Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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 ?m(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.

Abstract: 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.

Abstract: 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.