公开(公告)号：US20160164671A1

公开(公告)日：2016-06-09

申请号：US15009133

申请日：2016-01-28

申请人： International Business Machines Corporation ,  University of Bristol

发明人： Craig B. Gentry ,  Shai Halevi ,  Nigel P. Smart

IPC分类号： H04L9/00 ,  H04L9/16

CPC分类号： H04L9/0838 ,  H04L9/008 ,  H04L9/0618 ,  H04L9/08 ,  H04L9/16 ,  H04L9/30 ,  H04L9/38 ,  H04L63/0442 ,  H04L2209/24 ,  H04L2209/34

摘要： A homomorphic evaluation of a function is performed on input ciphertext(s), which were encrypted using an encryption scheme that includes multiple integer moduli. Each ciphertext contains one or more elements of an m-th cyclotomic number field, where m is an integer. Each ciphertext which is defined relative to one of the moduli q, each element a(X) of the m-th cyclotomic number field is represented via a matrix, with each row i of the matrix corresponding to an integer factor pi of the modulus q and each column j corresponding to a polynomial factor Fj(X) of the m-th cyclotomic polynomial Φm(X) modulo q. Content of the matrix in row i and column j corresponds to the element a(X) modulo pi and Fj(X). Performing the homomorphic evaluation of the function further includes performing operation(s) using one or more matrices from one or more of the ciphertexts.

摘要翻译： 对使用包括多个整数模数的加密方案加密的输入密文执行功能的同态评估。 每个密文包含第m个循环数字段的一个或多个元素，其中m是整数。 相对于模数q之一定义的每个密文，第m个循环数字段的每个元素a（X）经由矩阵表示，矩阵的每一行i对应于模q的整数因子pi 并且每个列j对应于模q的第m个循环多项式Φm（X）的多项式因子Fj（X）。 行i和列j中的矩阵的内容对应于元素a（X）模pi和Fj（X）。 执行功能的同态评估还包括使用来自一个或多个密文的一个或多个矩阵来执行操作。

公开(公告)号：US10057057B2

公开(公告)日：2018-08-21

申请号：US15294967

申请日：2016-10-17

申请人： International Business Machines Corporation ,  University of Bristol

发明人： Craig B. Gentry ,  Shai Halevi ,  Nigel P. Smart

IPC分类号： H04L29/04 ,  H04L9/08 ,  H04L29/06 ,  H04L9/00 ,  H04L9/38

CPC分类号： H04L9/0838 ,  H04L9/008 ,  H04L9/0618 ,  H04L9/08 ,  H04L9/16 ,  H04L9/30 ,  H04L9/38 ,  H04L63/0442 ,  H04L2209/24 ,  H04L2209/34

摘要： Homomorphic evaluations of functions are performed. The functions include operation(s). Variants of key switching and modulus switching are described and are performed prior to or after the operation(s). A key switching transformation converts a ciphertext with respect to a first secret key and a first modulus to a ciphertext with respect to a second secret key and a second modulus. A key switching transformation converts a first version of a ciphertext with respect to a first secret key and with some number r bits of precision to a second version of the selected ciphertext with respect to a second keys and with some other number r′ bits of precision. The ciphertexts may be operated on as polynomials represented using evaluation representation, which has benefits for multiplication and automorphism. Further, ciphertexts are associated with an estimate of noise, which is used to determine when to perform modulus switching on the ciphertexts.

公开(公告)号：US09281941B2

公开(公告)日：2016-03-08

申请号：US13746713

申请日：2013-01-22

申请人： International Business Machines Corporation ,  University of Bristol

发明人： Craig B. Gentry ,  Shai Halevi ,  Nigel P. Smart

IPC分类号： G06F21/00 ,  H04L9/08 ,  H04L9/00

CPC分类号： H04L9/0838 ,  H04L9/008 ,  H04L9/0618 ,  H04L9/08 ,  H04L9/16 ,  H04L9/30 ,  H04L9/38 ,  H04L63/0442 ,  H04L2209/24 ,  H04L2209/34

摘要： Homomorphic evaluations of functions are performed. The functions include operation(s). Variants of key switching and modulus switching are described and are performed prior to or after the operation(s). A key switching transformation converts a ciphertext with respect to a first secret key and a first modulus to a ciphertext with respect to a second secret key and a second modulus. A key switching transformation converts a first version of a ciphertext with respect to a first secret key and with some number r bits of precision to a second version of the selected ciphertext with respect to a second keys and with some other number r′ bits of precision. The ciphertexts may be operated on as polynomials represented using evaluation representation, which has benefits for multiplication and automorphism. Further, ciphertexts are associated with an estimate of noise, which is used to determine when to perform modulus switching on the ciphertexts.

摘要翻译： 执行功能的同态评估。 这些功能包括操作。 关键切换和模数切换的变型被描述并且在操作之前或之后进行。 关键切换变换相对于第二秘密密钥和第二模数将关于第一秘密密钥和第一模数的密文转换为密文。 密钥交换变换相对于第二密钥将第一版本的密文相对于第一秘密密钥和一些精确的r位转换为所选择的密文的第二版本，并且具有一些其他数字的精确位数r' 。 密文可以作为使用评估表示表示的多项式来操作，这对于乘法和自相似性有益。 此外，密文与噪声估计相关联，用于确定何时在密文上执行模数切换。

公开(公告)号：US20180109376A1

公开(公告)日：2018-04-19

申请号：US15294967

申请日：2016-10-17

申请人： International Business Machines Corporation ,  University of Bristol

发明人： Craig B. Gentry ,  Shai Halevi ,  Nigel P. Smart

IPC分类号： H04L9/08 ,  H04L29/06 ,  H04L9/00 ,  H04L9/38

CPC分类号： H04L9/0838 ,  H04L9/008 ,  H04L9/0618 ,  H04L9/08 ,  H04L9/16 ,  H04L9/30 ,  H04L9/38 ,  H04L63/0442 ,  H04L2209/24 ,  H04L2209/34

摘要： Homomorphic evaluations of functions are performed. The functions include operation(s). Variants of key switching and modulus switching are described and are performed prior to or after the peration(s). A key switching transformation converts a ciphertext with respect to a first secret key and a first modulus to a ciphertext with respect to a second secret key and a second modulus. A key switching transformation converts a first version of a ciphertext with respect to a first secret key and with some number r bits of precision to a second version of the selected ciphertext with respect to a second keys and with some other number r′ bits of precision. The ciphertexts may be operated on as polynomials represented using evaluation representation, which has benefits for multiplication and automorphism. Further, ciphertexts are associated with an estimate of noise, which is used to determine when to perform modulus switching on the ciphertexts.

公开(公告)号：US09608817B2

公开(公告)日：2017-03-28

申请号：US15008921

申请日：2016-01-28

申请人： International Business Machines Corporation ,  University of Bristol

发明人： Craig B. Gentry ,  Shai Halevi ,  Nigel P. Smart

IPC分类号： G06F21/00 ,  H04L9/16 ,  H04L9/08 ,  H04L9/00 ,  H04L9/06 ,  H04L9/30

CPC分类号： H04L9/0838 ,  H04L9/008 ,  H04L9/0618 ,  H04L9/08 ,  H04L9/16 ,  H04L9/30 ,  H04L9/38 ,  H04L63/0442 ,  H04L2209/24 ,  H04L2209/34

摘要： Homomorphic evaluation of a function is performed on input ciphertext(s), which were encrypted using a public key of an encryption scheme that also includes multiple secret keys. Each input ciphertext includes multiple real numbers that are kept with finite precision. Performing the homomorphic evaluation of the function includes performing operation(s). Performing each of one or more operations includes the following. A key-switching transformation is performed on selected ciphertext(s), including converting a first version of a selected ciphertext with respect to a first of the secret keys and with some number r bits of precision to a second version of the selected ciphertext with respect to a second of the secret keys and with some other number r′ bits of precision, r′>r. Each key switching transformation is performed prior to or after the operation(s) are evaluated. Results of the operation(s) are output.

公开(公告)号：US20160164670A1

公开(公告)日：2016-06-09

申请号：US15008921

申请日：2016-01-28

申请人： International Business Machines Corporation ,  University of Bristol

发明人： Craig B. Gentry ,  Shai Halevi ,  Nigel P. Smart

IPC分类号： H04L9/00 ,  H04L9/06

CPC分类号： H04L9/0838 ,  H04L9/008 ,  H04L9/0618 ,  H04L9/08 ,  H04L9/16 ,  H04L9/30 ,  H04L9/38 ,  H04L63/0442 ,  H04L2209/24 ,  H04L2209/34

摘要： Homomorphic evaluation of a function is performed on input ciphertext(s), which were encrypted using a public key of an encryption scheme that also includes multiple secret keys. Each input ciphertext includes multiple real numbers that are kept with finite precision. Performing the homomorphic evaluation of the function includes performing operation(s). Performing each of one or more operations includes the following. A key-switching transformation is performed on selected ciphertext(s), including converting a first version of a selected ciphertext with respect to a first of the secret keys and with some number r bits of precision to a second version of the selected ciphertext with respect to a second of the secret keys and with some other number r′ bits of precision, r′>r. Each key switching transformation is performed prior to or after the operation(s) are evaluated. Results of the operation(s) are output.

摘要翻译： 对输入密文执行功能的同态评估，其使用还包括多个秘密密钥的加密方案的公开密钥进行加密。 每个输入密文包括有限精度保留的多个实数。 执行功能的同态评估包括执行操作。 执行一个或多个操作中的每一个操作包括以下内容。 对所选择的密文执行密钥切换变换，包括相对于第一密钥将所选择的密文的第一版本转换成所选择的密文的第二版本，并且将所选择的密文的第一版本相对于 到一秒钟的秘密密钥和一些其他r'位精度r'> r。 每个按键切换变换在评估操作之前或之后进行。 输出操作结果。

公开(公告)号：US09742566B2

公开(公告)日：2017-08-22

申请号：US15008718

申请日：2016-01-28

申请人： International Business Machines Corporation ,  University of Bristol

发明人： Craig B. Gentry ,  Shai Halevi ,  Nigel P. Smart

IPC分类号： G06F21/00 ,  H04L9/16 ,  H04L9/08 ,  H04L9/00 ,  H04L9/06 ,  H04L9/30

CPC分类号： H04L9/0838 ,  H04L9/008 ,  H04L9/0618 ,  H04L9/08 ,  H04L9/16 ,  H04L9/30 ,  H04L9/38 ,  H04L63/0442 ,  H04L2209/24 ,  H04L2209/34

摘要： Homomorphic evaluation of a function is performed on input ciphertext(s), which were encrypted using a public key of an encryption scheme that also includes multiple secret keys and multiple integer moduli. The homomorphic evaluation of the function includes performing operations(s) on the input ciphertexts. The function includes operation(s) including one or more of addition, multiplication, and automorphism. A key-switching transformation is performed on selected input ciphertext(s), and includes converting a first version of a selected ciphertext with respect to a first of the multiple secret keys and a first modulus to a second version of the selected ciphertext with respect to a second of the multiple secret keys and a second modulus, where the second modulus is an integer factor p times the first modulus, p>1. Each of the key switching transformations is performed prior to or after the operation(s) are evaluated. Results of the operation(s) are output.

公开(公告)号：US20160164676A1

公开(公告)日：2016-06-09

申请号：US15008718

申请日：2016-01-28

申请人： International Business Machines Corporation ,  University of Bristol

发明人： Craig B. Gentry ,  Shai Halevi ,  Nigel P. Smart

IPC分类号： H04L9/16 ,  H04L9/30 ,  H04L9/00

CPC分类号： H04L9/0838 ,  H04L9/008 ,  H04L9/0618 ,  H04L9/08 ,  H04L9/16 ,  H04L9/30 ,  H04L9/38 ,  H04L63/0442 ,  H04L2209/24 ,  H04L2209/34

摘要： Homomorphic evaluation of a function is performed on input ciphertext(s), which were encrypted using a public key of an encryption scheme that also includes multiple secret keys and multiple integer moduli. The homomorphic evaluation of the function includes performing operations(s) on the input ciphertexts. The function includes operation(s) including one or more of addition, multiplication, and automorphism. A key-switching transformation is performed on selected input ciphertext(s), and includes converting a first version of a selected ciphertext with respect to a first of the multiple secret keys and a first modulus to a second version of the selected ciphertext with respect to a second of the multiple secret keys and a second modulus, where the second modulus is an integer factor p times the first modulus, p>1. Each of the key switching transformations is performed prior to or after the operation(s) are evaluated. Results of the operation(s) are output.

摘要翻译： 对使用加密方案的公开密钥加密的输入密文执行功能的同态评估，加密方案还包括多个密钥和多个整数模数。 该功能的同态评估包括对输入密文执行操作。 该功能包括包括一个或多个加法，乘法和自动同步的操作。 对所选择的输入密文执行密钥切换变换，并且包括相对于多个秘密密钥中的第一密钥将所选择的密文的第一版本转换为所选密文的第二版本，相对于 多个秘密密钥中的第二个和第二个模数，其中第二个模量是第一个模数p的整数因子p，p> 1。 关键切换转换中的每一个在评估操作之前或之后执行。 输出操作结果。

公开(公告)号：US20130216044A1

公开(公告)日：2013-08-22

申请号：US13746713

申请日：2013-01-22

申请人： International Business Machines Corporation

发明人： Craig B. Gentry ,  Shai Halevi ,  Nigel P. Smart

IPC分类号： H04L9/08

CPC分类号： H04L9/0838 ,  H04L9/008 ,  H04L9/0618 ,  H04L9/08 ,  H04L9/16 ,  H04L9/30 ,  H04L9/38 ,  H04L63/0442 ,  H04L2209/24 ,  H04L2209/34

摘要： Homomorphic evaluations of functions are performed. The functions include operation(s). Variants of key switching and modulus switching are described and are performed prior to or after the operation(s). A key switching transformation converts a ciphertext with respect to a first secret key and a first modulus to a ciphertext with respect to a second secret key and a second modulus. A key switching transformation converts a first version of a ciphertext with respect to a first secret key and with some number r bits of precision to a second version of the selected ciphertext with respect to a second keys and with some other number r′ bits of precision. The ciphertexts may be operated on as polynomials represented using evaluation representation, which has benefits for multiplication and automorphism. Further, ciphertexts are associated with an estimate of noise, which is used to determine when to perform modulus switching on the ciphertexts.

摘要翻译： 执行功能的同态评估。 这些功能包括操作。 关键切换和模数切换的变型被描述并且在操作之前或之后进行。 关键切换变换相对于第二秘密密钥和第二模数将关于第一秘密密钥和第一模数的密文转换为密文。 密钥交换变换相对于第二密钥将第一版本的密文相对于第一秘密密钥和一些精确的r位转换为所选择的密文的第二版本，并且具有一些其他数字的精确位数r' 。 密文可以作为使用评估表示表示的多项式来操作，这对于乘法和自相似性有益。 此外，密文与噪声估计相关联，用于确定何时在密文上执行模数切换。