Apparatus and computer program product for performing data compression processing using algebraic torus
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.
1. An information processing apparatus, comprising:
an arithmetic processing unit that executes a predetermined arithmetic operation and outputs an arithmetic result as an element on an algebraic torus; and
a compressing unit that outputs an element belonging to a specific set as a compression result of the arithmetic result, 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 an affine representation, the specific set being predetermined and does not overlap a set to which the compression result obtained by compressing the arithmetic result, which is not the exceptional point, according to the compression map belongs.
2. The apparatus according to claim 1 , wherein the compressing unit outputs, when the arithmetic result is not the exceptional point, a compression result obtained by compressing the arithmetic result according to the compression map.
3. The apparatus according to claim 1 , further comprising a determining unit that determines whether the arithmetic result is the exceptional point, wherein
the compressing unit outputs, when it is determined by the determining unit that the arithmetic result is the exceptional point, an element belonging to the specific set as the compression result.
4. The apparatus according to claim 1 , wherein
the element of the algebraic torus is represented by an element on a predetermined finite field,
the compression map is a map for calculating an inverse element of the element on the finite field representing the element on the algebraic torus and compressing the element on the algebraic torus into the affine representation using the calculated inverse element, and
the compressing unit outputs, when the arithmetic result is the exceptional point represented by a zero element on the finite field that is an element, an inverse element of which cannot be calculated, the compression result as an element belonging to the specific set by compressing the arithmetic result into the affine representation according to the compression map using the zero element as an inverse element of the zero element.
5. The apparatus according to claim 1 , wherein the specific set is a set including elements obtained by excluding, from a two-dimensional affine space on a predetermined finite field, an element obtained by compressing elements other than a unit element on the algebraic torus according to the compression map.
6. The apparatus according to claim 1 , wherein the specific set includes an element converted into the exceptional point according to a decompression map corresponding to the compression map.
7. The apparatus according to claim 1 , wherein the arithmetic processing unit outputs the arithmetic result that is encrypted data obtained by encrypting plain data according to cryptography based on a discrete logarithm problem on the algebraic torus.
8. A non-transitory computer readable medium including programmed instructions for performing information processing, wherein the instructions, when executed by a computer, cause the computer to perform:
executing a predetermined arithmetic operation and outputting an arithmetic result as an element on an algebraic torus; and
outputting an element belonging to a specific set as a compression result of the arithmetic result, 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, the specific set being predetermined and does not overlap a set to which a compression result obtained by compressing the arithmetic result, which is not the exceptional point, according to the compression map belongs.