint indicative of a condition on reuse between a content or the multiple content and a content other than the content or the multiple content from the license information of the content or the multiple content; an instruction generator that generates an operation execution instruction of reusing the content or the multiple content according to the constraint obtained by the reuse license processor; a reusing unit that reuses the content or the multiple content based on the operation execution instruction generated by the instruction generator; and an editor that edits the content or the multiple content reused by the reusing unit.

Abstract: A digital signature generation apparatus includes memory to store finite field Fq and section D(ux(s, t), uy(s, t), s, t) as secret key, section being one of surfaces of three-dimensional manifold A(x, y, s, t) which is expressed by x-coordinate, y-coordinate, parameter s, and parameter t and is defined on finite field Fq, x-coordinate and y-coordinate of section being expressed by functions of parameter s and parameter t, calculates hash value of message m, generates hash value polynomial by embedding hash value in 1-variable polynomial h(t) defined on finite field Fq, and generates digital signature Ds(Ux(t), Uy(t), t) which is curve on section, the x-coordinate and y-coordinate of curve being expressed by functions of parameter t, by substituting hash value polynomial in parameter s of section.

Abstract: A playlist acquisition unit acquires a playlist including a view segment of contents for a user. The view segment has a start position and an end position in the contents. A copyright information acquisition unit acquires copyright information of the contents from a copyright management apparatus via a network. The copyright management apparatus manages copyright information of each content. A view right information acquisition unit acquires view right information of the user to view the contents. A viewable playlist composition unit composes a viewable playlist by editing the playlist using the copyright information and the view right information. The viewable playlist includes restriction information of the view segment.

Abstract: A digital signature generation apparatus includes memory to store finite field Fq and section D(ux(s, t), uy(s, t), s, t) as secret key, section being one of surfaces of three-dimensional manifold A(x, y, s, t) which is expressed by x-coordinate, y-coordinate, parameter s, and parameter t and is defined on finite field Fq, x-coordinate and y-coordinate of section being expressed by functions of parameter s and parameter t, calculates hash value of message m, generates hash value polynomial by embedding hash value in 1-variable polynomial h(t) defined on finite field Fq, and generates digital signature Ds(Ux(t), Uy(t), t) which is curve on section, the x-coordinate and y-coordinate of curve being expressed by functions of parameter t, by substituting hash value polynomial in parameter s of section.

Abstract: A digital signature generation apparatus includes memory to store finite field Fq and section D(ux(s, t), uy(s, t), s, t) as secret key, section being one of surfaces of three-dimensional manifold A(x, y, s, t) which is expressed by x-coordinate, y-coordinate, parameter s, and parameter t and is defined on finite field Fq, x-coordinate and y-coordinate of section being expressed by functions of parameter s and parameter t, calculates hash value of message m, generates hash value polynomial by embedding hash value in 1-variable polynomial h(t) defined on finite field Fq, and generates digital signature Ds(Ux(t), Uy(t), t) which is curve on section, the x-coordinate and y-coordinate of curve being expressed by functions of parameter t, by substituting hash value polynomial in parameter s of section.

Abstract: An encryption apparatus includes a plaintext embedding unit that embeds a message m as a coefficient of a three-variable plaintext polynomial m(x,y,t), an identification polynomial generating unit that generates a three-variable identification polynomial f(x,y,t), a polynomial generating unit that randomly generates three-variable polynomials r1(x,y,t), r2(x,y,t), s1(x,y,t), and s2(x,y,t), and an encrypting unit that generates encrypted texts F1 and F2 by performing an arithmetic operation with respect to these three-variable polynomials.

Abstract: A digital signature generation apparatus includes memory to store finite field Fq and section D(ux(s, t), uy(s, t), s, t) as secret key, section being one of surfaces of three-dimensional manifold A(x, y, s, t) which is expressed by x-coordinate, y-coordinate, parameter s, and parameter t and is defined on finite field Fq, x-coordinate and y-coordinate of section being expressed by functions of parameter s and parameter t, calculates hash value of message m, generates hash value polynomial by embedding hash value in 1-variable polynomial h(t) defined on finite field Fq, and generates digital signature Ds(Ux(t), Uy(t), t) which is curve on section, the x-coordinate and y-coordinate of curve being expressed by functions of parameter t, by substituting hash value polynomial in parameter s of section.

Abstract: A decryption apparatus includes a section assignment unit which assigns a section D to a plurality of encrypted texts Fi(x,y,t) (i=1, . . . , k), a one-variable polynomial arithmetic unit which subtracts L pairs of polynomials he(t) and hw(t) after the assignment, and a greatest common divisor arithmetic unit which obtains the greatest common divisor ?(t) of L polynomials gj(t)(=he(t)?hw(t)) (j=1, . . . , L) as a result of the subtraction.

Abstract: A key generating apparatus generates a fibration X(x, y, t)=0 of an algebraic surface X serving as a part of a public key and defined on a finite field Fq (where q=pr [p is a prime number and r is an extended degree]) and a private key which is two sections D1 and D2 corresponding to the fibration X(x, y, t)=0. The fibration X(x, y, t) is generated such that a term (cij(t)xiyj) of xiyj having a 1-variable polynomial cij(t) of t as a coefficient is included in the fibration X(x, y, t).

Abstract: A method whereby an encryption apparatus encrypts a message on the basis of a fibration X(x, y, t) serving as a public key when private keys are two or more sections corresponding to fibration X(x, y, t)=0 of an algebraic surface X, the method comprises embedding plaintext M obtained by concatenating the message to a random number as the coefficients of plaintext polynomial M(t) of degree l?1 or less, and generating encrypted text F=Epk(M, p, q, f, X) from the plaintext polynomial M(t) by an encrypting process of performing operations including at least one of addition, subtraction, and multiplication of random polynomials p(x, y, t), q(x, y, t), a random irreducible polynomial f(t) of degree l or more, and the fibration X(x, y, t) with respect to the plaintext polynomial M(t).