Secure multi-party computation
protocols for privacy-preserving data
analysis
Introduction
In today’s data-driven world, organizations increasingly need to compute
analytics over sensitive private data contributed by multiple parties.
However, directly pooling and analyzing such data risks privacy breaches
through unintended information leakage or internal data misuse. Secure
multi-party computation (MPC) provides a solution by enabling distributed
parties to jointly compute functions over their private inputs without
revealing anything except the output.
This report analyzes the research landscape of MPC protocols for privacy-
preserving data analysis. It begins with an overview of concepts like secure
function evaluation in the multi-party setting. Specific MPC protocols
including Yao’s Garbled Circuits, GMW and SPDZ will then be detailed. The
practical applications of MPC for data mining tasks like decision trees, linear
regression and neural network training will also be discussed. Overall, the
aim is to demonstrate how MPC enables securely leveraging big private
datasets for analytics in a privacy-preserving manner.
Secure Multi-Party Computation Overview
In the classic secure function evaluation (SFE) problem introduced by Yao in
1982, two parties aim to compute a function f(x,y) over their respective
private inputs x and y, without revealing anything else. MPC generalizes this
problem to more than two parties, where each party holds private inputs and
the goal is to jointly compute any parameterized function f on the inputs
while preserving privacy.
Some key properties of secure MPC include:
- Privacy: No coalition of parties learns anything beyond the output,
even if all but one party collude.
- Correctness: Honest parties obtain the correct output of the function.
- Termination: All honest parties terminate with the correct output.
Common adversaries considered are semi-honest (curious but follows
protocol) or malicious (can deviate arbitrarily from protocol). Most MPC
protocols provide security against semi-honest adversaries with some
tolerating a fraction of malicious parties as well.
Yao’s Garbled Circuits
Yao’s protocol published in 1982 provides a general solution to securely
evaluate any Boolean circuit. It follows a “garble-and-evaluate” approach
using Oblivious Transfer.
In garbling phase, the function circuit is represented as a Boolean garbled
circuit where each wire is assigned two randomly generated encrypted labels
(keys) representing binary 0 and 1.
Then, using 1-2 Oblivious Transfer in the evaluation phase, the party with
input x obtains the proper keys to “decode” the garbled output labels
without learning anything else.
Modern optimizations improve efficiency through row-reduction techniques,
free-XOR and half-gates. Garbled circuits are actively used in practical
deployments due to their generality and performance in 2-party settings.
However, complexity scales with circuit size, limiting applications with large
circuits.
GMW Protocol
The Goldreich-Micali-Wigderson (GMW) protocol introduced in 1987 provides
a theoretically optimal solution to MPC based on secret sharing and
multiplication triples.
Inputs are secret shared additively between parties over a finite field F. To
evaluate a function f, it is represented as an arithmetic or Boolean circuit.
Multiplication gates are securely evaluated using precomputed random
triples (a,b,c) where c=a*b.
Additions are simply local operations on shares. Reconstruction uses linear
combinations to obtain the output without revealing individual shares.
GMW is secure against a malicious majority and provides rigorous security
definitions and proofs in the honest-but-curious model. However, the
overhead of shared multiplication is prohibitive for large circuits or many
parties.
SPDZ Protocol
The SPDZ protocol developed by Damgård et al. in 2012 optimizes GMW for
efficient secure multiplication using “online offline” paradigm.
Inputs are secret shared using additive secret sharing during offline phase
which produces random multiplication triples. Online phase evaluates the
function circuit on secret-shared inputs using free additions and a single
offline-produced multiplication triple for each multiplication gate.
Output reconstruction uses Information Theoretic MACs to prevent cheating.
SPDZ provides security against malicious adversaries and achieves better
asymptotic and concrete efficiency than GMW for large circuits/networks
across many cores/servers using MPC-friendly parallellization.
It has Inspired numerous followup works and deployed in production for
sensitive analytics like fraud detection and medical data analysis by
companies. Overall, SPDZ is considered the current state-of-the-art
theoretical and practical MPC protocol.
Applications in Data Mining
MPC enables leveraging private datasets to train predictive machine learning
models cooperatively while keeping the data distributed and confidential.
This facilitates collaboration in healthcare, fintech and other sensitive
domains.
Some examples include:
- Secure Decision Trees: Parties cooperatively learn an optimal decision
tree for classification or regression based on vertically partitioned
datasets. The tree structure and splits are computed privately without
revealing inputs.
- Secure Linear Regression: Multiple parties can jointly compute a linear
regression model over horizontally partitioned data. Only the
regression coefficients are revealed without leaking individual records.
- Secure Neural Networks: Deep learning models can be trained using
MPC on distributed private datasets. This protects sensitive inputs
while enabling joint modeling of diverse medical, financial or
proprietary databases.
- Graph Analyses: Companies can compute collaborative analytics like
fraud detection by privately combining transaction graphs reflecting
customers, merchants and relationships.
- Differential Privacy: MPC works with DP techniques to enable analysis
with formal privacy guarantees even from passive adversaries.
Overall, MPC protocols facilitate secure cooperation on big data problems in
fields like healthcare, fintech and cybersecurity by enabling analytics over
distributed private datasets.
Privacy-Preserving Decision Tree Learning
Decision trees are one of the most widely used machine learning models
owing to their simplicity, interpretability and performance. Privacy-preserving
distributed learning of decision trees is important for collaborative modeling
across hospitals, research institutions or companies.
Some MPC-based approaches for decision tree induction include:
1) Secure Comparison-based Methods: Parties jointly evaluate the splits
by securely comparing feature values without revealing them, using
protocols for secure equality/inequality testing. This computes the
entropy/information gain criteria privately.
2) Randomized Response: Parties add random noise or perturbation to
local inputs before pooling. Secure aggregation then trains the tree on
the randomized yet representative synthetic data.Provides plausible
deniability while enabling collaboration.
3) Oblivious Transfer: Choices about which branches to traverse during
prediction is designed as an oblivious transfer between server and
clients. This protects user data during inference over pre-trained
private decision trees.
4) Homomorphic Encryption: Feature vectors are encrypted and
aggregated homomorphically to compute statistics for splits. Works
best with small discrete/categorical datasets.
Overall, MPC enables distributed learning of high-accuracy decision tree
models over private datasets across organizations for sensitive domains like
healthcare. The resulting models can then be used privately.
Privacy-Preserving Linear Regression
Linear regression finds applications in diverse domains like healthcare,
finance, autonomous systems by modeling relationships between
explanatory variables and target variable. Multi-party computation enables
securely learning regression models from distributed datasets.
Common approaches include:
1) Secret Sharing-based Techniques: Data owners additively secret share
their private records. Secure summations and multiplications allow
distributed computation of normal equations to recover regression
coefficients privately.
2) Designing as Optimization Problem: Objective function is restructured
as a series of secure comparison and addition protocols to minimize
the cost function in a distributed manner.
3) Homomorphic Encryption: Features are packed and encrypted column-
wise. Adding ciphertext entries securely via partially homomorphic
operations recovers coefficients in encrypted form.
4) Differentially Private Perturbation: Local datasets are privatized before
pooling. Regression on randomized synthetic data yields a
representative model without revealing raw inputs.
MPC-based linear regression finds use cases across sectors like predicting
clinical outcomes from medical records held by hospitals, modeling trading
patterns from financial transactions or demand forecasting based on sales
data owned by retailers.
Secure Neural Network Training
Training deep learning models requires enormous amounts of labeled data,
which often reside in a distributed manner across entities for privacy or
competitive reasons. Secure multi-party computation enables jointly training
deep neural networks over private datasets.
Popular approaches include:
- Secret Sharing the weights/activations and securely evaluating
linear/non-linear layers using GC/SPDZ protocols to prevent information
leakage during forward/backward passes.
- Homomorphic Encryption to perform inference directly on encrypted
inputs or recursively homomorphically aggregate locally encrypted
gradients.
- Randomized Perturbation to add noise before pooling for differentially
private federated learning models.
- Secure aggregation of encrypted gradient vectors from clients by a
coordinating server to iteratively improve the centralized model.
This facilitates collaborative modeling in domains like healthcare, where
disease phenotypes can be jointly modeled across institutional electronic
health records, or cybersecurity where malware detection models benefit
from pooling enterprise logs. Applications also include financial fraud
detection using pooled transaction data.
Overall, MPC and associated techniques enable secure, privacy-preserving
distributed training of powerful deep learning models which were previously
infeasible due to data siloing across organizations.
Applications in Cybersecurity
MPC enables enhanced cyber defense capabilities by securely combining
institutional security telemetry at scale. Example applications include:
- Joint malware detection by training more accurate AI/ML models on
pooled yet distributed enterprise endpoint, network and cloud logs.
- Collaborative threat intelligence by computing metrics like sharing
indicators of compromise privately across critical infrastructure sector
partners.
- Cross-organizational attack graph analyses to identify emerging
threats by correlating private event histories from multiple
organizations.
- Privacy-preserving vulnerability assessments by running penetration
testing and red teaming simulations on distributed systems
infrastructure models.
- Combating cybercrime like phishing or financial fraud through shared
modeling of criminal infrastructure using private institutional
transaction records and darkweb datasets.
Overall, MPC allows cyber defense teams to benchmark resilience, rapidly
detect emerging threats and strengthen security posture through calibrated
access and joint modeling of sensitive operational data – all while balancing
privacy, confidentiality and regulatory norms. This boosts collective security.
Conclusion
In summary, secure multi-party computation provides technical solutions to
enable organizations to collaboratively realize the benefits of big data
analytics while respecting individual privacy constraints. MPC protocols
generalize secure function evaluation techniques to the multi-party setting,
facilitating distributed data processing tasks over databases spanning
multiple entities.
This empowers fields facing regulatory barriers to pooling sensitive
information due to privacy risks, such as healthcare, finance and
cybersecurity. MPC enables deriving business insights through advanced
algorithms like machine learning applied jointly to private datasets. Overall,
it is a critical privacy-enhancing technology for deriving value from growing
data stores in a trusted, compliant manner. Further optimizations and
applications of MPC ensure responsible data sharing continues powering
tomorrow’s innovation.
In today’s data-driven world, organizations increasingly need to compute
analytics over sensitive private data contributed by multiple parties.
However, directly pooling and analyzing such data risks privacy breaches
through unintended information leakage or internal data misuse. Secure
multi-party computation (MPC) provides a solution by enabling distributed
parties to jointly compute functions over their private inputs without
revealing anything except the output.
This report analyzes the research landscape of MPC protocols for privacy-
preserving data analysis. It begins with an overview of concepts like secure
function evaluation in the multi-party setting. Specific MPC protocols
including Yao’s Garbled Circuits, GMW and SPDZ will then be detailed. The
practical applications of MPC for data mining tasks like decision trees, linear
regression and neural network training will also be discussed. Overall, the
aim is to demonstrate how MPC enables securely leveraging big private
datasets for analytics in a privacy-preserving manner.
Secure Multi-Party Computation Overview
In the classic secure function evaluation (SFE) problem introduced by Yao in
1982, two parties aim to compute a function f(x,y) over their respective
private inputs x and y, without revealing anything else. MPC generalizes this
problem to more than two parties, where each party holds private inputs and
the goal is to jointly compute any parameterized function f on the inputs
while preserving privacy.
Some key properties of secure MPC include:
- Privacy: No coalition of parties learns anything beyond the output,
even if all but one party collude.
- Correctness: Honest parties obtain the correct output of the function.
- Termination: All honest parties terminate with the correct output.
Common adversaries considered are semi-honest (curious but follows
protocol) or malicious (can deviate arbitrarily from protocol). Most MPC
protocols provide security against semi-honest adversaries with some
tolerating a fraction of malicious parties as well.
Yao’s Garbled Circuits
Yao’s protocol published in 1982 provides a general solution to securely
evaluate any Boolean circuit. It follows a “garble-and-evaluate” approach
using Oblivious Transfer.
In garbling phase, the function circuit is represented as a Boolean garbled
circuit where each wire is assigned two randomly generated encrypted labels
(keys) representing binary 0 and 1.
Then, using 1-2 Oblivious Transfer in the evaluation phase, the party with
input x obtains the proper keys to “decode” the garbled output labels
without learning anything else.
Modern optimizations improve efficiency through row-reduction techniques,
free-XOR and half-gates. Garbled circuits are actively used in practical
deployments due to their generality and performance in 2-party settings.
However, complexity scales with circuit size, limiting applications with large
circuits.
GMW Protocol
The Goldreich-Micali-Wigderson (GMW) protocol introduced in 1987 provides
a theoretically optimal solution to MPC based on secret sharing and
multiplication triples.
Inputs are secret shared additively between parties over a finite field F. To
evaluate a function f, it is represented as an arithmetic or Boolean circuit.
Multiplication gates are securely evaluated using precomputed random
triples (a,b,c) where c=a*b.
Additions are simply local operations on shares. Reconstruction uses linear
combinations to obtain the output without revealing individual shares.
GMW is secure against a malicious majority and provides rigorous security
definitions and proofs in the honest-but-curious model. However, the
overhead of shared multiplication is prohibitive for large circuits or many
parties.
SPDZ Protocol
The SPDZ protocol developed by Damgård et al. in 2012 optimizes GMW for
efficient secure multiplication using “online offline” paradigm.
Inputs are secret shared using additive secret sharing during offline phase
which produces random multiplication triples. Online phase evaluates the
function circuit on secret-shared inputs using free additions and a single
offline-produced multiplication triple for each multiplication gate.
Output reconstruction uses Information Theoretic MACs to prevent cheating.
SPDZ provides security against malicious adversaries and achieves better
asymptotic and concrete efficiency than GMW for large circuits/networks
across many cores/servers using MPC-friendly parallellization.
It has Inspired numerous followup works and deployed in production for
sensitive analytics like fraud detection and medical data analysis by
companies. Overall, SPDZ is considered the current state-of-the-art
theoretical and practical MPC protocol.
Applications in Data Mining
MPC enables leveraging private datasets to train predictive machine learning
models cooperatively while keeping the data distributed and confidential.
This facilitates collaboration in healthcare, fintech and other sensitive
domains.
Some examples include:
- Secure Decision Trees: Parties cooperatively learn an optimal decision
tree for classification or regression based on vertically partitioned
datasets. The tree structure and splits are computed privately without
revealing inputs.
- Secure Linear Regression: Multiple parties can jointly compute a linear
regression model over horizontally partitioned data. Only the
regression coefficients are revealed without leaking individual records.
- Secure Neural Networks: Deep learning models can be trained using
MPC on distributed private datasets. This protects sensitive inputs
while enabling joint modeling of diverse medical, financial or
proprietary databases.
- Graph Analyses: Companies can compute collaborative analytics like
fraud detection by privately combining transaction graphs reflecting
customers, merchants and relationships.
- Differential Privacy: MPC works with DP techniques to enable analysis
with formal privacy guarantees even from passive adversaries.
Overall, MPC protocols facilitate secure cooperation on big data problems in
fields like healthcare, fintech and cybersecurity by enabling analytics over
distributed private datasets.
Privacy-Preserving Decision Tree Learning
Decision trees are one of the most widely used machine learning models
owing to their simplicity, interpretability and performance. Privacy-preserving
distributed learning of decision trees is important for collaborative modeling
across hospitals, research institutions or companies.
Some MPC-based approaches for decision tree induction include:
1) Secure Comparison-based Methods: Parties jointly evaluate the splits
by securely comparing feature values without revealing them, using
protocols for secure equality/inequality testing. This computes the
entropy/information gain criteria privately.
2) Randomized Response: Parties add random noise or perturbation to
local inputs before pooling. Secure aggregation then trains the tree on
the randomized yet representative synthetic data.Provides plausible
deniability while enabling collaboration.
3) Oblivious Transfer: Choices about which branches to traverse during
prediction is designed as an oblivious transfer between server and
clients. This protects user data during inference over pre-trained
private decision trees.
4) Homomorphic Encryption: Feature vectors are encrypted and
aggregated homomorphically to compute statistics for splits. Works
best with small discrete/categorical datasets.
Overall, MPC enables distributed learning of high-accuracy decision tree
models over private datasets across organizations for sensitive domains like
healthcare. The resulting models can then be used privately.
Privacy-Preserving Linear Regression
Linear regression finds applications in diverse domains like healthcare,
finance, autonomous systems by modeling relationships between
explanatory variables and target variable. Multi-party computation enables
securely learning regression models from distributed datasets.
Common approaches include:
1) Secret Sharing-based Techniques: Data owners additively secret share
their private records. Secure summations and multiplications allow
distributed computation of normal equations to recover regression
coefficients privately.
2) Designing as Optimization Problem: Objective function is restructured
as a series of secure comparison and addition protocols to minimize
the cost function in a distributed manner.
3) Homomorphic Encryption: Features are packed and encrypted column-
wise. Adding ciphertext entries securely via partially homomorphic
operations recovers coefficients in encrypted form.
4) Differentially Private Perturbation: Local datasets are privatized before
pooling. Regression on randomized synthetic data yields a
representative model without revealing raw inputs.
MPC-based linear regression finds use cases across sectors like predicting
clinical outcomes from medical records held by hospitals, modeling trading
patterns from financial transactions or demand forecasting based on sales
data owned by retailers.
Secure Neural Network Training
Training deep learning models requires enormous amounts of labeled data,
which often reside in a distributed manner across entities for privacy or
competitive reasons. Secure multi-party computation enables jointly training
deep neural networks over private datasets.
Popular approaches include:
- Secret Sharing the weights/activations and securely evaluating
linear/non-linear layers using GC/SPDZ protocols to prevent information
leakage during forward/backward passes.
- Homomorphic Encryption to perform inference directly on encrypted
inputs or recursively homomorphically aggregate locally encrypted
gradients.
- Randomized Perturbation to add noise before pooling for differentially
private federated learning models.
- Secure aggregation of encrypted gradient vectors from clients by a
coordinating server to iteratively improve the centralized model.
This facilitates collaborative modeling in domains like healthcare, where
disease phenotypes can be jointly modeled across institutional electronic
health records, or cybersecurity where malware detection models benefit
from pooling enterprise logs. Applications also include financial fraud
detection using pooled transaction data.
Overall, MPC and associated techniques enable secure, privacy-preserving
distributed training of powerful deep learning models which were previously
infeasible due to data siloing across organizations.
Applications in Cybersecurity
MPC enables enhanced cyber defense capabilities by securely combining
institutional security telemetry at scale. Example applications include:
- Joint malware detection by training more accurate AI/ML models on
pooled yet distributed enterprise endpoint, network and cloud logs.
- Collaborative threat intelligence by computing metrics like sharing
indicators of compromise privately across critical infrastructure sector
partners.
- Cross-organizational attack graph analyses to identify emerging
threats by correlating private event histories from multiple
organizations.
- Privacy-preserving vulnerability assessments by running penetration
testing and red teaming simulations on distributed systems
infrastructure models.
- Combating cybercrime like phishing or financial fraud through shared
modeling of criminal infrastructure using private institutional
transaction records and darkweb datasets.
Overall, MPC allows cyber defense teams to benchmark resilience, rapidly
detect emerging threats and strengthen security posture through calibrated
access and joint modeling of sensitive operational data – all while balancing
privacy, confidentiality and regulatory norms. This boosts collective security.
Conclusion
In summary, secure multi-party computation provides technical solutions to
enable organizations to collaboratively realize the benefits of big data
analytics while respecting individual privacy constraints. MPC protocols
generalize secure function evaluation techniques to the multi-party setting,
facilitating distributed data processing tasks over databases spanning
multiple entities.
This empowers fields facing regulatory barriers to pooling sensitive
information due to privacy risks, such as healthcare, finance and
cybersecurity. MPC enables deriving business insights through advanced
algorithms like machine learning applied jointly to private datasets. Overall,
it is a critical privacy-enhancing technology for deriving value from growing
data stores in a trusted, compliant manner. Further optimizations and
applications of MPC ensure responsible data sharing continues powering
tomorrow’s innovation.
In today’s data-driven world, organizations increasingly need to compute
analytics over sensitive private data contributed by multiple parties.
However, directly pooling and analyzing such data risks privacy breaches
through unintended information leakage or internal data misuse. Secure
multi-party computation (MPC) provides a solution by enabling distributed
parties to jointly compute functions over their private inputs without
revealing anything except the output.
This report analyzes the research landscape of MPC protocols for privacy-
preserving data analysis. It begins with an overview of concepts like secure
function evaluation in the multi-party setting. Specific MPC protocols
including Yao’s Garbled Circuits, GMW and SPDZ will then be detailed. The
practical applications of MPC for data mining tasks like decision trees, linear
regression and neural network training will also be discussed. Overall, the
aim is to demonstrate how MPC enables securely leveraging big private
datasets for analytics in a privacy-preserving manner.
Secure Multi-Party Computation Overview
In the classic secure function evaluation (SFE) problem introduced by Yao in
1982, two parties aim to compute a function f(x,y) over their respective
private inputs x and y, without revealing anything else. MPC generalizes this
problem to more than two parties, where each party holds private inputs and
the goal is to jointly compute any parameterized function f on the inputs
while preserving privacy.
Some key properties of secure MPC include:
- Privacy: No coalition of parties learns anything beyond the output,
even if all but one party collude.
- Correctness: Honest parties obtain the correct output of the function.
- Termination: All honest parties terminate with the correct output.
Common adversaries considered are semi-honest (curious but follows
protocol) or malicious (can deviate arbitrarily from protocol). Most MPC
protocols provide security against semi-honest adversaries with some
tolerating a fraction of malicious parties as well.
Yao’s Garbled Circuits
Yao’s protocol published in 1982 provides a general solution to securely
evaluate any Boolean circuit. It follows a “garble-and-evaluate” approach
using Oblivious Transfer.
In garbling phase, the function circuit is represented as a Boolean garbled
circuit where each wire is assigned two randomly generated encrypted labels
(keys) representing binary 0 and 1.
Then, using 1-2 Oblivious Transfer in the evaluation phase, the party with
input x obtains the proper keys to “decode” the garbled output labels
without learning anything else.
Modern optimizations improve efficiency through row-reduction techniques,
free-XOR and half-gates. Garbled circuits are actively used in practical
deployments due to their generality and performance in 2-party settings.
However, complexity scales with circuit size, limiting applications with large
circuits.
GMW Protocol
The Goldreich-Micali-Wigderson (GMW) protocol introduced in 1987 provides
a theoretically optimal solution to MPC based on secret sharing and
multiplication triples.
Inputs are secret shared additively between parties over a finite field F. To
evaluate a function f, it is represented as an arithmetic or Boolean circuit.
Multiplication gates are securely evaluated using precomputed random
triples (a,b,c) where c=a*b.
Additions are simply local operations on shares. Reconstruction uses linear
combinations to obtain the output without revealing individual shares.
GMW is secure against a malicious majority and provides rigorous security
definitions and proofs in the honest-but-curious model. However, the
overhead of shared multiplication is prohibitive for large circuits or many
parties.
SPDZ Protocol
The SPDZ protocol developed by Damgård et al. in 2012 optimizes GMW for
efficient secure multiplication using “online offline” paradigm.
Inputs are secret shared using additive secret sharing during offline phase
which produces random multiplication triples. Online phase evaluates the
function circuit on secret-shared inputs using free additions and a single
offline-produced multiplication triple for each multiplication gate.
Output reconstruction uses Information Theoretic MACs to prevent cheating.
SPDZ provides security against malicious adversaries and achieves better
asymptotic and concrete efficiency than GMW for large circuits/networks
across many cores/servers using MPC-friendly parallellization.
It has Inspired numerous followup works and deployed in production for
sensitive analytics like fraud detection and medical data analysis by
companies. Overall, SPDZ is considered the current state-of-the-art
theoretical and practical MPC protocol.
Applications in Data Mining
MPC enables leveraging private datasets to train predictive machine learning
models cooperatively while keeping the data distributed and confidential.
This facilitates collaboration in healthcare, fintech and other sensitive
domains.
Some examples include:
- Secure Decision Trees: Parties cooperatively learn an optimal decision
tree for classification or regression based on vertically partitioned
datasets. The tree structure and splits are computed privately without
revealing inputs.
- Secure Linear Regression: Multiple parties can jointly compute a linear
regression model over horizontally partitioned data. Only the
regression coefficients are revealed without leaking individual records.
- Secure Neural Networks: Deep learning models can be trained using
MPC on distributed private datasets. This protects sensitive inputs
while enabling joint modeling of diverse medical, financial or
proprietary databases.
- Graph Analyses: Companies can compute collaborative analytics like
fraud detection by privately combining transaction graphs reflecting
customers, merchants and relationships.
- Differential Privacy: MPC works with DP techniques to enable analysis
with formal privacy guarantees even from passive adversaries.
Overall, MPC protocols facilitate secure cooperation on big data problems in
fields like healthcare, fintech and cybersecurity by enabling analytics over
distributed private datasets.
Privacy-Preserving Decision Tree Learning
Decision trees are one of the most widely used machine learning models
owing to their simplicity, interpretability and performance. Privacy-preserving
distributed learning of decision trees is important for collaborative modeling
across hospitals, research institutions or companies.
Some MPC-based approaches for decision tree induction include:
5) Secure Comparison-based Methods: Parties jointly evaluate the splits
by securely comparing feature values without revealing them, using
protocols for secure equality/inequality testing. This computes the
entropy/information gain criteria privately.
6) Randomized Response: Parties add random noise or perturbation to
local inputs before pooling. Secure aggregation then trains the tree on
the randomized yet representative synthetic data.Provides plausible
deniability while enabling collaboration.
7) Oblivious Transfer: Choices about which branches to traverse during
prediction is designed as an oblivious transfer between server and
clients. This protects user data during inference over pre-trained
private decision trees.
8) Homomorphic Encryption: Feature vectors are encrypted and
aggregated homomorphically to compute statistics for splits. Works
best with small discrete/categorical datasets.
Overall, MPC enables distributed learning of high-accuracy decision tree
models over private datasets across organizations for sensitive domains like
healthcare. The resulting models can then be used privately.
Privacy-Preserving Linear Regression
Linear regression finds applications in diverse domains like healthcare,
finance, autonomous systems by modeling relationships between
explanatory variables and target variable. Multi-party computation enables
securely learning regression models from distributed datasets.
Common approaches include:
5) Secret Sharing-based Techniques: Data owners additively secret share
their private records. Secure summations and multiplications allow
distributed computation of normal equations to recover regression
coefficients privately.
6) Designing as Optimization Problem: Objective function is restructured
as a series of secure comparison and addition protocols to minimize
the cost function in a distributed manner.
7) Homomorphic Encryption: Features are packed and encrypted column-
wise. Adding ciphertext entries securely via partially homomorphic
operations recovers coefficients in encrypted form.
8) Differentially Private Perturbation: Local datasets are privatized before
pooling. Regression on randomized synthetic data yields a
representative model without revealing raw inputs.
MPC-based linear regression finds use cases across sectors like predicting
clinical outcomes from medical records held by hospitals, modeling trading
patterns from financial transactions or demand forecasting based on sales
data owned by retailers.
Secure Neural Network Training
Training deep learning models requires enormous amounts of labeled data,
which often reside in a distributed manner across entities for privacy or
competitive reasons. Secure multi-party computation enables jointly training
deep neural networks over private datasets.
Popular approaches include:
- Secret Sharing the weights/activations and securely evaluating
linear/non-linear layers using GC/SPDZ protocols to prevent information
leakage during forward/backward passes.
- Homomorphic Encryption to perform inference directly on encrypted
inputs or recursively homomorphically aggregate locally encrypted
gradients.
- Randomized Perturbation to add noise before pooling for differentially
private federated learning models.
- Secure aggregation of encrypted gradient vectors from clients by a
coordinating server to iteratively improve the centralized model.
This facilitates collaborative modeling in domains like healthcare, where
disease phenotypes can be jointly modeled across institutional electronic
health records, or cybersecurity where malware detection models benefit
from pooling enterprise logs. Applications also include financial fraud
detection using pooled transaction data.
Overall, MPC and associated techniques enable secure, privacy-preserving
distributed training of powerful deep learning models which were previously
infeasible due to data siloing across organizations.
Applications in Cybersecurity
MPC enables enhanced cyber defense capabilities by securely combining
institutional security telemetry at scale. Example applications include:
- Joint malware detection by training more accurate AI/ML models on
pooled yet distributed enterprise endpoint, network and cloud logs.
- Collaborative threat intelligence by computing metrics like sharing
indicators of compromise privately across critical infrastructure sector
partners.
- Cross-organizational attack graph analyses to identify emerging
threats by correlating private event histories from multiple
organizations.
- Privacy-preserving vulnerability assessments by running penetration
testing and red teaming simulations on distributed systems
infrastructure models.
- Combating cybercrime like phishing or financial fraud through shared
modeling of criminal infrastructure using private institutional
transaction records and darkweb datasets.
Overall, MPC allows cyber defense teams to benchmark resilience, rapidly
detect emerging threats and strengthen security posture through calibrated
access and joint modeling of sensitive operational data – all while balancing
privacy, confidentiality and regulatory norms. This boosts collective security.
Conclusion
In summary, secure multi-party computation provides technical solutions to
enable organizations to collaboratively realize the benefits of big data
analytics while respecting individual privacy constraints. MPC protocols
generalize secure function evaluation techniques to the multi-party setting,
facilitating distributed data processing tasks over databases spanning
multiple entities.
This empowers fields facing regulatory barriers to pooling sensitive
information due to privacy risks, such as healthcare, finance and
cybersecurity. MPC enables deriving business insights through advanced
algorithms like machine learning applied jointly to private datasets. Overall,
it is a critical privacy-enhancing technology for deriving value from growing
data stores in a trusted, compliant manner. Further optimizations and
applications of MPC ensure responsible data sharing continues powering
tomorrow’s innovation.
In today’s data-driven world, organizations increasingly need to compute
analytics over sensitive private data contributed by multiple parties.
However, directly pooling and analyzing such data risks privacy breaches
through unintended information leakage or internal data misuse. Secure
multi-party computation (MPC) provides a solution by enabling distributed
parties to jointly compute functions over their private inputs without
revealing anything except the output.
This report analyzes the research landscape of MPC protocols for privacy-
preserving data analysis. It begins with an overview of concepts like secure
function evaluation in the multi-party setting. Specific MPC protocols
including Yao’s Garbled Circuits, GMW and SPDZ will then be detailed. The
practical applications of MPC for data mining tasks like decision trees, linear
regression and neural network training will also be discussed. Overall, the
aim is to demonstrate how MPC enables securely leveraging big private
datasets for analytics in a privacy-preserving manner.
Secure Multi-Party Computation Overview
In the classic secure function evaluation (SFE) problem introduced by Yao in
1982, two parties aim to compute a function f(x,y) over their respective
private inputs x and y, without revealing anything else. MPC generalizes this
problem to more than two parties, where each party holds private inputs and
the goal is to jointly compute any parameterized function f on the inputs
while preserving privacy.
Some key properties of secure MPC include:
- Privacy: No coalition of parties learns anything beyond the output,
even if all but one party collude.
- Correctness: Honest parties obtain the correct output of the function.
- Termination: All honest parties terminate with the correct output.
Common adversaries considered are semi-honest (curious but follows
protocol) or malicious (can deviate arbitrarily from protocol). Most MPC
protocols provide security against semi-honest adversaries with some
tolerating a fraction of malicious parties as well.
Yao’s Garbled Circuits
Yao’s protocol published in 1982 provides a general solution to securely
evaluate any Boolean circuit. It follows a “garble-and-evaluate” approach
using Oblivious Transfer.
In garbling phase, the function circuit is represented as a Boolean garbled
circuit where each wire is assigned two randomly generated encrypted labels
(keys) representing binary 0 and 1.
Then, using 1-2 Oblivious Transfer in the evaluation phase, the party with
input x obtains the proper keys to “decode” the garbled output labels
without learning anything else.
Modern optimizations improve efficiency through row-reduction techniques,
free-XOR and half-gates. Garbled circuits are actively used in practical
deployments due to their generality and performance in 2-party settings.
However, complexity scales with circuit size, limiting applications with large
circuits.
GMW Protocol
The Goldreich-Micali-Wigderson (GMW) protocol introduced in 1987 provides
a theoretically optimal solution to MPC based on secret sharing and
multiplication triples.
Inputs are secret shared additively between parties over a finite field F. To
evaluate a function f, it is represented as an arithmetic or Boolean circuit.
Multiplication gates are securely evaluated using precomputed random
triples (a,b,c) where c=a*b.
Additions are simply local operations on shares. Reconstruction uses linear
combinations to obtain the output without revealing individual shares.
GMW is secure against a malicious majority and provides rigorous security
definitions and proofs in the honest-but-curious model. However, the
overhead of shared multiplication is prohibitive for large circuits or many
parties.
SPDZ Protocol
The SPDZ protocol developed by Damgård et al. in 2012 optimizes GMW for
efficient secure multiplication using “online offline” paradigm.
Inputs are secret shared using additive secret sharing during offline phase
which produces random multiplication triples. Online phase evaluates the
function circuit on secret-shared inputs using free additions and a single
offline-produced multiplication triple for each multiplication gate.
Output reconstruction uses Information Theoretic MACs to prevent cheating.
SPDZ provides security against malicious adversaries and achieves better
asymptotic and concrete efficiency than GMW for large circuits/networks
across many cores/servers using MPC-friendly parallellization.
It has Inspired numerous followup works and deployed in production for
sensitive analytics like fraud detection and medical data analysis by
companies. Overall, SPDZ is considered the current state-of-the-art
theoretical and practical MPC protocol.
Applications in Data Mining
MPC enables leveraging private datasets to train predictive machine learning
models cooperatively while keeping the data distributed and confidential.
This facilitates collaboration in healthcare, fintech and other sensitive
domains.
Some examples include:
- Secure Decision Trees: Parties cooperatively learn an optimal decision
tree for classification or regression based on vertically partitioned
datasets. The tree structure and splits are computed privately without
revealing inputs.
- Secure Linear Regression: Multiple parties can jointly compute a linear
regression model over horizontally partitioned data. Only the
regression coefficients are revealed without leaking individual records.
- Secure Neural Networks: Deep learning models can be trained using
MPC on distributed private datasets. This protects sensitive inputs
while enabling joint modeling of diverse medical, financial or
proprietary databases.
- Graph Analyses: Companies can compute collaborative analytics like
fraud detection by privately combining transaction graphs reflecting
customers, merchants and relationships.
- Differential Privacy: MPC works with DP techniques to enable analysis
with formal privacy guarantees even from passive adversaries.
Overall, MPC protocols facilitate secure cooperation on big data problems in
fields like healthcare, fintech and cybersecurity by enabling analytics over
distributed private datasets.
Privacy-Preserving Decision Tree Learning
Decision trees are one of the most widely used machine learning models
owing to their simplicity, interpretability and performance. Privacy-preserving
distributed learning of decision trees is important for collaborative modeling
across hospitals, research institutions or companies.
Some MPC-based approaches for decision tree induction include:
9) Secure Comparison-based Methods: Parties jointly evaluate the splits
by securely comparing feature values without revealing them, using
protocols for secure equality/inequality testing. This computes the
entropy/information gain criteria privately.
10) Randomized Response: Parties add random noise or perturbation
to local inputs before pooling. Secure aggregation then trains the tree
on the randomized yet representative synthetic data.Provides plausible
deniability while enabling collaboration.
11) Oblivious Transfer: Choices about which branches to traverse
during prediction is designed as an oblivious transfer between server
and clients. This protects user data during inference over pre-trained
private decision trees.
12) Homomorphic Encryption: Feature vectors are encrypted and
aggregated homomorphically to compute statistics for splits. Works
best with small discrete/categorical datasets.
Overall, MPC enables distributed learning of high-accuracy decision tree
models over private datasets across organizations for sensitive domains like
healthcare. The resulting models can then be used privately.
Privacy-Preserving Linear Regression
Linear regression finds applications in diverse domains like healthcare,
finance, autonomous systems by modeling relationships between
explanatory variables and target variable. Multi-party computation enables
securely learning regression models from distributed datasets.
Common approaches include:
9) Secret Sharing-based Techniques: Data owners additively secret share
their private records. Secure summations and multiplications allow
distributed computation of normal equations to recover regression
coefficients privately.
10) Designing as Optimization Problem: Objective function is
restructured as a series of secure comparison and addition protocols to
minimize the cost function in a distributed manner.
11) Homomorphic Encryption: Features are packed and encrypted
column-wise. Adding ciphertext entries securely via partially
homomorphic operations recovers coefficients in encrypted form.
12) Differentially Private Perturbation: Local datasets are privatized
before pooling. Regression on randomized synthetic data yields a
representative model without revealing raw inputs.
MPC-based linear regression finds use cases across sectors like predicting
clinical outcomes from medical records held by hospitals, modeling trading
patterns from financial transactions or demand forecasting based on sales
data owned by retailers.
Secure Neural Network Training
Training deep learning models requires enormous amounts of labeled data,
which often reside in a distributed manner across entities for privacy or
competitive reasons. Secure multi-party computation enables jointly training
deep neural networks over private datasets.
Popular approaches include:
- Secret Sharing the weights/activations and securely evaluating
linear/non-linear layers using GC/SPDZ protocols to prevent information
leakage during forward/backward passes.
- Homomorphic Encryption to perform inference directly on encrypted
inputs or recursively homomorphically aggregate locally encrypted
gradients.
- Randomized Perturbation to add noise before pooling for differentially
private federated learning models.
- Secure aggregation of encrypted gradient vectors from clients by a
coordinating server to iteratively improve the centralized model.
This facilitates collaborative modeling in domains like healthcare, where
disease phenotypes can be jointly modeled across institutional electronic
health records, or cybersecurity where malware detection models benefit
from pooling enterprise logs. Applications also include financial fraud
detection using pooled transaction data.
Overall, MPC and associated techniques enable secure, privacy-preserving
distributed training of powerful deep learning models which were previously
infeasible due to data siloing across organizations.
Applications in Cybersecurity
MPC enables enhanced cyber defense capabilities by securely combining
institutional security telemetry at scale. Example applications include:
- Joint malware detection by training more accurate AI/ML models on
pooled yet distributed enterprise endpoint, network and cloud logs.
- Collaborative threat intelligence by computing metrics like sharing
indicators of compromise privately across critical infrastructure sector
partners.
- Cross-organizational attack graph analyses to identify emerging
threats by correlating private event histories from multiple
organizations.
- Privacy-preserving vulnerability assessments by running penetration
testing and red teaming simulations on distributed systems
infrastructure models.
- Combating cybercrime like phishing or financial fraud through shared
modeling of criminal infrastructure using private institutional
transaction records and darkweb datasets.
Overall, MPC allows cyber defense teams to benchmark resilience, rapidly
detect emerging threats and strengthen security posture through calibrated
access and joint modeling of sensitive operational data – all while balancing
privacy, confidentiality and regulatory norms. This boosts collective security.
Conclusion
In summary, secure multi-party computation provides technical solutions to
enable organizations to collaboratively realize the benefits of big data
analytics while respecting individual privacy constraints. MPC protocols
generalize secure function evaluation techniques to the multi-party setting,
facilitating distributed data processing tasks over databases spanning
multiple entities.
This empowers fields facing regulatory barriers to pooling sensitive
information due to privacy risks, such as healthcare, finance and
cybersecurity. MPC enables deriving business insights through advanced
algorithms like machine learning applied jointly to private datasets. Overall,
it is a critical privacy-enhancing technology for deriving value from growing
data stores in a trusted, compliant manner. Further optimizations and
applications of MPC ensure responsible data sharing continues powering
tomorrow’s innovation.
In today’s data-driven world, organizations increasingly need to compute
analytics over sensitive private data contributed by multiple parties.
However, directly pooling and analyzing such data risks privacy breaches
through unintended information leakage or internal data misuse. Secure
multi-party computation (MPC) provides a solution by enabling distributed
parties to jointly compute functions over their private inputs without
revealing anything except the output.
This report analyzes the research landscape of MPC protocols for privacy-
preserving data analysis. It begins with an overview of concepts like secure
function evaluation in the multi-party setting. Specific MPC protocols
including Yao’s Garbled Circuits, GMW and SPDZ will then be detailed. The
practical applications of MPC for data mining tasks like decision trees, linear
regression and neural network training will also be discussed. Overall, the
aim is to demonstrate how MPC enables securely leveraging big private
datasets for analytics in a privacy-preserving manner.
Secure Multi-Party Computation Overview
In the classic secure function evaluation (SFE) problem introduced by Yao in
1982, two parties aim to compute a function f(x,y) over their respective
private inputs x and y, without revealing anything else. MPC generalizes this
problem to more than two parties, where each party holds private inputs and
the goal is to jointly compute any parameterized function f on the inputs
while preserving privacy.
Some key properties of secure MPC include:
- Privacy: No coalition of parties learns anything beyond the output,
even if all but one party collude.
- Correctness: Honest parties obtain the correct output of the function.
- Termination: All honest parties terminate with the correct output.
Common adversaries considered are semi-honest (curious but follows
protocol) or malicious (can deviate arbitrarily from protocol). Most MPC
protocols provide security against semi-honest adversaries with some
tolerating a fraction of malicious parties as well.
Yao’s Garbled Circuits
Yao’s protocol published in 1982 provides a general solution to securely
evaluate any Boolean circuit. It follows a “garble-and-evaluate” approach
using Oblivious Transfer.
In garbling phase, the function circuit is represented as a Boolean garbled
circuit where each wire is assigned two randomly generated encrypted labels
(keys) representing binary 0 and 1.
Then, using 1-2 Oblivious Transfer in the evaluation phase, the party with
input x obtains the proper keys to “decode” the garbled output labels
without learning anything else.
Modern optimizations improve efficiency through row-reduction techniques,
free-XOR and half-gates. Garbled circuits are actively used in practical
deployments due to their generality and performance in 2-party settings.
However, complexity scales with circuit size, limiting applications with large
circuits.
GMW Protocol
The Goldreich-Micali-Wigderson (GMW) protocol introduced in 1987 provides
a theoretically optimal solution to MPC based on secret sharing and
multiplication triples.
Inputs are secret shared additively between parties over a finite field F. To
evaluate a function f, it is represented as an arithmetic or Boolean circuit.
Multiplication gates are securely evaluated using precomputed random
triples (a,b,c) where c=a*b.
Additions are simply local operations on shares. Reconstruction uses linear
combinations to obtain the output without revealing individual shares.
GMW is secure against a malicious majority and provides rigorous security
definitions and proofs in the honest-but-curious model. However, the
overhead of shared multiplication is prohibitive for large circuits or many
parties.
SPDZ Protocol
The SPDZ protocol developed by Damgård et al. in 2012 optimizes GMW for
efficient secure multiplication using “online offline” paradigm.
Inputs are secret shared using additive secret sharing during offline phase
which produces random multiplication triples. Online phase evaluates the
function circuit on secret-shared inputs using free additions and a single
offline-produced multiplication triple for each multiplication gate.
Output reconstruction uses Information Theoretic MACs to prevent cheating.
SPDZ provides security against malicious adversaries and achieves better
asymptotic and concrete efficiency than GMW for large circuits/networks
across many cores/servers using MPC-friendly parallellization.
It has Inspired numerous followup works and deployed in production for
sensitive analytics like fraud detection and medical data analysis by
companies. Overall, SPDZ is considered the current state-of-the-art
theoretical and practical MPC protocol.
Applications in Data Mining
MPC enables leveraging private datasets to train predictive machine learning
models cooperatively while keeping the data distributed and confidential.
This facilitates collaboration in healthcare, fintech and other sensitive
domains.
Some examples include:
- Secure Decision Trees: Parties cooperatively learn an optimal decision
tree for classification or regression based on vertically partitioned
datasets. The tree structure and splits are computed privately without
revealing inputs.
- Secure Linear Regression: Multiple parties can jointly compute a linear
regression model over horizontally partitioned data. Only the
regression coefficients are revealed without leaking individual records.
- Secure Neural Networks: Deep learning models can be trained using
MPC on distributed private datasets. This protects sensitive inputs
while enabling joint modeling of diverse medical, financial or
proprietary databases.
- Graph Analyses: Companies can compute collaborative analytics like
fraud detection by privately combining transaction graphs reflecting
customers, merchants and relationships.
- Differential Privacy: MPC works with DP techniques to enable analysis
with formal privacy guarantees even from passive adversaries.
Overall, MPC protocols facilitate secure cooperation on big data problems in
fields like healthcare, fintech and cybersecurity by enabling analytics over
distributed private datasets.
Privacy-Preserving Decision Tree Learning
Decision trees are one of the most widely used machine learning models
owing to their simplicity, interpretability and performance. Privacy-preserving
distributed learning of decision trees is important for collaborative modeling
across hospitals, research institutions or companies.
Some MPC-based approaches for decision tree induction include:
13) Secure Comparison-based Methods: Parties jointly evaluate the
splits by securely comparing feature values without revealing them,
using protocols for secure equality/inequality testing. This computes
the entropy/information gain criteria privately.
14) Randomized Response: Parties add random noise or perturbation
to local inputs before pooling. Secure aggregation then trains the tree
on the randomized yet representative synthetic data.Provides plausible
deniability while enabling collaboration.
15) Oblivious Transfer: Choices about which branches to traverse
during prediction is designed as an oblivious transfer between server
and clients. This protects user data during inference over pre-trained
private decision trees.
16) Homomorphic Encryption: Feature vectors are encrypted and
aggregated homomorphically to compute statistics for splits. Works
best with small discrete/categorical datasets.
Overall, MPC enables distributed learning of high-accuracy decision tree
models over private datasets across organizations for sensitive domains like
healthcare. The resulting models can then be used privately.
Privacy-Preserving Linear Regression
Linear regression finds applications in diverse domains like healthcare,
finance, autonomous systems by modeling relationships between
explanatory variables and target variable. Multi-party computation enables
securely learning regression models from distributed datasets.
Common approaches include:
13) Secret Sharing-based Techniques: Data owners additively secret
share their private records. Secure summations and multiplications
allow distributed computation of normal equations to recover
regression coefficients privately.
14) Designing as Optimization Problem: Objective function is
restructured as a series of secure comparison and addition protocols to
minimize the cost function in a distributed manner.
15) Homomorphic Encryption: Features are packed and encrypted
column-wise. Adding ciphertext entries securely via partially
homomorphic operations recovers coefficients in encrypted form.
16) Differentially Private Perturbation: Local datasets are privatized
before pooling. Regression on randomized synthetic data yields a
representative model without revealing raw inputs.
MPC-based linear regression finds use cases across sectors like predicting
clinical outcomes from medical records held by hospitals, modeling trading
patterns from financial transactions or demand forecasting based on sales
data owned by retailers.
Secure Neural Network Training
Training deep learning models requires enormous amounts of labeled data,
which often reside in a distributed manner across entities for privacy or
competitive reasons. Secure multi-party computation enables jointly training
deep neural networks over private datasets.
Popular approaches include:
- Secret Sharing the weights/activations and securely evaluating
linear/non-linear layers using GC/SPDZ protocols to prevent information
leakage during forward/backward passes.
- Homomorphic Encryption to perform inference directly on encrypted
inputs or recursively homomorphically aggregate locally encrypted
gradients.
- Randomized Perturbation to add noise before pooling for differentially
private federated learning models.
- Secure aggregation of encrypted gradient vectors from clients by a
coordinating server to iteratively improve the centralized model.
This facilitates collaborative modeling in domains like healthcare, where
disease phenotypes can be jointly modeled across institutional electronic
health records, or cybersecurity where malware detection models benefit
from pooling enterprise logs. Applications also include financial fraud
detection using pooled transaction data.
Overall, MPC and associated techniques enable secure, privacy-preserving
distributed training of powerful deep learning models which were previously
infeasible due to data siloing across organizations.
Applications in Cybersecurity
MPC enables enhanced cyber defense capabilities by securely combining
institutional security telemetry at scale. Example applications include:
- Joint malware detection by training more accurate AI/ML models on
pooled yet distributed enterprise endpoint, network and cloud logs.
- Collaborative threat intelligence by computing metrics like sharing
indicators of compromise privately across critical infrastructure sector
partners.
- Cross-organizational attack graph analyses to identify emerging
threats by correlating private event histories from multiple
organizations.
- Privacy-preserving vulnerability assessments by running penetration
testing and red teaming simulations on distributed systems
infrastructure models.
- Combating cybercrime like phishing or financial fraud through shared
modeling of criminal infrastructure using private institutional
transaction records and darkweb datasets.
Overall, MPC allows cyber defense teams to benchmark resilience, rapidly
detect emerging threats and strengthen security posture through calibrated
access and joint modeling of sensitive operational data – all while balancing
privacy, confidentiality and regulatory norms. This boosts collective security.
Conclusion
In summary, secure multi-party computation provides technical solutions to
enable organizations to collaboratively realize the benefits of big data
analytics while respecting individual privacy constraints. MPC protocols
generalize secure function evaluation techniques to the multi-party setting,
facilitating distributed data processing tasks over databases spanning
multiple entities.
This empowers fields facing regulatory barriers to pooling sensitive
information due to privacy risks, such as healthcare, finance and
cybersecurity. MPC enables deriving business insights through advanced
algorithms like machine learning applied jointly to private datasets. Overall,
it is a critical privacy-enhancing technology for deriving value from growing
data stores in a trusted, compliant manner. Further optimizations and
applications of MPC ensure responsible data sharing continues powering
tomorrow’s innovation.
