公开(公告)号：US20210111864A1

公开(公告)日：2021-04-15

申请号：US17132286

申请日：2020-12-23

申请人： International Business Machines Corporation

发明人： Craig B. Gentry ,  Shai Halevi

IPC分类号： H04L9/00 ,  H04L9/06 ,  G06F21/60

摘要： A request is received for specific information that can be deteunined using data in a database on a first computer system. Either at least some of the data is encrypted or the request is encrypted. The first computer system does not have a decryption key to decrypt the encrypted data or request. The first computer system performs compressible HE operations on the data to determine compressed ciphertext(s) that correspond to the specific information. The operations include using a first uncompressed HE scheme and a second compressed HE scheme. The first HE scheme is used on the data to create other multiple ciphertexts and the second HE scheme is used on the other multiple ciphertexts to pack the other multiple ciphertexts into fewer ciphertexts that are compressed. Both the HE schemes use a same secret key. The first computer system sends a response including compressed ciphertext(s) corresponding to the specific information.

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：US09252954B2

公开(公告)日：2016-02-02

申请号：US14511507

申请日：2014-10-10

申请人： International Business Machines Corporation

发明人： Shai Halevi ,  Craig B. Gentry ,  Vinod Vaikuntanathan

IPC分类号： H04K1/00 ,  H04L9/30 ,  H04L9/00 ,  H04L9/08

CPC分类号： H04L9/30 ,  H04L9/008 ,  H04L9/0861 ,  H04L9/3093 ,  H04L2209/08 ,  H04L2209/24

摘要： In one exemplary embodiment, a computer readable storage medium tangibly embodying a program of instructions executable by a machine for performing operations including: receiving information B to be encrypted as a ciphertext C in accordance with an encryption scheme having an encrypt function; and encrypting B in accordance with the encrypt function to obtain C, the scheme utilizes at least one public key A, where B, C, and A are matrices, the encrypt function receives as inputs A and B and outputs C as C←AS+pX+B(mod q), S is a random matrix, X is an error matrix, p is in integer, q is an odd prime number. In other exemplary embodiments, the encryption scheme includes a decrypt function that receives as inputs at least one private key T (a matrix) and C and outputs B as B=T−1·(TCTt mod q)·(Tt)−1 mod p.

摘要翻译： 在一个示例性实施例中，一种有形地体现由机器执行的用于执行操作的指令程序的计算机可读存储介质，包括：根据具有加密功能的加密方案，接收要加密的信息B作为密文C; 并根据加密函数对B进行加密以获得C，该方案利用至少一个公钥A，其中B，C和A是矩阵，加密函数接收作为输入A和B，并将C作为C←AS + pX + B（mod q），S是随机矩阵，X是误差矩阵，p是整数，q是奇素数。 在其他示例性实施例中，加密方案包括解密功能，其接收至少一个私钥T（矩阵）和C的输入，并将B输出为B = T-1·（TCTt mod q）·（Tt）-1 mod p。

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。

公开(公告)号：US11502821B2

公开(公告)日：2022-11-15

申请号：US17132388

申请日：2020-12-23

申请人： International Business Machines Corporation

发明人： Craig B. Gentry ,  Shai Halevi

IPC分类号： H04L9/00 ,  G06F21/60 ,  H04L9/06 ,  H04N21/235 ,  G06N20/00 ,  H04L9/08

摘要： A request is received for specific information that can be determined using data in a database on a first computer system. Either at least some of the data is encrypted or the request is encrypted. The first computer system does not have a decryption key to decrypt the encrypted data or request. The first computer system performs compressible HE operations on the data to determine compressed ciphertext(s) that correspond to the specific information. The operations include using a first uncompressed HE scheme and a second compressed HE scheme. The first HE scheme is used on the data to create other multiple ciphertexts and the second HE scheme is used on the other multiple ciphertexts to pack the other multiple ciphertexts into fewer ciphertexts that are compressed. Both the HE schemes use a same secret key. The first computer system sends a response including compressed ciphertext(s) corresponding to the specific information.

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：US09621346B2

公开(公告)日：2017-04-11

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 ,  Nibel 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： 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.

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：US20140140514A1

公开(公告)日：2014-05-22

申请号：US14097472

申请日：2013-12-05

申请人： International Business Machines Corporation

发明人： Craig B. Gentry

IPC分类号： H04L9/08

CPC分类号： H04L9/0822 ,  H04L9/008 ,  H04L9/14 ,  H04L2209/08 ,  H04L2209/46 ,  H04L2209/50

摘要： A method includes encrypting information in accordance with an encryption scheme that uses a public key; encrypting a plurality of instances of a secret key, each being encrypted using at least one additional instance of the public key; sending the encrypted information and the plurality of encrypted instances of the secret key to a destination; receiving an encrypted result from the destination; and decrypting the encrypted result. A further method includes receiving a plurality of encrypted secret keys and information descriptive of a function to be performed on data; converting the information to a circuit configured to perform the function on the data; and applying the data to inputs of the circuit and evaluating the data using, in turn, the plurality of encrypted secret keys.

摘要翻译： 一种方法包括根据使用公钥的加密方案对信息进行加密; 加密秘密密钥的多个实例，每一个都使用公开密钥的至少一个附加实例进行加密; 将加密信息和密钥的多个加密实例发送到目的地; 从目的地接收加密结果; 并解密加密结果。 另一种方法包括接收多个加密的秘密密钥和描述要在数据上执行的功能的信息; 将所述信息转换成被配置为对所述数据执行所述功能的电路; 以及将数据应用于电路的输入并使用多个加密的秘密密钥来评估数据。