Periodic Reporting for period 1 - NFITSC (New Frontiers in Information-Theoretic Secure Computation)
Reporting period: 2023-05-01 to 2025-10-31
Modern computational environments are highly distributed. Users’ data is collected, combined, and stored across multiple entities, raising significant privacy and integrity concerns. These scenarios are naturally addressed by the powerful framework of Secure Multiparty Computation (MPC). This framework enables a group of parties to jointly compute a function without revealing any additional information about their private inputs. In its most general form, MPC can be viewed as a "complete" cryptographic primitive that subsumes many specific cryptographic tasks, such as zero-knowledge proofs, electronic voting, and even foundational primitives like encryption and digital signatures.
This project primarily focuses on Information-Theoretic (IT) MPC that provides security against computationally unbounded adversaries. The IT setting has several important useful features: It does not rely on the validity of unproven computational intractability assumptions, it is robust to the exact computational model of the adversary (e.g. classical vs. quantum), and it offers everlasting security against adversaries that gather data during the protocol's execution and later invest huge amounts of resources in order to extract information from the collected data. Importantly, for many cryptographic problems, the best existing solutions are based on an information-theoretic core construction that is enhanced with a simple cryptographic tool. Taking a broader view, many central problems that deal with ``fault-tolerance'' from areas like coding theory, distributed computing and computational complexity can be formulated as concrete instances of IT-MPC problems.
Despite its foundational importance, our understanding of IT-MPC remains limited. This project addresses this fundamental question through three complementary, yet independently motivated, research directions: First, we aim to improve the complexity of general secret sharing schemes. Such schemes can be viewed as the information-theoretic analog of encryption schemes, and accordingly they have numerous applications for distributed storage of static data. Our second objective is to improve the efficiency and extend the applicability of Secure Non-Interactive Reductions -- a powerful tool that allows to securely represent a complicated computational task by a simpler one. Finally, our third objective is to expand our theoretical understanding of constant-round information-theoretic protocols, optimize their round complexity, and study their computational complexity. The project bridges across different regions of computer science such as coding theory, cryptography, computational complexity, and communication complexity. It is expected to impact central problems in cryptography, while enriching the general landscape of theoretical computer science.
This project primarily focuses on Information-Theoretic (IT) MPC that provides security against computationally unbounded adversaries. The IT setting has several important useful features: It does not rely on the validity of unproven computational intractability assumptions, it is robust to the exact computational model of the adversary (e.g. classical vs. quantum), and it offers everlasting security against adversaries that gather data during the protocol's execution and later invest huge amounts of resources in order to extract information from the collected data. Importantly, for many cryptographic problems, the best existing solutions are based on an information-theoretic core construction that is enhanced with a simple cryptographic tool. Taking a broader view, many central problems that deal with ``fault-tolerance'' from areas like coding theory, distributed computing and computational complexity can be formulated as concrete instances of IT-MPC problems.
Despite its foundational importance, our understanding of IT-MPC remains limited. This project addresses this fundamental question through three complementary, yet independently motivated, research directions: First, we aim to improve the complexity of general secret sharing schemes. Such schemes can be viewed as the information-theoretic analog of encryption schemes, and accordingly they have numerous applications for distributed storage of static data. Our second objective is to improve the efficiency and extend the applicability of Secure Non-Interactive Reductions -- a powerful tool that allows to securely represent a complicated computational task by a simpler one. Finally, our third objective is to expand our theoretical understanding of constant-round information-theoretic protocols, optimize their round complexity, and study their computational complexity. The project bridges across different regions of computer science such as coding theory, cryptography, computational complexity, and communication complexity. It is expected to impact central problems in cryptography, while enriching the general landscape of theoretical computer science.
We continue with a brief summary of our main achievements.
1. Succinct Computational Secret Sharing (STOC’23): We present the first secret sharing scheme for general access structures with polynomial share size, dramatically improving on prior work that required exponential size.
2. Optimal-Round Statistical MPC (STOC’23): Building on a foundational result from 1989, we resolve a long-standing open question by showing that any functionality can be securely computed in just four rounds with statistical security and honest majority, which is provably optimal. As part of this, we introduce the first optimal-round statistically secure VSS and show tight bounds for related cryptographic tasks.
3. Near-Threshold Secret Sharing (Crypto’23–’24, TCC’24): We revisit linear secret sharing (LSS) for near-threshold access structures and achieve efficiency levels previously thought impossible. Our contributions include: MPC-friendly LSS with 1-bit shares, LSS reconstructible via a linear number of additions, and protocols for distributively sampling secret shares with constant communication per party. These advances significantly enhance the efficiency of threshold cryptography and secure computation.
4. Hardness of Information-Theoretic Lower Bounds (FOCS’23, STOC’25): We tackle a major open question: why is it so hard to prove strong communication lower bounds for basic information-theoretic cryptographic tasks? Our recent works—on Advisor-Verifier-Prover games (FOCS’23) and on the meta-complexity of secret sharing (STOC’25)—propose a new unified framework for understanding this difficulty and introduce tools that could guide future breakthroughs.
5.Secret Sharing for NP Statements (Crypto’25): We define and construct the first information-theoretic NP secret sharing (NPSS) scheme, enabling secure sharing of NP statements. This leads to major applications—including new NIZK proof techniques and the first 3-round MPC protocol from only one-way functions. We also present a leakage-resilient variant of this notion and show that it can amplify non-interactive zero-knowledge proofs – resolving an open question.
1. Succinct Computational Secret Sharing (STOC’23): We present the first secret sharing scheme for general access structures with polynomial share size, dramatically improving on prior work that required exponential size.
2. Optimal-Round Statistical MPC (STOC’23): Building on a foundational result from 1989, we resolve a long-standing open question by showing that any functionality can be securely computed in just four rounds with statistical security and honest majority, which is provably optimal. As part of this, we introduce the first optimal-round statistically secure VSS and show tight bounds for related cryptographic tasks.
3. Near-Threshold Secret Sharing (Crypto’23–’24, TCC’24): We revisit linear secret sharing (LSS) for near-threshold access structures and achieve efficiency levels previously thought impossible. Our contributions include: MPC-friendly LSS with 1-bit shares, LSS reconstructible via a linear number of additions, and protocols for distributively sampling secret shares with constant communication per party. These advances significantly enhance the efficiency of threshold cryptography and secure computation.
4. Hardness of Information-Theoretic Lower Bounds (FOCS’23, STOC’25): We tackle a major open question: why is it so hard to prove strong communication lower bounds for basic information-theoretic cryptographic tasks? Our recent works—on Advisor-Verifier-Prover games (FOCS’23) and on the meta-complexity of secret sharing (STOC’25)—propose a new unified framework for understanding this difficulty and introduce tools that could guide future breakthroughs.
5.Secret Sharing for NP Statements (Crypto’25): We define and construct the first information-theoretic NP secret sharing (NPSS) scheme, enabling secure sharing of NP statements. This leads to major applications—including new NIZK proof techniques and the first 3-round MPC protocol from only one-way functions. We also present a leakage-resilient variant of this notion and show that it can amplify non-interactive zero-knowledge proofs – resolving an open question.
Item 1 (Succinct Computational Secret Sharing – SCSS): Until recently, it was unknown whether secret sharing with only polynomial complexity was even possible. Our work answers this long-standing question with a surprising and positive result. This breakthrough could open the door to more efficient cryptographic constructions. Future directions include relaxing the strong RSA-based assumption (e.g. using symmetric-key tools like random oracles), or showing that public-key cryptography is essential for such schemes.
Item 2 (Optimal-Round Statistical VSS): We solve a long-open problem: building a statistically secure, optimal-round Verifiable Secret Sharing (VSS) protocol in the honest-majority setting. Our solution introduces several new techniques—including virtualization, Hadamard-based sharing, and a novel information-theoretic GMW compiler. While our current protocol has exponential overhead, making it polynomial remains a key challenge.
Item 3 (Practical Advances in LSS): Our improvements in linear secret sharing (LSS) may have real-world impact. To realize this, we need to better understand the constants in graph-based codes, implement our protocols, and test them in practical settings.
Item 4 (Understanding Lower Bounds): We take a first step toward explaining why strong lower bounds remain elusive in information-theoretic cryptography. Our new frameworks—based on Advisor-Verifier-Prover (AVP) games and meta-complexity —introduce tools that could guide future research. Next steps include designing improved AVP protocols and meta-algorithms to estimate secret-sharing complexity more efficiently.
Item 5 (Secret Sharing for NP Statements – NPSS): This work introduces the first information-theoretic version of NPSS and builds new tools to realize it for any threshold. Our approach, based on a new MPC model and a variant of the MPC-in-the-head paradigm, also leads to unexpected applications like NIZK combiners and amplifiers. Further exploration could reveal broader uses for this technique in cryptography.
Item 2 (Optimal-Round Statistical VSS): We solve a long-open problem: building a statistically secure, optimal-round Verifiable Secret Sharing (VSS) protocol in the honest-majority setting. Our solution introduces several new techniques—including virtualization, Hadamard-based sharing, and a novel information-theoretic GMW compiler. While our current protocol has exponential overhead, making it polynomial remains a key challenge.
Item 3 (Practical Advances in LSS): Our improvements in linear secret sharing (LSS) may have real-world impact. To realize this, we need to better understand the constants in graph-based codes, implement our protocols, and test them in practical settings.
Item 4 (Understanding Lower Bounds): We take a first step toward explaining why strong lower bounds remain elusive in information-theoretic cryptography. Our new frameworks—based on Advisor-Verifier-Prover (AVP) games and meta-complexity —introduce tools that could guide future research. Next steps include designing improved AVP protocols and meta-algorithms to estimate secret-sharing complexity more efficiently.
Item 5 (Secret Sharing for NP Statements – NPSS): This work introduces the first information-theoretic version of NPSS and builds new tools to realize it for any threshold. Our approach, based on a new MPC model and a variant of the MPC-in-the-head paradigm, also leads to unexpected applications like NIZK combiners and amplifiers. Further exploration could reveal broader uses for this technique in cryptography.