Abstract: A technique to remotely identify potential compromise of a service provider that performs homomorphic inferencing on a model. For a set of real data samples on which the inferencing is to take place, at least first and second permutations of a set of trigger samples are generated. Every set of samples (both trigger and real samples) are then sent for homomorphic inferencing on the model at least twice, and in a secret permutated way. To improve performance, a permutation is packaged with the real data samples prior to encryption using a general purpose data structure, a tile tensor, that allows users to store multi-dimensional arrays (tensors) of arbitrary shapes and sizes. In response to receiving one or more results from the HE-based model inferencing, a determination is made whether the service provider is compromised. Upon a determination that the service provider is compromised, a given mitigation action is taken.

Abstract: Evaluating polynomials for use under fully homomorphic encryption (FHE) is provided. An input polynomial of degree n is received, wherein n is equal to 2{circumflex over (?)}m. An input ciphertext containing an input value is also received. The input value is duplicated in n/2 slots. Two plaintext vectors each containing half of the roots in the polynomial are subtracted from the input ciphertext, obtaining second and third ciphertexts, which are multiplied elementwise to produce a result ciphertext comprising n/2 slots. The result ciphertext is rotated by 2{circumflex over (?)}i to generate a rotated ciphertext (i=iteration number) and multiplied by the rotated ciphertext to produce a new result ciphertext, for m?1 iterations. The final result ciphertext is multiplied with a leading coefficient of the polynomial, resulting in a final polynomial evaluation. An operation not supported under FHE is estimated according to the final evaluation.

Abstract: An example system includes a processor that can receive a number of complex packed tensors, wherein each of the complex packed tensors include real numbers encoded as imaginary parts of complex numbers. The processor can execute a single instruction, multiple data (SIMD) operation on the complex packed tensors using an integrated circuit of real and complex packed tensors in a complex domain to generate a result.

Abstract: Mechanisms are provided for increasing the speed of an encoding process. The mechanisms classify operations in the encoding process based on learned associations between patterns of input data and corresponding encoding result types generated from encoding the patterns of input data. The mechanisms identify operations in the encoding process that can be pruned based on the classifications, to thereby generate a set of prune operations. In addition, the mechanisms replace operations in the set of prune operations with replacement operations that retrieve a corresponding previously generated result. Moreover, the mechanisms emit optimized encoding code comprising the replacement operations in replacement of the set of prune operations that are pruned, for execution of the encoding process using the optimized encoding code.

Abstract: Parallelizing functions in deep learning models within homomorphic encryption environments is provided. The method comprises arranging layers in a deep learning model architecture. The layers comprise a first layer computed using a sign function and a second layer having components that can be pre-computed or ignored once computing the sign function on the second layer, wherein the first layer and second layer are adjacent within the deep learning model architecture. The deep learning model architecture is trained with a number of hyper-parameters, and the trained deep learning model architecture is run under homomorphic encryption.

Abstract: Mechanisms are provided for parallel execution of an application. The application is partitioned into slices. For each slice, a simulation of an execution of the slice with regard to pairings of tile tensor shape for input data to the corresponding slice, and number of available devices to execute the slice, is executed, which generates a plurality of simulation results, each having performance metric(s) for a corresponding pairing. A set of one or more tile tensor shapes for one or more slices in the plurality of slices is generated based on one or more simulation results in the plurality of simulation results. The selected tile tensor shape for each slice is used to pack data for input to a corresponding slice in the one or more slices. Furthermore, the application is executed using the selected set of one or more tile tensor shapes for the one or more slices.

Abstract: Provided are a computer program product, system, and method for processing a subset of a feature set to determine where to process a query. One of the following is performed: 1) in response to the determining to process the query at a first machine learning model, forwarding non-sensitive input data of the query to the first machine learning model to produce a first query result to return to an initiator of the query; and 2) in response to determining to process the query at a second machine learning model, forwarding sensitive input data and the non-sensitive input data to an encryption engine to encrypt to send to the second machine learning model; and receiving an encrypted second query result from the second machine learning model to decrypt to produce a second query result to return to the initiator of the query.

Abstract: Mechanisms are provided for performing homomorphic cryptographic operations. The mechanisms receive a specification of a homomorphic encryption (HE) operation to be performed on workloads comprising one or more input ciphertexts and generate a circuit of HE computations for performing the HE operation. The circuit comprises authentication tag checking logic at one or more inputs of the circuit, and nullification logic inserted into the circuit. The nullification logic operates to delete one or more HE encrypted ciphertexts received by the circuit. The mechanisms process the workloads by the circuit of HE computations to generate one or more output ciphertexts that are results of the HE operation executed on the one or more input ciphertexts, which are returned to a source computing system. The nullification logic deletes an input ciphertext of the one or more input ciphertexts when the authentication tag is invalid.

Abstract: An embodiment appends, into a concatenated table, a second plurality of records in a second table to a first plurality of records in a first table. An embodiment sorts, according to each identification value in the concatenated table, the concatenated table. An embodiment generates, using an equality mask derived from each identification value in the sorted table, an intersection table, the intersection table comprising a record in the first plurality of records with a first identifier value matching a second identifier value in a record in the second plurality of records. An embodiment generates, using a not-in-intersection mask derived from the equality mask, a not-in-intersection table. An embodiment adds contents of the intersection table and contents of the not-in-intersection table together, resulting in a join table.

Abstract: An embodiment appends, into a concatenated table, a second plurality of records in a second table to a first plurality of records in a first table. An embodiment sorts, according to each identification value in the concatenated table, the concatenated table. An embodiment generates, using an equality mask derived from each identification value in the sorted table, an intersection table, the intersection table comprising a record in the first plurality of records with a first identifier value matching a second identifier value in a record in the second plurality of records. An embodiment generates, using a not-in-intersection mask derived from the equality mask, a not-in-intersection table. An embodiment adds contents of the intersection table and contents of the not-in-intersection table together, resulting in a join table.

Abstract: Reducing homomorphic encryption (HE) rotations is provided. Input of a source tensor of HE ciphertexts is received and a mapping of elements from the source tensor to a target tensor. For each ciphertext, a vector of required rotations is computed according to the mapping plus a list of unique rotations. A first and second list of rotations are generated which have a combined number of rotations less than the list of unique rotations. For each rotation in the first list a ciphertext vector is computed that holds selected elements cyclically rotated by that rotation. For each rotation in the second list a subset of elements is selected from the ciphertext which is summed with ciphertext vectors generated according to the first list. A rotated ciphertext is generated from this sum rotated by the rotation in the second list. Rotated ciphertexts are summed, and the target tensor is output.

Abstract: Reducing homomorphic encryption (HE) rotations is provided. Input of a source tensor of HE ciphertexts is received and a mapping of elements from the source tensor to a target tensor. For each ciphertext, a vector of required rotations is computed according to the mapping plus a list of unique rotations. A first and second list of rotations are generated which have a combined number of rotations less than the list of unique rotations. For each rotation in the first list a ciphertext vector is computed that holds selected elements cyclically rotated by that rotation. For each rotation in the second list a subset of elements is selected from the ciphertext which is summed with ciphertext vectors generated according to the first list. A rotated ciphertext is generated from this sum rotated by the rotation in the second list. Rotated ciphertexts are summed, and the target tensor is output.

Abstract: Evaluating polynomials for use under fully homomorphic encryption (FHE) is provided. An input polynomial of degree n is received, wherein n is equal to 2{circumflex over (?)}m. An input ciphertext containing an input value is also received. The input value is duplicated in n/2 slots. Two plaintext vectors each containing half of the roots in the polynomial are subtracted from the input ciphertext, obtaining second and third ciphertexts, which are multiplied elementwise to produce a result ciphertext comprising n/2 slots. The result ciphertext is rotated by 2{circumflex over (?)}i to generate a rotated ciphertext (i=iteration number) and multiplied by the rotated ciphertext to produce a new result ciphertext, for m-1 iterations. The final result ciphertext is multiplied with a leading coefficient of the polynomial, resulting in a final polynomial evaluation. An operation not supported under FHE is estimated according to the final evaluation.

Abstract: Mechanisms are provided for performing homomorphic cryptographic operations. The mechanisms receive a specification of a homomorphic encryption (HE) operation to be performed on workloads comprising one or more input ciphertexts and generate a circuit of HE computations for performing the HE operation. The circuit comprises authentication tag checking logic at one or more inputs of the circuit, and nullification logic inserted into the circuit. The nullification logic operates to nullify one or more HE encrypted ciphertexts generated by the circuit. The mechanisms process the workloads by the circuit of HE computations to generate one or more output ciphertexts that are results of the HE operation executed on the one or more input ciphertexts, which are returned to a source computing system. The nullification logic masks an input ciphertext of the one or more input ciphertexts which, based on authentication information associated with the input ciphertext, cannot be authenticated.

Abstract: Mechanisms are provided for performing ciphertext nullification operations. The mechanisms receive a ciphertext in nullification logic of a cryptographic circuit, where the cryptographic circuit comprises one or more cryptographic functions to be performed on the ciphertext. The mechanisms determine, by the nullification logic, whether the received ciphertext is to be nullified. In response to the determination indicating that the ciphertext is to be nullified, the mechanisms generate, by the nullification logic, a nullified ciphertext and output the nullified ciphertext. In response to the determination indicating that the ciphertext is not to be nullified, the nullification logic outputs the received ciphertext.

Abstract: A method, apparatus and computer program product for privacy-preserving homomorphic inferencing using one-hot data representations. In this approach, a client interacting with a cloud-based server submits one-hot maps of a Chinese Remainder Theorem (CRT)-based representation of an data element, and the server expands these maps in an online phase to obtain a full one-hot map for the element. After the server obtains the full one-hot map, it performs an operation, e.g., a comparison operation associated with inferencing on a decision tree, on the one-hot map under homomorphic encryption, and in response generates a result. The result is provided back to the client.

Abstract: An example system includes a processor to mask a ciphertext using four random elements to generate masked ciphertexts. The processor can send the masked ciphertexts to a server device. The processor can receive masked plaintexts from the server device. The processor can unmask the masked plaintexts using the four random elements to generate unmasked plaintexts.

Abstract: An example system includes a processor to receive a ciphertext including an encrypted packed plaintext. The processor can, in response to detecting that a reshape is to be executed for a data structure including the packed ciphertext, identify a target shape for the data structure and execute the reshape based on the identified target shape. The reshape is executed using multiplication by an identity element. The processor can then execute a homomorphic computation using the reshaped data structure.

Abstract: Mechanisms are provided for performing a tournament selection process of a computer function. A request is received to execute the computer function on an input vector data structure, where a result of the computer function is provided by executing the tournament selection process. The input vector data structure is received, comprising a plurality of values where each value corresponds to a vector slot. An index vector data structure is received that comprises indices of the vector slots of the input vector. Iteration(s) of the tournament selection process are executed to identify a value in the input vector satisfying a criterion of the computer function. An operation is performed on the index vector data structure to generate an indicator vector data structure that uniquely identifies a slot in the input vector data structure that is a result of the computer function being executed on the input vector data structure.

Abstract: A computer-implemented method comprising: receiving, as input, a ciphertext x representing a computational result of an approximated fully-homomorphic encryption (FHE) scheme, wherein ciphertext x comprises an underlying number m and an accumulated computational error e; iteratively, (i) performing a bit extraction operation to extract a current most significant bit (MSB) x? of ciphertext x, (ii) calculating accuracy parameters ?, ? associated with x?; (iii) applying a step function to the extracted MSB x?, based, at least in part, on the calculated accuracy parameters ?, ?, to reduce or remove the accumulated computational error e and to return a clean MSB b, and (iv) repeating steps (i)-(iii) for all bits included in the underlying number m; and reconstructing and outputting, from all of the returned clean MSBs b, the number m.