10.4 Secure multi-party computation
4 min read•august 15, 2024
lets multiple parties work together on data without revealing their individual inputs. It's like having a trusted friend do math for you and your pals, but without anyone seeing each other's numbers.
This topic builds on cryptographic concepts we've learned, showing how they can be combined to solve real-world problems. From secret sharing to , we'll see how these tools enable secure collaboration in various applications.
Secure Multi-Party Computation
Fundamentals and Objectives
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- Secure multi-party computation () enables multiple parties to jointly compute a function over private inputs without revealing those inputs
- MPC achieves privacy-preserving distributed computation while maintaining confidentiality of individual data
- Simulates a trusted third party receiving all inputs, performing computation, and returning results
- Ensures input privacy, of computation, and in result distribution
- Applications include privacy-preserving data analysis, secure auctions, and collaborative machine learning
- Introduced by in 1982 through the "millionaires' problem" (comparing net worth without revealing actual values)
- Designed to resist various adversaries (semi-honest and malicious)
Security Properties and Adversary Models
- Input privacy protects confidentiality of each party's individual data
- Correctness guarantees accurate computation results
- Fairness ensures all parties receive results simultaneously
- Semi-honest (honest-but-curious) adversaries follow protocol but attempt to learn additional information
- may deviate from protocol to compromise security
- behave maliciously but fear detection
- provides unconditional protection against computationally unbounded adversaries
- relies on hardness assumptions of certain mathematical problems
Cryptographic Techniques in Secure Multi-Party Computation
Foundational Cryptographic Primitives
- Secret sharing schemes () split data among participants
- Example: Distributing encryption key shares among multiple parties
- Homomorphic encryption enables computations on encrypted data
- Example: Performing statistical analysis on encrypted medical records
- (OT) protocols transfer one piece of information without revealing which was selected
- Example: Private information retrieval from a database
- represent functions as encrypted boolean circuits for secure two-party computation
- Example: Secure evaluation of decision trees in machine learning
- verify computation correctness without revealing additional information
- Example: Proving knowledge of a solution to a puzzle without revealing the solution
Advanced Cryptographic Techniques
- distributes trust and enhances security
- Example: Distributed key generation for a cryptocurrency wallet
- ensure parties cannot change inputs or intermediate results
- Example: Committing to a bid in a sealed-bid auction
- protects privacy in collaborative model training
- Example: Privacy-preserving federated learning across multiple organizations
- finds common elements without revealing full sets
- Example: Identifying common contacts between two users without sharing entire contact lists
- aggregates values without revealing individual inputs
- Example: Calculating average salary across companies without disclosing individual salaries
Secure Multi-Party Computation Schemes
Classic MPC Protocols
- Millionaires' problem using for secure two-party computation
- Compares two values without revealing them
- Threshold secret sharing distributes sensitive information among multiple parties
- Example: -out-of- scheme requires shares to reconstruct the secret
- Secure sum protocols for distributed data aggregation
- Example: Computing total votes in an election without revealing individual votes
- Privacy-preserving set intersection using oblivious polynomial evaluation
- Finds common elements between two sets without revealing the sets themselves
Advanced MPC Applications
- Secure multiparty machine learning for privacy-preserving model training
- Example: Collaborative training of a neural network across multiple hospitals
- Secure auction systems protecting bid privacy while determining the winner
- Example: Second-price sealed-bid auctions without a trusted auctioneer
- Privacy-preserving voting schemes preserving voter privacy and ensuring correct tallies
- Example: Homomorphic encryption-based e-voting systems
- Secure multiparty linear regression for collaborative data analysis
- Example: Analyzing financial trends across multiple banks without sharing raw data
Security and Efficiency of Secure Multi-Party Computation Protocols
Security Analysis and Models
- Semi-honest model assumes parties follow protocol but may attempt to learn additional information
- Malicious model considers adversaries who may arbitrarily deviate from the protocol
- Covert model addresses adversaries who may cheat but fear detection
- Information-theoretic security provides unconditional protection against unbounded adversaries
- Computational security relies on hardness assumptions of mathematical problems
- Example: Difficulty of factoring large numbers in RSA encryption
- ensures security when combining multiple MPC primitives
- protects against implementation-specific vulnerabilities
- Example: Timing attacks on cryptographic operations
Efficiency Considerations and Trade-offs
- measures round complexity and bandwidth requirements
- Example: Number of messages exchanged in a distributed key generation protocol
- assesses scalability with respect to parties and input size
- Example: Time complexity of secure multiparty sorting algorithms
- Trade-offs between security guarantees and efficiency in practical implementations
- Example: Using garbled circuits vs. homomorphic encryption for different computations
- Scalability challenges in large-scale MPC deployments
- Example: Performance degradation in protocols with many participants
- Optimization techniques for improving MPC efficiency
- Example: Preprocessing phases to reduce online computation time
Key Terms to Review (27)
Andrew Yao: Andrew Yao is a prominent computer scientist known for his groundbreaking contributions to theoretical computer science and cryptography, particularly in the area of secure multi-party computation. His work laid the foundations for how multiple parties can compute a function over their inputs while keeping those inputs private, addressing key challenges in distributed computing and privacy.
Commitment Schemes: Commitment schemes are cryptographic protocols that allow one party to commit to a chosen value while keeping it hidden from others, with the ability to reveal the value later. This process involves two phases: the commitment phase, where the value is hidden and locked in, and the reveal phase, where the committed value can be disclosed. These schemes are vital for ensuring honesty and integrity in various cryptographic applications, such as proving knowledge without revealing it and facilitating secure computations among multiple parties.
Communication complexity: Communication complexity is a measure of the amount of communication required between parties to compute a function collaboratively. In the context of secure multi-party computation, it reflects how much data needs to be exchanged among multiple parties to achieve a common goal while ensuring that private information is not disclosed.
Computational Complexity: Computational complexity is a field of study that focuses on classifying computational problems based on their inherent difficulty and the resources required to solve them, typically in terms of time and space. It explores how the complexity of problems affects algorithms, particularly in understanding how efficiently a problem can be solved and the limits of what can be computed. This concept becomes critical in areas like cryptography, where the security of systems often relies on the computational difficulty of certain mathematical problems.
Computational security: Computational security refers to the level of security provided by a cryptographic system that relies on the computational complexity of certain mathematical problems. It ensures that breaking the encryption requires an impractical amount of time and resources, making it feasible to protect information even against powerful adversaries. This form of security is crucial in secure multi-party computation, where multiple parties need to jointly compute a function over their inputs while keeping those inputs private.
Correctness: Correctness refers to the property of an algorithm or protocol ensuring that it produces the expected output for all valid inputs. In secure multi-party computation, correctness is crucial because it guarantees that all parties involved will receive accurate results after a computation, without compromising their private inputs. This means that even when inputs are secret, the final output reflects the true computation based on those inputs.
Covert Adversaries: Covert adversaries refer to entities or individuals that operate in secret, using stealthy methods to undermine or attack a target without revealing their identity or intentions. In the context of secure multi-party computation, these adversaries can influence the computation process while remaining hidden, making it essential to design protocols that ensure security even against such hidden threats.
Fairness: Fairness in the context of secure multi-party computation refers to the property that ensures no party can gain an unfair advantage or influence the outcome of the computation in a way that would benefit them at the expense of others. This is crucial in scenarios where multiple parties collaboratively compute a function over their inputs while ensuring that all participants are treated equally and without bias, which fosters trust and cooperation among them.
Garbled circuits: Garbled circuits are a cryptographic technique used to enable secure multi-party computation, allowing multiple parties to jointly compute a function without revealing their private inputs. This method involves encoding the function into a form that obscures the inputs and outputs, making it impossible for any party to learn anything about the other parties' inputs during the computation process. Garbled circuits serve as a cornerstone for privacy-preserving computations in various applications, including secure voting and private data analysis.
Homomorphic encryption: Homomorphic encryption is a form of encryption that allows computations to be performed on ciphertexts, generating an encrypted result that, when decrypted, matches the result of operations performed on the plaintext. This property makes it possible to process and analyze sensitive data without exposing it, greatly enhancing privacy and security. It plays a crucial role in secure multi-party computation, aligns with current trends in cryptographic research focusing on privacy-preserving technologies, and significantly impacts how we think about cryptography in relation to personal data protection.
Information-theoretic security: Information-theoretic security is a level of security that ensures that the ciphertext provides no information about the plaintext, even if the adversary has unlimited computational power. This concept is crucial in cryptography, as it guarantees that any attempts to decipher the message will yield no advantage, ensuring complete confidentiality and privacy regardless of any technological advancements in decryption methods.
Malicious adversaries: Malicious adversaries are entities or individuals that intentionally try to disrupt, manipulate, or compromise a system for their own gain. In the context of secure multi-party computation, these adversaries aim to undermine the privacy and security of the participants by executing dishonest strategies to learn private information or influence outcomes. Understanding their behavior and motivations is crucial in designing systems that can withstand such threats.
MPC: MPC stands for Multi-Party Computation, a cryptographic protocol that allows multiple parties to compute a function over their inputs while keeping those inputs private. This method ensures that no single party has access to the complete data, promoting confidentiality and privacy in collaborative scenarios. By using MPC, parties can work together on computations without revealing their sensitive information, which is crucial in applications like secure voting, privacy-preserving data analysis, and collaborative machine learning.
Oblivious Transfer: Oblivious transfer is a cryptographic protocol that allows a sender to send one of potentially many pieces of information to a receiver, without the sender knowing which piece was received. This concept ensures that the sender remains oblivious to the specific choice made by the receiver, while still allowing the receiver to obtain the desired information securely. It plays a crucial role in enabling secure multi-party computation and enhancing privacy in various cryptographic applications.
Privacy: Privacy refers to the ability of individuals or groups to control their personal information and decide when, how, and to what extent it is shared with others. It is a fundamental aspect of data protection and security, influencing trust in digital systems and interactions. Maintaining privacy often involves techniques and protocols that ensure data confidentiality, anonymity, and secure communication between parties.
Privacy-preserving set intersection: Privacy-preserving set intersection is a cryptographic protocol that enables multiple parties to determine the common elements between their datasets without revealing any other information about those datasets. This method ensures that while participants learn only the intersection of their sets, sensitive data remains confidential, addressing privacy concerns in collaborative data analysis.
Protocol composability: Protocol composability refers to the ability to combine multiple cryptographic protocols in a way that preserves their security properties when they are used together. This concept is crucial for secure multi-party computation, where different parties collaborate on a computation without revealing their private inputs, ensuring that the overall system remains secure even when individual components are added or changed.
Scalability issues: Scalability issues refer to the challenges faced by a system or process when attempting to handle an increasing amount of work or accommodate growth without compromising performance. In the context of cryptography, these issues can arise in secure multi-party computations where the complexity and resources required can grow significantly with the number of participants or the size of the data being processed. Additionally, current research trends focus on addressing these scalability challenges to improve efficiency and applicability in real-world scenarios.
Secure multi-party computation: Secure multi-party computation (SMPC) is a cryptographic technique that allows multiple parties to jointly compute a function over their inputs while keeping those inputs private. This concept emphasizes collaboration without revealing any confidential information, which is crucial for applications where privacy and security are paramount, such as in secret sharing and threshold cryptography. SMPC is also tied to modern research trends in cryptography, particularly in ensuring privacy and obfuscation of sensitive data.
Secure multiparty machine learning: Secure multiparty machine learning refers to a set of techniques that allow multiple parties to collaboratively train machine learning models while keeping their individual data private. This is achieved through secure multi-party computation (SMPC), which enables participants to compute functions over their inputs without revealing them to each other. This approach enhances privacy and security in scenarios where data sharing is restricted or sensitive, ensuring that even during the training process, no party can access another party's raw data.
Secure Sum Computation: Secure sum computation is a cryptographic technique that allows multiple parties to compute the sum of their private inputs without revealing those inputs to each other. This method is essential in secure multi-party computation, enabling collaboration while preserving data privacy. It leverages various cryptographic protocols to ensure that the final result is computed accurately, without exposing individual contributions, thus maintaining confidentiality and trust among participants.
Semi-honest adversaries: Semi-honest adversaries are participants in a secure multi-party computation scenario who follow the protocol as specified but attempt to gain additional information from the data they receive. They do not deviate from the protocol but may exploit their knowledge to infer private information about other participants. This makes them a significant concern in designing secure protocols, as they balance between honesty and potential malicious intent.
Shamir's Secret Sharing: Shamir's Secret Sharing is a cryptographic method that allows a secret to be divided into parts, giving each participant a unique share such that only a specific number of shares can reconstruct the original secret. This technique is based on polynomial interpolation and ensures that a secret can remain secure even if some shares are lost or compromised. The method highlights the importance of trust and collaboration in secure computations, especially in distributed systems.
Side-channel attack resistance: Side-channel attack resistance refers to the ability of a cryptographic system to withstand attacks that exploit information leaked during its operation, rather than attacking the algorithm itself. This type of resistance is crucial for ensuring that sensitive data remains secure, as attackers may use various physical observations like timing information, power consumption, or electromagnetic leaks to gain insights into secret keys or other critical components. By enhancing side-channel attack resistance, cryptographic protocols can provide stronger security guarantees in environments where physical security cannot be assured.
Threshold cryptography: Threshold cryptography is a cryptographic technique that allows a group of participants to jointly perform cryptographic operations, such as signing or decrypting data, while ensuring that a minimum number of them must collaborate to achieve the desired outcome. This method enhances security by distributing trust among multiple parties, making it harder for a single entity to compromise the system. The concept integrates well with advanced techniques to ensure secure computations and utilizes mathematical structures to facilitate shared secret management.
Yao's garbled circuits: Yao's garbled circuits is a cryptographic protocol designed for secure multi-party computation, allowing two parties to jointly compute a function while keeping their inputs private. It transforms a boolean circuit into a 'garbled' version, where the input values are hidden, enabling each party to evaluate the circuit without revealing their own data. This technique has become a foundation for privacy-preserving computations and has significant implications in various applications, including secure data analysis and privacy-preserving outsourcing.
Zero-Knowledge Proofs: Zero-knowledge proofs are cryptographic methods that allow one party to prove to another that they know a value without revealing any information about the value itself. This concept is crucial for enhancing privacy and security in various applications, as it allows parties to authenticate information without sharing sensitive data. Zero-knowledge proofs can be integrated into systems like cryptocurrencies to enable secure transactions, support elliptic curve cryptography for efficient signing and verification, and facilitate secure multi-party computation while maintaining privacy across different parties.