Abstract: In aspects of multiplication operations on homomorphic encrypted data, a computing device stores homomorphic encrypted data as a dataset, and implements an encryption application that can perform multiplication operations on ciphertexts in the homomorphic encrypted data, where the ciphertexts include polynomial variables of the ciphertexts. The encryption application can compute and store intermediate polynomial variables that are computed as the multiplication operations are performed. The encryption application can then utilize one or more of the intermediate polynomial variables rather than recomputing the intermediate polynomial variables as the multiplication operations are performed on the ciphertexts.

Abstract: In aspects of string matching in encrypted data, a computing device stores homomorphic encrypted data as a dataset, and implements a string matching application that receives an encrypted query string as a query of the homomorphic encrypted data. The string matching application can then apply algorithms to perform addition and multiplication operations, and determine whether there are matching strings of the encrypted query string in the dataset. The string matching application can compute, for each row of the dataset, a sum of some function of dataset bits and query bits for a row result, and multiply the row results of the computed rows to determine matching strings. Alternatively, the string matching application can compute, for each row of the dataset, a product over some function of the dataset bits and the query bits for a row result, and add the row results of the computed rows to determine matching strings.

Abstract: In aspects of high-precision rational number arithmetic in homomorphic encryption, a computing device stores homomorphic encrypted data as a dataset, and implements an encryption application that can encode integers into plaintext polynomials, where the integers are representative of initial data received for encryption. The encryption application can encrypt the plaintext polynomials into ciphertexts of the homomorphic encrypted data, and perform homomorphic operations as rational number arithmetic on the ciphertexts, generating updated ciphertexts while the homomorphic encrypted data remains encrypted. The encryption application can then decrypt the updated ciphertexts to modified plaintext polynomials that can be resolved back to the plaintext polynomials effective to recover the integers that represent the initial data. The encryption application can also decode the modified plaintext polynomials back to the integers effective to recover the initial data in an unencrypted form.

Abstract: In aspects of variable relinearization in homomorphic encryption, a computing device stores homomorphic encrypted data as a dataset, and implements an encryption application that can perform a multiplication operation on a ciphertext in the homomorphic encrypted data, where the multiplication operation contributes to increase a noise component in the ciphertext. The encryption application can determine a relinearization amount by which to relinearize the ciphertext after the multiplication operation, where the determination is effective to optimize a noise increase in the ciphertext based at least in part on projected subsequent multiplication operations on the ciphertext. The encryption application can then relinearize the ciphertext utilizing the determined relinearization amount that optimizes the noise increase in the ciphertext for optimal relinearization performance.

Abstract: In aspects of high-precision rational number arithmetic in homomorphic encryption, a computing device stores homomorphic encrypted data as a dataset, and implements an encryption application that can encode integers into plaintext polynomials, where the integers are representative of initial data received for encryption. The encryption application can encrypt the plaintext polynomials into ciphertexts of the homomorphic encrypted data, and perform homomorphic operations as rational number arithmetic on the ciphertexts, generating updated ciphertexts while the homomorphic encrypted data remains encrypted. The encryption application can then decrypt the updated ciphertexts to modified plaintext polynomials that can be resolved back to the plaintext polynomials effective to recover the integers that represent the initial data. The encryption application can also decode the modified plaintext polynomials back to the integers effective to recover the initial data in an unencrypted form.

Abstract: In aspects of variable relinearization in homomorphic encryption, a computing device stores homomorphic encrypted data as a dataset, and implements an encryption application that can perform a multiplication operation on a ciphertext in the homomorphic encrypted data, where the multiplication operation contributes to increase a noise component in the ciphertext. The encryption application can determine a relinearization amount by which to relinearize the ciphertext after the multiplication operation, where the determination is effective to optimize a noise increase in the ciphertext based at least in part on projected subsequent multiplication operations on the ciphertext. The encryption application can then relinearize the ciphertext utilizing the determined relinearization amount that optimizes the noise increase in the ciphertext for optimal relinearization performance.

Abstract: In aspects of multiplication operations on homomorphic encrypted data, a computing device stores homomorphic encrypted data as a dataset, and implements an encryption application that can perform multiplication operations on ciphertexts in the homomorphic encrypted data, where the ciphertexts include polynomial variables of the ciphertexts. The encryption application can compute and store intermediate polynomial variables that are computed as the multiplication operations are performed. The encryption application can then utilize one or more of the intermediate polynomial variables rather than recomputing the intermediate polynomial variables as the multiplication operations are performed on the ciphertexts.

Abstract: In aspects of string matching in encrypted data, a computing device stores homomorphic encrypted data as a dataset, and implements a string matching application that receives an encrypted query string as a query of the homomorphic encrypted data. The string matching application can then apply algorithms to perform addition and multiplication operations, and determine whether there are matching strings of the encrypted query string in the dataset. The string matching application can compute, for each row of the dataset, a sum of some function of dataset bits and query bits for a row result, and multiply the row results of the computed rows to determine matching strings. Alternatively, the string matching application can compute, for each row of the dataset, a product over some function of the dataset bits and the query bits for a row result, and add the row results of the computed rows to determine matching strings.