1. Introduction
In the real world, performing entity resolution over data from varied and distributed data sources is a challenging problem. For example, consider two different patient databases belonging to different hospitals, the first one containing records for Peter and Bruce, and the second for Tony, Pet, and Brvce (Pet is an abbreviation for Peter & Brvce is a misspelling of Bruce).
The entity resolution (ER) task here is to identify records from the two databases that belong to the same patients. An ER algorithm will compare the information present in the records (e.g. names, home or work address, phone numbers), and determine if the records refer to the same person. The principal challenge with this is that the two hospitals may record patient information in different formats (i.e. the first may use separate fields for first and last name, whereas the second may store the full name as one field). The privacypreserving entity resolution (PPER) task is an extension of the ER task, with the additional requirement to not reveal sensitive information to any party present in the computation or to an adversary. Specifically, each party learns which of its records are present on other parties, but nothing about any other records; an adversary should learn nothing about any records of any party. Illustrating this with our original example, the first hospital may learn that the second hospital has records for Peter and Bruce, but should not learn about a record for Tony, or any other information about the patients themselves unless explicitly disclosed by the second hospital. Likewise, the second hospital should only learn about Peter & Bruce’s records in the first hospital’s database.
Privacy preservation adds significant challenges and computational overhead in solving ER as the data must be obfuscated to preserve privacy, making similarity comparisons difficult and costly. This is especially the case for fuzzy or approximate matching, which is required to account for differences in formats and data structures. In our case, using encryption techniques (like secure multiparty computation (Yao, 1982) or homomorphic encryption (Abbas Acar, 2018)) for privacy preservation disallow the use of direct or equality comparisons as there is no support for such operators over encrypted records. Operators, in general, including arithmetic, bit, logical, and others are limited in these tools.
Contributions This paper presents AMPPERE, an abstract computation model for performing privacypreserving entity resolution offering platformagnostic, algorithmic abstractions using variants of Jaccard similarity (Jaccard, 1901). The provided abstractions are universal
: they support widely used arithmetic and vector operations and firstclass support for private matrix manipulation. The abstraction model is presented as a pipeline that can be instantiated via simple privacypreserving operations. We demonstrate the feasibility of
AMMPERE’s abstraction model by transparently implementing it atop the secure multiparty computation platform Sharemind (Bogdanov, 2008)and the opensource latticebased homomorphic encryption library PALISADE
(team, 2020). We undertake a rigorous evaluation of our system which demonstrates the efficacy of our abstraction model, and a precise characterization of the induced overheads resulting from the strong cryptographic protections provided by AMPPERE.Roadmap The paper is structured as follows: section 2.1
algorithmically defines the ER & privacypreserving ER problems as well as evaluation metrics; the rest of
section 2 introduces the technical machinery that form the algorithmic components of AMPPERE; section 3 describes and analyzes AMPPERE, the operators supported, and how it can be adapted to concrete implementations. Section 4 reports the settings, results, and findings of our experiments; section 5 lists prior approaches to PPER, and finally section 6 presents our conclusions and directions for further work.2. Algorithmic definition and tools
2.1. Problem definition
We formalize the ER problem as a triple where and are two different datasets consisting of a collection of unique records. denotes the matching record pairs between the two datasets, that is, where indicates that and refer to the same entity in the real world. With PPER, we still deal with , , and
, however, we additionally say the probability that the data owners of
, learn any information outside of what record pairs exist in is negligible, and the probability that an adversary learns anything, including or any part of , is negligible.Additionally, we define a full comparison between and to be , and the number of candidate pairs to be , the Cartesian product between sizes of and (i.e. ). We focus on tokenbased entity resolution algorithms for finding , where each record is represented by a set of unique tokens . Blocking algorithms prune by removing pairs that are unlikely to be part of the solution . Invertedindex blocking algorithms are popular methods that use a function to encode each record into blocking keys , preserving candidate record pairs that share at least one . Therefore, the pruned candidate pair set is defined as . A good blocking algorithm reduces as many candidate pairs as possible without losing truly matched pairs (Michelson and Knoblock, 2006). We use pairs completeness () to measure the percentage of true pairs that are blocked, and reduction ratio () to measure how well the method reduces the number of candidate pairs. These are formally defined as: , , and .
We now introduce our main algorithmic tools for entity resolution: the set similarity metric of Jaccard similarity (Jaccard, 1901) and its derivative MinHashLSH (Leskovec et al., 2014), which is a MinHashbased variant of Local Sensitive Hashing (LSH) designed for searching similar documents from a large corpus. We also introduce the two main cryptographic and privacy tools that we leverage in our implementations of AMPPERE: secure multiparty computation (MPC) (Yao, 1982) and homomorphic encryption (HE) (Abbas Acar, 2018).
2.2. Jaccard similarity
Jaccard similarity (Jaccard, 1901) is a wellknown and widely used setbased similarity metric, commonly used for feature generation and similarity measurement in data mining and information retrieval tasks. Given two sets of tokens and , Jaccard similarity refers to the size of the intersection divided by the size of the union of the tokensets, that is, .
Some existing PPER approaches (Sehili et al., 2015) extend the Jaccard similarity metric to privacypreserving settings by encrypting input sets into bit arrays (or fingerprints), and comparing them using Tanimoto similarity (Tanimoto, 1958), which computes similarity in a manner similar to Jaccard: , where and denotes the number of set bits (cardinality) in the bit array and respectively. We use Jaccard similarity to perform ER by selecting a threshold such that , if .
2.3. MinHashLSH
MinHash exploits minwise independent permutations to generate similaritypreserving signatures for each record. The probability of getting two similar MinHash signatures from two permutations of sets is identical to applying Jaccard directly over the them; formally, where denotes MinHash and denotes the random permutation function. The LSH algorithm then splits the signature into smaller bands (chunks) of a fixed length where only the records that share at least one band are considered to be potentially similar (i.e. they have partially common signatures). MinHashLSH Blocking (Leskovec et al., 2014) is an invertedindex inspired method utilizing MinHashLSH bands as blocking keys and associated record ids as values.
MinHashLSH is statistically robust and efficient for finding similar records or documents; since blocking keys are signatures, they do not reveal information relating to original records. For these reasons, we use it as our blocking method of choice in section 3.1.3.
2.4. Privacy tools
Secure multiparty computation (MPC) (Yao, 1982) ensures that a set of mutually distrusting parties involved in the same distributed computation correctly derive the result of the computation, even when a subset of parties are dishonest, without revealing any new information other than the result of computation. Formally, if the parties are and their private data is , a MPC protocol defines the public function which computes the result over the private data, i.e., while preserving the secrecy of .
Homomorphic Encryption (HE) is a publickey cryptographic scheme that enables certain computations (e.g. addition, multiplication) to be performed directly over encrypted data, without a need for decryption (Abbas Acar, 2018). Conceptually, it can be defined as an algorithmic quadruple of (, , , ): produces a public, private key pair ; is an encryption algorithm that uses to encrypt a given plaintext , outputting a corresponding ciphertext ; is an evaluation function to be directly evaluated over ciphertexts , outputting representing the encrypted computation; is a deterministic algorithm that takes in , decrypts it using , and outputs the result: . The most important component of HE is it’s homomorphic property: suppose an that operates on inputs & , and outputs . For all , it must hold that if = , , and , then is negligible (where refers to a homomorphic operation) (Sen, 2013).
Threshold HE Threshold homomorphic encryption combines the use of threshold cryptography (Desmedt, 2011) and HE to provide functionality via MPC. Here, different parties interact, initially, to compute a joint public and private key, where the private key is split into secret shares, one per party. Each party encrypts their own data using the public key, and the encrypted result is then decrypted, collectively, by some subset of parties assuming that a majority of them are not malicious (Cramer et al., 2001).
3. Amppere
We propose AMPPERE, a platformagnostic abstract machine for privacypreserving entity resolution. We first introduce the specific challenges regarding PPER, present our computation model, and then two concrete implementations.
Challenges of PPER Privacy preservation adds another dimension to the entity resolution problem, making it much more challenging and computationally difficult. Keeping in mind our original example, hospital 1 & 2, contrary to regular ER approaches, cannot directly compare their records to determine that records for Peter and Bruce overlap between their databases. In the privacypreserving setting, their records need to firstly be encrypted, and distributed to a trusted computation host who can perform the data matching. Once encrypted, however, there is limited support in computing equality, similarity or joins, in terms of generalpurpose functionality and scalability. Furthermore, oneway hashing techniques are rendered ineffective as they are susceptible to statisticalbased attacks, and different data sources may have different representations making it hard to apply them.
3.1. Abstraction model
Our model is presented such that it can be instantiated using only simple platformagnostic, privacypreserving primitive operations. As shown in fig. 1, both dataset providers (i.e. , ) negotiate on parameters first (e.g., Jaccard, blocking threshold), then apply encoding on each of their records, individually, while also computing blocks. Encoded records and blocks are then uploaded and stored in a cloud owned by a third party (i.e ), where blocks are merged and deduplicated, and candidate pairs are filtered. ER (privately) is performed on the remaining qualified pairs. The accuracy, in performing PPER, of our abstractions and algorithms is 100% given correct implementations, as evidenced by section 3.2 & section 3.3.
Category  Name 

Primitive operators  , 
Set intersection size  Pairwise join, Vector rotation, Vector extension, Sorting, Matrix join 
Ternary operations  
Private matrix manipulation  , 
3.1.1. Core operations
Our abstraction model relies on several core operations, listed in table 1, that should be defined first. The model assumes that the following primitive operators for vector and matrix data structures are available: Add for addition, Sub for subtraction, Mul for multiplication, and their corresponding elementwise versions: EAdd/ESub/EMul. Additionally, DotProduct for computing dot products, LShift/RShift for shifting vectors left and right, Size for getting the size of a vector or matrix, and Transpose for transposing a vector or matrix. Enc and Dec are encryption & decryption operators. Additional parameters (e.g. cryptographic keys, etc.) may be required, but are omitted here for simplicity. Optionally, logic and bit operators may be used wherever applicable, but we provide workarounds using only arithmetic operations.
The first essential step in computing Jaccard similarity is calculating set intersection size: the intersection size of two tokenizedrecord sets. We list and compare several possible approaches using the primitive operators mentioned above; choosing the appropriate approach depends on the implementation of the operations that it relies on. We use , to indicate two input tokensets (vectors) that contain only unique entries.

Pairwise join (PJ) Compare entries in and in a pairwise manner while accumulating the results into a counter. Since this method must be computed serially, it is inefficient and does not allow the use of optimized primitive operators.

Vector rotation (VR) Fix the longer of the two input vectors (e.g.
), pad the smaller (e.g.
) with arbitrary, noninteger elements not a part of or until the sizes are equal (if necessary), and count the number of overlapping elements represented by zeroes in . This calculation must be done steps as each iteration requires a right shift of by one entry. For example, say and , then and remains unchanged. Computing in the first iteration returns , giving us one 0, repeat this process for iterations. The total number of 0’s represents the number of overlapping elements. Note, this method is an adaptation of basic PSI (private set intersection) protocol presented by Chen et al (Chen et al., 2017). 
Vector extension (VE) Extend to by repeating the it times, and extend to by repeating each element of times; the total number of 0’s in is the number of overlapping elements. For example, say and , then and , hence, and the overlap is 1. This approach offers an alternative to VR (in terms of space vs. time complexity) by preallocating memory for all possible entrywise comparisons and only needing one direct comparison (subtraction) between the two resulting vectors.

Sorting (SO) Merge and into , sort , and then count overlaps between two derived vectors from : the first not including the first entry, and the second not including the last. For example, say , , and ; then computing gives us an overlap of 1.

Matrix join (MJ) Compute the join between and and count the size of the result.
Control flow statements are involved in almost all programs. Choice (e.g. if) and loop (e.g. for, while) based flows require conditional expressions for execution; in privacypreserving settings, however, encrypted Boolean values cannot be used in conditional operations in order to avoid exposing the execution path, unless they are decrypted. Ternary operations can be designed to bypass this limitation: they take a condition followed by two values; if the condition is true, the first value is returned, otherwise the latter (e.g. if/else or :?). If the two values have the same data type and dimension, the return value can be determined by pure arithmetic. We design a set of obliviousstyle ternary operators (Ohrimenko et al., 2016; Constable and Chapin, 2018) which work with encrypted conditions and inputs in various forms (numbers, vectors and matrices) in algorithm 1.
We also define functionality for getting & setting values for encrypted vectors and matrices. We refer to the set of these operations as private matrix manipulation, described in algorithm 2. To privately access vectors and matrices, arithmetic operations need to run over a special mask generated from an encrypted index (, , ). In MaskGen (Line 13), EEq elementwisely compares if and are equal, and sets the corresponding element in the result to be 1 if equal and 0 if not. This procedure generally uses a logical operator, but can also be achieved via arithmetic operations as follows: where is a small offset added to prevent dividing by zero (, must be integers). If a division operator is not available, an element can be multiplied by a randomlysampled encrypted plaintext element , generated by or , i.e. . can decrypt this product and compute its reciprocal, , in clear. Finally, it can encrypt this value and multiply with to output the reciprocal of : .
3.1.2. Entity resolution
We model two datasets, and (e.g. ), each containing encrypted records (e.g. ) where each record is formed by a set of tokens (e.g. ). To represent records as tokensets, we use gram (Banerjee and Pedersen, 2003) tokenization, a generalpurpose, faulttolerant method to tokenize each record with ASCII encoding, represented in 8 bits. We choose a (bigram) encoding, therefore each token occupies 16 bits allowing us to use any data type that has more than 16 bits as a container. In particular, we use the 64 bit container (e.g. uint64), so 4 encoded tokens to be placed in one, as 4 falls
, the commonlyused range of ngrams
(Lesher et al., 1999).The input for entity resolution, besides and , is a threshold , and the output is a sized encrypted, Boolean matrix whose rowindices indicate record ids from , and columnindices indicate record ids from ; a cell’s value indicates if the corresponding records are in the solution . We use Jaccard similarity to compute how similar two records are based on their tokens, and only consider a match if the similarity is greater than . We thereby define the similarity for a candidate record pair to be where indicates the set intersection size of two tokensets and is a value added for tolerating the accuracy of floating point representation.
3.1.3. Blocking
Blocks are represented using a hashmap where each key is a blocking key, and each value is an encrypted vector containing record ids; that is, . Blocks are generated by each party () individually, and are subsequently merged by if they have the same blocking key. Record ids in a block coming from different datasets are grouped into candidate pairs.
Algorithm 3 shows how blocks are used in our entity resolution pipeline. Lines 110 represent block merging and deduplication. Block deduplication refers to the process of determining which encrypted record id pairs have the same blocking key, but are from different datasets; this is done to avoid duplicated candidate pairs and duplicate comparisons. Our approach uses an encrypted Boolean matrix with the same dimensions & indices as , where True values denote candidate pairs. This provides a simple solution to the difficult problem of constructing privacypreserving inverted indices for deduplication (Wang et al., 2015a). VectorLookup retrieves record ids in encrypted form, and MatrixUpdate privately labels candidate pairs. In order to execute entity resolution on the candidate pairs, the program needs to get the record ids of each pair in clear. Even if there exists a method that is able to fetch records and invoke filtering with encrypted record ids, it is inevitable that an attacker could sniff memory or time the code block to detect if certain record pairs are faked. Our solution to not leak the total number of candidate pairs and certain combinations of record pairs is to obfuscate the candidate pair matrix before decryption. In Line 11, the matrix is converted to by adding (unioning) random truthy values with AddNoise before it is decrypted. The matrix is then created along with the matrix (Line 1213). After applying filtering and ER (Line 1417), the results are privately chosen from or via ChooseMatExt with the help of (Line 18), and the added noise is automatically eliminated. If a random number generator for AddNoise is not supported on
, a random matrix can be pregenerated and encrypted by
or for obfuscation.3.1.4. Privacy analysis
This section analyzes the privacy properties of AMPPERE from end to end. Firstly, we note that AMPPERE provides cryptographic protections for privacypreservation: the MPCbased implementation provides privacy of computation to all parties subject to a majority being corrupted (Katz and Lindell, 2014) whereas the HEbased implementation provides privacy against a honestbutcurious adversary. Next, we note that , first encode their input records and perform blocking on their end, and then send their corresponding encrypted data (records & record ids) to . Blocking keys are sent to in clear. The output from is an encrypted matrix where , are responsible for finally decrypting it to retrieve the matching record pairs. needs the vector sizes to calculate the size of the set intersection, resulting in disclosure of the encoded record sizes. Block merging, deduplication, candidate pair generation and filtering use ternary & private matrix operations, all which need to invoke the Size primitive. Consequently, the total number of blocks, the size of each block, and the size of each dataset are disclosed. Therefore, after a complete run, , learn the size of each dataset and the matched record id pairs only. learns the size of each dataset, the size of each encoded record, the size of each block and all blocking keys. No record content is disclosed and because of that no useful information is revealed to . Additionally, the blocking key is the partial MinHash signature, which is irreversible; the total number of blocks as well as the size of each block also do not provide any valuable information. Strictly, two blocks with the same key will be merged, but only knows the size of each block before merging. If two typical blocks with the same key are and , the maximum possible matches could be found in merged block is . Records often appear in multiple blocks, making it difficult for
to estimate the number of matches. The total number of candidate pairs is also protected. Because of obfuscation, its value is somewhere between
to , making it such that an attacker is not able to identify which pairs are noisy and which are real.3.2. Sharemind implementation
SecreC (Cybernetica, 2019a) is a Clike domainspecific programming language designed for the Sharemind platform application (Randmets and others, 2017). SecreC provides generic programming facilities, hiding details of its underlying secure protocol; it has many differences as compared to generalpurpose languages: (i) SecreC distinguishes between public and private data types at the system level via a security type (separate from the data type). The programmer must indicate whether certain data is public or private, and then the implementation can automatically convert oneway from public to private if necessary. (ii) Operations on private data types are limited. For example, bool, int, uint and float do not support bitwise and and bitwise or operators. (iii) Private values cannot be used in conditional statements. (iv) No file system access. The host machine and running environment can exchange data only via input arguments, via keydb, a key value store based on Redis, or via a vectorbased table_database; the data has to be batched and preuploaded through command line arguments to these containers.
Our implementation has two components: upload and link. upload loads encoded records and blocks to the Sharemind keydb instance and link is used for entity resolution. The key for a record is a public string in the form {dataset id}_{record id}, and the value is a private uint64 array which stores encoded tokens. The format of a block is similar to a record, but the key has an additional prefix as a namespace. For a record, if the associated blocking key exists, the program will fetch the corresponding vector back and merge the record id into it with the cat function;
The blocking keys belonging to are acquired from the keydb instance, and are constructed with the blocking keys with ’s identifier; the blocks belonging to different datasets, but with the same blocking key are fetched, candidate pairs are generated and deduplicated, and finally stored into with matrixUpdate. After this, the link program obfuscates the candidate pairs, and runs filtering and ER. Utilizing Sharemind’s API, we implemented the following methods for computing set intersection size: Pairwise join, Vector extension (with internal function gather_uint64_vec), Sorting (with quicksort) and Matrix join (with tableJoinAes128). In the end, is reshaped to a 1D array (as Sharemind does not allow matrices to be returned) and is shipped back to the host.
3.3. PALISADE implementation
Our PALISADE implementations work with the BrakersiGentryVaikuntanathan (BGV) (Brakerski et al., 2011) (for integer arithmetic) and the CheonKimKimSong (CKKS) (Jung Hee Cheon, 2017) (for approximate numbers) constructions, in the form of their respective RNS (residue number system) variants (Craig Gentry, 2012)(Jung Hee Cheon & Kyoohyung Han, 2019). As a first step in utilizing any scheme within PALISADE, one must instantiate a corresponding CryptoContext object for encryption functionality. Each context must be configured with relevant parameters that provide certain bitsecurity levels and performance; in our implementations we configured the following: multiplicative depth, scale factor bits, plaintext modulus, batch size, key switching technique, and security level. Both BGV and CKKS are fully homomorphic (FHE) in the sense that they both support (an arbitrary, unbounded number of) additive and multiplicative homomorphic operations (Gentry, 2009). In PALISADE, these schemes work as parametrized, leveled versions, meaning computations are computed up to a predetermined depth. To establish a fair comparison between both schemes, we keep their corresponding ring dimensions and CRT moduli (Albrecht et al., 2019) the same. Table 2 displays our value choices for the parameters above; further finetuning can be done for potentially more efficient runtimes.
Parameter  BGV  CKKS 

ring dim.  4096  4096, 8192 (B) 
mult. depth  1  1, 2 (B) 
scale factor bits    40 
plaintext mod.  65537   
batch size    16 
key switching  BV  BV 
security level  128 bits  128 bits 
We developed 4 specific implementations in PALISADE: a two party protocol in both BGV and CKKS respectively, and their corresponding threshold (MPC) variants. In the two party protocol, encrypts their data, sends it to who then operates with ’s encrypted data, and their own data (in clear). In the MPC version, we apply threshold HE where and must first agree on a public/private keypair to be used for encryption, and distributed decryption. Then, both parties encrypt and send their data to to carry out the computation over both of their (encrypted) data. Parties are modeled via individual datastructures, each referencing public/private keys generated via the KeyGen function and are realized as separate entities through different threads that take on the evaluation compute. We implemented the Pairwise join, Vector extension, and Vector rotation set intersection size approaches within PALISADE. PJ encodes each token of each record as a separate Ciphertext object with the value of the integer located at slot 0, whereas VR and VE are able to take advantage of plaintext packing (i.e. how many plaintexts you can fit into a single ciphertext slot) by encoding an entire record of tokens together as one ciphertext (Single Instruction Multiple Data (SIMD) computations). PJ computes the ER process in serial, and only relies on the PALISADE function EvalSub to homomorphically compare each token of one record, pairwise with each token of another record. VR and VE both utilize EvalAtIndex to homomorphically rotate (right shift) along with EvalSub for subtractions, while VE additionally uses EvalSum to repeat elements for a certain batchSize over the ring dimension.
We implemented blocking in the CKKS scheme. A discussion around why we chose CKKS vs. BGV for blocking is located in section 4.2.2. We used our own custom HE implementation of ternary operators (algorithm 1) and private matrix manipulation (algorithm 2) for deduplication and filtering (algorithm 3).
4. Experiments
4.1. Datasets and settings
This section describes the dataset used for evaluation and the configurations used for our two implementations.
Febrl dataset Febrl is a synthetic dataset generated using dsgen (Christen, 2005)
, a tool to produce census records including a customizable amount of noise. We generated it using the following settings: Maximal number of duplicates for one original record: 5, Maximum number of modifications per field: 5, Maximum number of modifications per record: 5, Probability distribution for duplicates: zipf, Type of modification: typo, ocr, phonetic. Our dataset used for experiments contains 100 records, split into a 20% component for
and 80% component for . Since our purpose of experimentation is to demonstrate the feasibility, not scalability of AMPPERE, we did not generate any larger datasets. We further processed our dataset using a Python script to create bigram, integer tokens for each record, and to compute MinHashLSH blocking keys for each record with thresholds ranging from 0.1 to 0.9 with step 0.1.Expected performance To better understand the dataset, we created a Python script to apply the same blocking and ER methods in a nonprivacy preserving setting, computing precision, recall, , and . Figure 3
shows that ER precision and recall reach 1.0 when the threshold is in range 0.4 to 0.6.
remains 1.0 when the threshold is to 0.5 and climbs shapely in that range.We used Datasketch (Zhu, 2017) to calculate MinHash signatures for records and to generate LSH blocking keys. We set the number of permutations to 128, and the relative importance of false positive/negative probability to 0.5 each. Datasketch calculates range and band to minimize the weighted sum of probabilities of false positives/negatives with all range and band combinations under a given threshold. The optimal blocking key sizes (the same as range) in different thresholds are shown in fig. 4. The blocking key size is correlated with the : the blocking threshold.
Environment settings The experiments on our Sharemind and PALISADE implementations are conducted on three virtual Ubuntu 18.04.4 LTS servers each with 2 CPUs from Intel Xeon CPU E52690 v4 @ 2.60GHz and 4GB memory. All servers are in the same network and the average PING latency is around 0.120.23ms.
The Sharemind runtime environment (Cybernetica, 2019b) and implementations are deployed on all three servers, as for the SecreC program the shared3p private domain requires distributed across 3 different nodes. For the fairest comparison of evaluation results with Sharemind, we used the following configurations in PALISADE: compiled the PALISADE cmake project with the DWITHNATIVEOPT flag set to on; used singlethreaded runtimes to establish baselines between systems, configured via export OMPNUMTHREADS=1; turned CPU scaling off. We also disabled obfuscation (for both platforms) to achieve the most optimal running time possible.
4.2. Entity resolution performance
We tested the efficiency of executing Jaccard similarity with the different approaches for computing set intersection size described in section 3.1.1. For each approach, we recorded the execution time of Jaccard similarity on 100 randomly sampled single pairs.
4.2.1. Sharemind performance
In Sharemind, we adopted PJ, VE, SO and MJ respectively. Since PJ is extremely slow compared with other approaches, the time cost of all its runs have been divided by 5 in order to be shown properly in one diagram. Figure 4(a) shows that except for PJ, which takes on average 8k ms per record pair, the other three approaches have around the same performance: around 1.8k4k ms per record pair. PJ executes the two loops serially and does not benefit from any parallelism of vector operations. VE achieved the best efficiency, likely a result of Sharemind’s gather_uint64_vec
internal method which saves DSL level operations. The shortcoming of VE, however, is that if the input records were long, overhead due to memory allocation could be a problem. The results of SO show more variance because quick sort is not a stable sorting algorithm; MJ is almost identical to SO. Notice that MJ uses Sharemind’s
tableJoinAes128 function which requires the input records to be encoded in xor_uint32 and this limitation halves the capacity of input containers (which is uint64). Overall, if the average length of records is not long, VE and MJ can be good choices, otherwise SO is better suited.4.2.2. PALISADE performance
In PALISADE, we adopted the PJ, VR, and VE method in both BGV and CKKS. The runtime efficiency here is better than Sharemind’s because these experiments are not distributed across three machines. We perform the experiments in two modes: senderreceiver or (2 party protocol) and threeparty computation or (threshold variant). The VR and VE approaches both performed significantly faster than PJ, as reflected in fig. 4(b) and fig. 4(c), with VR being the fastest of the three. VR is able to reach speeds of 125175 ms per record pair for both BGV and CKKS in the senderreceiver variation and between 1.5 and 4 seconds in the the corresponding threshold (3PC) version. VR and VE are much faster than PJ because they use plaintext packing as described in section 3.3. Additionally, VR is faster than VE because VR only relies on primitive operations (rotations and subtractions), while VE requires extending records using an expensive operation for repeating elements in encrypted form (EvalSum). Consistent with Sharemind, the PJ approach computes ER serially and does not benefit from any parallelization or packing. There are other ways to implement VE and VR in PALISADE that might perform faster or slower, depending on what you try to optimize (time or space).
BGV vs. CKKS Performance BGV generally had equal or better runtime efficiency as compared to CKKS, which is expected. The main difference between the two schemes is that CKKS is an approximation algorithm that supports fast rescaling while dealing with fixedprecision arithmetic. BGV, depending on implementation, either does not support this type of rescaling or requires bootstrapping, which is a much more expensive operation. Since BGV works with exact numbers, when numbers are multiplied, they should not wrap around the plaintext modulus, whereas in CKKS, rescaling is supported after every multiplication. Since our nonblocking approaches did not require a multiplicative depth greater than 1 (because there was no need for sequential homomorphic multiplications), BGV becomes an ideal choice; however, when nestedmultiplications are involved, BGV becomes quickly inefficient as its ciphertext modulus for depth , must be at least , where is also a power of . CKKS is the ideal choice in these situations as it can rescale each time, keeping the parameters small.
Takeaway Determining the optimal approach for privacypreserving entity resolution may vary with the computational platform and the concrete implementation, but our experiments above show many options are applicable and reasonably efficient.
4.3. Blocking performance
In this experiment, we show the effectiveness of blocking in performing (private) entity resolution with the two implementations. We used the nonblocking approach as the baseline (performs all 1,600 pairwise comparisons) and ran blocking with a MinHashLSH threshold of t=0.2, 0.5, and 0.8. The blocking key sizes corresponding to these threshold values are 28, 25 and 9 (resp.) and the numbers of distinct comparisons after blocking are limited to 1,314, 118 and 36 (resp.) as compared to the overall 1,600.
Figure 5(b) demonstrates the total and step time cost of PPER with blocking in Sharemind. The baseline takes around 6,000 seconds to make all 1,600 pairwise similarity comparisons, whereas, for the blocking version, the dataset upload cost depends on the size of blocking keys. Hence, when , it takes the least amount of time to upload data as there are only 9 keys per record and block merging, deduplication and candidate pair generation costs are minor. In the entity resolution step, when , it needs 1,314 comparisons, which while smaller than the baseline, shows an overall longer runtime due to extra overhead incurred via data upload and block operations. When , the number of comparisons along with execution time drops drastically, and this trend continues when , but with recall loss as a tradeoff cost.
As with Sharemind, blocking in PALISADE shows great time cost savings as it filters out unnecessary pairwise record comparisons. Figure 5(c) shows the overall time cost resulting in PALISADE with the various blocking thresholds against the nonblocking baseline. We implement blocking in both the and variants with CKKS as opposed to BGV due to the optimized performance in dealing with rescaling after multiplications, and because of good support for scalar/plaintext & ciphertext operations in implementing ternary operators presented in algorithm 1. Unlike Sharemind, we perform blocking in PALISADE we three main steps: preprocessing (generating block data structures), block merging + deduplication + candidate pair generation, and filtering + ER calculations. In fig. 5(c), we group the runtime of steps 1 and 2 into one bar as, for all blocking threshold levels, preprocessing remains second. For both and variants, when , the overall timecost is actually longer than the baseline (just like with Sharemind), because while filtering is applied through deduplication and candidate pair generation, it only removes around 300 overall comparisons, which does not outweigh the overhead incurred by those steps. When , blocking and filtering is able to brunt much of the computation, by limiting the number of comparisons needed drastically, allowing for the ER calculation to be as minimal as possible.
Takeaway The incurred cost of privacy preservation is significant and evident as shown in fig. 5(a). Filtering and ER takes between 0 and 0.013 seconds as compared to our PPER approaches: between 800 and 7,000 seconds in Sharemind, between 100 and 3,000 seconds in the variant, and between 200 and 7,000 seconds in the variant in PALISADE.
5. Related work
ER has been a wellstudied area for many decades, from specific matching algorithms including Jaccard to semi/full automatic frameworks. PPER, however, has only been investigated recently. Vatsalan et al. (Vatsalan et al., 2013, 2017) provide a taxonomy of some privacypreserving record linkage techniques, and suggest a general architecture. Some earlier work has explored (Dusserre et al., 1995; Quantin et al., 1998) exploiting secure oneway hashing and masking algorithms to protect the content of records, but this is limited as it does not allow for similar variants of records. Some algorithms that rely on certain probabilistic data structures (e.g. Bloom filters (Schnell et al., 2009; Niedermeyer et al., 2014)), though, do exist, and provide reasonable performance & privacy protection, while also maintaining relative similarity between records. Additionally, some record linking approaches depend on the modification of string matching algorithms (e.g. private edit distance (Wang et al., 2015b; Zhu and Huang, 2017), P4Join (Sehili et al., 2015)). With the increase of word/sentence embedding techniques, some methods including (Scannapieco et al., 2007; Bonomi et al., 2012) convert original records into multidimensional embedding vectors which still preserve some principle characteristics, and can be used in similarity comparison and clustering.
Very limited exploration (Lindell, 2005), however, of MPC or HE based approaches exists today, and what does exist only handles the case of exact matching (Emekci et al., 2006), due to expensive computation and lack of computational tool support. Currently, there is no general and comprehensive computational model like AMPPERE for privacypreserving blocking and ER. In recent times, though, many excellent MPC frameworks and HE libraries including Microsoft SEAL (SEAL, 2020), HELib (Halevi, 2021), OblivC (Zahur and Evans, 2015) have been developed and are becoming more applicable for largescale computing purposes. It is clear and evident that a general, precise, and scalable solution for ER based on these techniques will shine and break through in the near future.
6. Conclusion and future work
We proposed an abstract machine for PPER and adopted it to two concrete implementations (Sharemind & PALISADE). Our experiments showed that both implementations could produce results with the exact or relatively equivalent correctness to traditional ER methodologies, while maintaining privacy. This lends credence to the possibilities of solving ER problems with MPC and HE.
Under this direction, many possible and promising future works can be explored. For instance, how to tune and find the optimal parameters for the matching algorithm without revealing data via a privacypreserving adaptation of ground truth sampling and/or oracle annotation mechanisms. Moreover, dataset schema and metadata can also be utilized to further improve the accuracy and performance of matching results. And finally, scaling efficiently to larger and more complex datasets and realworld scenarios is also a nontrivial problem that can be explored, but this will become increasingly computationally feasible as MPC and HE implementations become more efficient.
Acknowledgements.
This project was supported by the DataSafes program with funding from Actuate and the Alfred P. Sloan Foundation.References
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