公开(公告)号：US08782114B2

公开(公告)日：2014-07-15

申请号：US13355642

申请日：2012-01-23

申请人： Tomoko Yonemura ,  Taichi Isogai ,  Hirofumi Muratani ,  Atsushi Shimbo ,  Yoshikazu Hanatani ,  Kenichiro Furuta ,  Kenji Ohkuma ,  Yuichi Komano ,  Hanae Ikeda

发明人： Tomoko Yonemura ,  Taichi Isogai ,  Hirofumi Muratani ,  Atsushi Shimbo ,  Yoshikazu Hanatani ,  Kenichiro Furuta ,  Kenji Ohkuma ,  Yuichi Komano ,  Hanae Ikeda

IPC分类号： G06F7/00 ,  H04L9/30

CPC分类号： H04L9/3073

摘要： 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.

摘要翻译： 根据一个实施例，表示转换单元将n个元素（h0，h1，...，hn-1）（hi：有限域Fp ^ m，0＆nlE; i＆nlE; n-1的成员）的集合转换为 是由一组n个元素表示的有限投影表示的n阶代数环面Tn（Fp ^ m）（n：正整数，p：素数，m：正整数）的成员g的投影表示 （h'0，h'1，...，h'n-1）（h'i：有限域Fp ^ m，0＆nlE; i＆nlE; n-1的成员），其中至少一个元素 n个元素是零元素0或身份元素1.算术单元省略了Fp ^ m操作的一部分，这是基于n个元素集合中的元素（h）的事实的有限域Fp ^ m中的算术运算 由有限的投影表示表示的'0，h'1，...，h'n-1'是执行Fp ^ mn操作时的零元素“0”或身份元素“1”，这是运算有限的 场Fp ^ mn结合 Fp ^ m操作。

公开(公告)号：US20100049777A1

公开(公告)日：2010-02-25

申请号：US12397648

申请日：2009-03-04

申请人： Tomoko Yonemura ,  Hirofumi Muratani ,  Kenji Ohkuma ,  Hanae Ikeda ,  Taichi Isogai ,  Kenichiro Furuta ,  Yoshikazu Hanatani

发明人： Tomoko Yonemura ,  Hirofumi Muratani ,  Kenji Ohkuma ,  Hanae Ikeda ,  Taichi Isogai ,  Kenichiro Furuta ,  Yoshikazu Hanatani

IPC分类号： G06F17/10

CPC分类号： G06F17/10

摘要： 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(Fq̂r), 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(Fq̂r) 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.

摘要翻译： 当代表二次代数圆环T2（Fqr）的投影表示转换代表二阶代数圆环T2r（Fq）（r是素数，q是整数）的仿射表示时，表示转换装置获取成员 （c0，c1，...，cr-2），（ci是有限域Fq的成员，其中0和nlE; i＆nlE; r-2）由仿射表示的2r代数圆环T2r（Fq） 表示。 该装置对获取的成员进行乘法运算。 乘法运算由二次代数圆环T2（Fqr）的成员包含在第二级代数圆环T2r（Fq）中的条件，二次扩展的模数和基数以及模数和 一个r度延伸的基础。 然后，表示转换装置执行由条件，模数和基数确定的加法和减法运算。

公开(公告)号：US20120239721A1

公开(公告)日：2012-09-20

申请号：US13422018

申请日：2012-03-16

申请人： Taichi ISOGAI ,  Kenichiro Furuta ,  Hirofumi Muratani ,  Kenji Ohkuma ,  Tomoko Yonemura ,  Yoshikazu Hanatani ,  Atsushi Shimbo ,  Hanae Ikeda ,  Yuichi Komano

发明人： Taichi ISOGAI ,  Kenichiro Furuta ,  Hirofumi Muratani ,  Kenji Ohkuma ,  Tomoko Yonemura ,  Yoshikazu Hanatani ,  Atsushi Shimbo ,  Hanae Ikeda ,  Yuichi Komano

IPC分类号： G06F7/52

CPC分类号： H04L9/003 ,  G06F7/725 ,  H04L9/3013

摘要： An arithmetic device includes an input unit inputting data that are elements of a group; a converting unit is configured, when the input data are in a second representation, to convert the input data into a first representation and to perform arithmetic operation on the converted first representation using an operand in the first representation in which at least one subcomponent is a zero element to convert the converted first representation into first converted data expressed in the first representation, and when the input data are in the first representation, to perform arithmetic operation on the input data using the operand in the first representation in which at least one subcomponent is a zero element to convert the input data into second converted data expressed in the first representation; and an operating unit that performs arithmetic processing on the first or the second converted data using secret information.

摘要翻译： 运算装置包括输入单元，输入作为组的要素的数据; 配置转换单元，当输入数据处于第二表示时，将输入数据转换为第一表示，并且使用第一表示中的操作数对转换的第一表示执行算术运算，其中至少一个子组件是 零元素以将转换后的第一表示转换为以第一表示表示的第一转换数据，以及当输入数据处于第一表示时，使用第一表示中的操作数对输入数据执行算术运算，其中至少一个子组件 是将输入数据转换成以第一表示表示的第二转换数据的零元素; 以及操作单元，其使用秘密信息对所述第一或第二转换数据执行算术处理。

公开(公告)号：US08233616B2

公开(公告)日：2012-07-31

申请号：US12406473

申请日：2009-03-18

申请人： Hirofumi Muratani ,  Tomoko Yonemura ,  Atsushi Shimbo ,  Kenji Ohkuma ,  Taichi Isogai ,  Yuichi Komano ,  Kenichiro Furuta ,  Yoshikazu Hanatani ,  Hanae Ikeda

发明人： Hirofumi Muratani ,  Tomoko Yonemura ,  Atsushi Shimbo ,  Kenji Ohkuma ,  Taichi Isogai ,  Yuichi Komano ,  Kenichiro Furuta ,  Yoshikazu Hanatani ,  Hanae Ikeda

IPC分类号： H04L1/00

CPC分类号： H04L9/3013 ,  H04L2209/30

摘要： 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.

摘要翻译： 加密处理单元执行预先决定的算术运算，并将运算结果作为代数圆环上的元素输出。 压缩单元输出当运算结果为代表代数环面上的元素的异常点时，压缩图不能被压缩图压缩成代数圆环上的元素，成为仿射表示，压缩结果按照 并且当算术结果为异常点时，输出属于预先确定的特定集合的元素，该元素不与通过压缩算术结果而获得的压缩结果的集合重叠，该算法结果不是例外 ，属于。

公开(公告)号：US08924448B2

公开(公告)日：2014-12-30

申请号：US13422018

申请日：2012-03-16

申请人： Taichi Isogai ,  Kenichiro Furuta ,  Hirofumi Muratani ,  Kenji Ohkuma ,  Tomoko Yonemura ,  Yoshikazu Hanatani ,  Atsushi Shimbo ,  Hanae Ikeda ,  Yuichi Komano

发明人： Taichi Isogai ,  Kenichiro Furuta ,  Hirofumi Muratani ,  Kenji Ohkuma ,  Tomoko Yonemura ,  Yoshikazu Hanatani ,  Atsushi Shimbo ,  Hanae Ikeda ,  Yuichi Komano

IPC分类号： G06F7/58 ,  G06F7/00 ,  H04L9/28 ,  H04L9/00 ,  G06F7/72 ,  H04L9/30

CPC分类号： H04L9/003 ,  G06F7/725 ,  H04L9/3013

摘要： An arithmetic device includes an input unit inputting data that are elements of a group; a converting unit is configured, when the input data are in a second representation, to convert the input data into a first representation and to perform arithmetic operation on the converted first representation using an operand in the first representation in which at least one subcomponent is a zero element to convert the converted first representation into first converted data expressed in the first representation, and when the input data are in the first representation, to perform arithmetic operation on the input data using the operand in the first representation in which at least one subcomponent is a zero element to convert the input data into second converted data expressed in the first representation; and an operating unit that performs arithmetic processing on the first or the second converted data using secret information.

摘要翻译： 运算装置包括输入单元，输入作为组的要素的数据; 配置转换单元，当输入数据处于第二表示时，将输入数据转换为第一表示，并且使用第一表示中的操作数对转换的第一表示执行算术运算，其中至少一个子组件是 零元素以将转换后的第一表示转换为以第一表示表示的第一转换数据，以及当输入数据处于第一表示时，使用第一表示中的操作数对输入数据执行算术运算，其中至少一个子组件 是将输入数据转换成以第一表示表示的第二转换数据的零元素; 以及操作单元，其使用秘密信息对所述第一或第二转换数据执行算术处理。

公开(公告)号：US08533243B2

公开(公告)日：2013-09-10

申请号：US12397648

申请日：2009-03-04

申请人： Tomoko Yonemura ,  Hirofumi Muratani ,  Kenji Ohkuma ,  Hanae Ikeda ,  Taichi Isogai ,  Kenichiro Furuta ,  Yoshikazu Hanatani

发明人： Tomoko Yonemura ,  Hirofumi Muratani ,  Kenji Ohkuma ,  Hanae Ikeda ,  Taichi Isogai ,  Kenichiro Furuta ,  Yoshikazu Hanatani

IPC分类号： G06F7/00 ,  G06F15/00

CPC分类号： G06F17/10

摘要： 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.

摘要翻译： 当表示代表二次代数环面T2（Fq ^ r）的投影表示将表示2r次代数圆环T2r（Fq）（r是素数，q是整数）的仿射表示转换为表示转换装置 获取成员（c0，c1，...，cr-2），（ci是有限域Fq的成员，其中0 @ i @ r-2）由2r代数圆环T2r（Fq） 仿射表示。 该装置对获取的成员进行乘法运算。 乘法运算由二次代数圆环T2（Fq ^ r）的成员包含在第二阶代数圆环T2r（Fq）中的条件，二次扩展的模数和基数，以及 模数和r度延伸的基数。 然后，表示转换装置执行由条件，模数和基数确定的加法和减法运算。

公开(公告)号：US20100046742A1

公开(公告)日：2010-02-25

申请号：US12406473

申请日：2009-03-18

申请人： Hirofumi MURATANI ,  Tomoko Yonemura ,  Atsushi Shimbo ,  Kenji Ohkuma ,  Taichi Isogai ,  Yuichi Komano ,  Kenichiro Furuta ,  Yoshikazu Hanatani ,  Hanae Ikeda

发明人： Hirofumi MURATANI ,  Tomoko Yonemura ,  Atsushi Shimbo ,  Kenji Ohkuma ,  Taichi Isogai ,  Yuichi Komano ,  Kenichiro Furuta ,  Yoshikazu Hanatani ,  Hanae Ikeda

IPC分类号： H04L9/28

CPC分类号： H04L9/3013 ,  H04L2209/30

摘要： 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.

摘要翻译： 加密处理单元执行预先决定的算术运算，并将运算结果作为代数圆环上的元素输出。 压缩单元输出当运算结果为代表代数环面上的元素的异常点时，压缩图不能被压缩图压缩成代数圆环上的元素，成为仿射表示，压缩结果按照 并且当算术结果为异常点时，输出属于预先确定的特定集合的元素，该元素不与通过压缩算术结果而获得的压缩结果的集合重叠，该算法结果不是例外 ，属于。

公开(公告)号：US08675874B2

公开(公告)日：2014-03-18

申请号：US12406507

申请日：2009-03-18

申请人： Hirofumi Muratani ,  Tomoko Yonemura ,  Atsushi Shimbo ,  Kenji Ohkuma ,  Taichi Isogai ,  Yuichi Komano ,  Kenichiro Furuta ,  Yoshikazu Hanatani

发明人： Hirofumi Muratani ,  Tomoko Yonemura ,  Atsushi Shimbo ,  Kenji Ohkuma ,  Taichi Isogai ,  Yuichi Komano ,  Kenichiro Furuta ,  Yoshikazu Hanatani

IPC分类号： H04L29/06

CPC分类号： H04L9/3073 ,  H04L9/3013 ,  H04L2209/30

摘要： 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.

摘要翻译： 压缩单元根据压缩图将代数环面上的元素压缩为仿射表示。 确定单元确定要压缩的代数环面上的目标元素是否是代表不能由压缩映射压缩的代数环面上的元素的异常点。 当确定目标元素是异常点时，压缩单元产生包括指示目标元素是异常点的异常信息的处理结果，并且当确定目标元素不是异常点时，生成 ，包括通过根据压缩图压缩目标元素获得的仿射表示的处理结果。

公开(公告)号：US20100046743A1

公开(公告)日：2010-02-25

申请号：US12406507

申请日：2009-03-18

申请人： Hirofumi Muratani ,  Tomoko Yonemura ,  Atsushi Shimbo ,  Kenji Ohkuma ,  Taichi Isogai ,  Yuichi Komano ,  Kenichiro Furuta ,  Yoshikazu Hanatani

发明人： Hirofumi Muratani ,  Tomoko Yonemura ,  Atsushi Shimbo ,  Kenji Ohkuma ,  Taichi Isogai ,  Yuichi Komano ,  Kenichiro Furuta ,  Yoshikazu Hanatani

IPC分类号： H04L9/28 ,  G06F17/30

CPC分类号： H04L9/3073 ,  H04L9/3013 ,  H04L2209/30

摘要： 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.

摘要翻译： 压缩单元根据压缩图将代数环面上的元素压缩为仿射表示。 确定单元确定要压缩的代数环面上的目标元素是否是代表不能由压缩映射压缩的代数环面上的元素的异常点。 当确定目标元素是异常点时，压缩单元产生包括指示目标元素是异常点的异常信息的处理结果，并且当确定目标元素不是异常点时，生成 ，包括通过根据压缩图压缩目标元素获得的仿射表示的处理结果。

公开(公告)号：US08438205B2

公开(公告)日：2013-05-07

申请号：US12393558

申请日：2009-02-26

申请人： Tomoko Yonemura ,  Hirofumi Muratani ,  Atsushi Shimbo ,  Kenji Ohkuma ,  Taichi Isogai ,  Yuichi Komano ,  Kenichiro Furuta ,  Yoshikazu Hanatani

发明人： Tomoko Yonemura ,  Hirofumi Muratani ,  Atsushi Shimbo ,  Kenji Ohkuma ,  Taichi Isogai ,  Yuichi Komano ,  Kenichiro Furuta ,  Yoshikazu Hanatani

IPC分类号： G06F17/10 ,  G06F7/38 ,  G06F7/52 ,  G06F7/50 ,  H04L9/28

CPC分类号： G06F17/10 ,  G06F7/724

摘要： 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.