Homomorphic Secret Sharing: Secure Computation and Beyond

Project Information

HSS

Grant agreement ID: 852952

DOI

10.3030/852952

Project terminated on 19 January 2026

EC signature date 23 January 2020

Start date 1 February 2020

End date 31 May 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 490 917,50

EU contribution

€ 1 490 917,50

Coordinated by

REICHMAN UNIVERSITY
Israel

Periodic Reporting for period 3 - HSS (Homomorphic Secret Sharing: Secure Computation and Beyond)

Reporting period: 2023-02-01 to 2024-07-31

Summary of the context and overall objectives of the project

Secure computation protocols allow mutually distrusting users to jointly compute on their private inputs, emulating the privacy and correctness guarantees of an incorruptible trusted third party. This includes privacy-preserving computation across sensitive data sets, as well as eliminating single points of failure within a system. A vast spectrum of cryptographic goals can be cast as specific cases of secure computation.

Theoretical advances in secure computation already have influenced real-world technologies, and hold great promise for the future. Just as public-key encryption and authentication revolutionized e-commerce, one can imagine an ideal future world where all computations are performed in a secure manner, wherein society can benefit and learn from masses of personal data, while simultaneously users can be assured their data is protected and only used how it should.

Although secure computation is already a prominent solution in applications where privacy/security is paramount, the current overheads incurred by performing a computation securely are still a significant distance from enabling such an ideal ubiquity. While continued investigation along existing directions is an important research agenda, the possibility becomes increasingly evident that shedding these limitations may require a new approach.

Project HSS serves to investigate a new paradigm for the design of secure computation and surrounding technologies, via a tool put forth by the PI, of homomorphic secret sharing (HSS). HSS-based techniques demonstrate exciting potential not only as a new paradigm toward efficient low-communication secure computation, but additionally as a means for greatly advancing supporting technologies within all paradigms, and even bridging to other disciplines, with developments and implications reaching beyond the realm of secure computation.

More concretely, the objectives of the project fall within three focus directions:

1. Foundations of HSS
2. Secure Computation
3. HSS Techniques Beyond Secure Computation

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Since the beginning of the project funding period, a great deal of progress has been made, including recruiting a team, performing cutting-edge research, and disseminating research results to the broader international research community.

The research team includes PhD students Pierre Meyer (MSc ENS Lyon) and Matan Hamilis (MSc Technion Israel), postdoctoral research fellows Dr. Cecilia Boschini (PhD University of Lugano) and soon-to-be-arriving Dr. Jack Doerner (PhD Northeastern University), graduate students Dor Banon and Yaxin Tu, as well as regular visiting students and scientists. (We note that an additional postdoc (Mark Simkin, PhD Aarhus University Denmark) and student (Tamalika Mukerjee, Purdue USA) were originally scheduled to arrive in 2020 but were ultimately unable to join the team due to global travel shutdowns of COVID-19 in the relevant time period.)

Within the first 30 months, the Project HSS team has successfully achieved significant research advancements toward the designated project goals. This includes new techniques for building HSS and the important primitive of Pseudorandom Correlation Generators (PCGs), for achieving secure computation with low communication complexity costs, for attaining security against strong malicious adversaries with low overhead, as well as beginning an exploration of connections of HSS to certain types of algorithms design.

Dissemination of project advancements has taken place via team presentations and participation in both local and international conferences, workshops, visits, and other events. This includes several events of the International Association for Cryptologic Research (IACR), such as annual flagship CRYPTO and EUROCRYPT conferences, the IACR Theory of Cryptography and Asiacrypt Conferences, and broader theory conferences such as FOCS and ITCS. It also includes workshop and school events such as the annual FOCS 2021 Workshop on Cryptography, the Women in Security and Cryptography 2021 workshop, the Bar-Ilan Winter School 2022, Women in Theory 2022 workshop, and the 2022 Simons Institute Workshop on Quantum and Lattices, as well as invited presentations at various university seminars.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The work described above constitutes significant progress beyond the state of the art in the field. This includes:
- Further understanding and constructions of the underlying foundational cryptographic primitive of HSS, and the related object of Function Secret Sharing (FSS).
- Constructions of Pseudorandom Correlation Generators and extended tools, for new useful correlations, and with better efficiency and security properties.
- New compliers for secure computation protocols converting from security against weak "passive" adversaries to stronger security against "active" or "malicious" adversaries.
- Low-communication secure protocols for important tasks, ranging from the core of Byzantine consensus and targeted protocols for specific concrete tasks, to general results for arbitrary efficient computations.
Within each direction, the Project HSS team had multiple research papers appearing in top-tier peer-reviewed scientific venues. Collectively, these advances have resulted in new protocols achieving state-of-the-art efficiency for secure computation, and have strong indications for even greater future gains.

In the period continuing from now to the end of the project, we expect further significant advances along these paths as well as new approaches forward. This includes goals of the following kind:
- Developing the next generation of HSS and PCG constructions, including new understanding of feasibility.
- Deep exploration of breaking the "circuit-size" barrier for secure computation, including new protocol construction approaches with communication complexity that is asymptotically sublinear in the computation circuit size.
- Further understanding of the required communication complexity of multi-party Byzantine consensus and other robust distributed protocols.
- New asymptotically and concretely efficient protocols and compilers for strong malicious security, which beat the state-of-the-art approaches to the extent that they become the primary standard.
- New protocols and lower bounds for feasibility of topology-hiding computation, as well as applications to broader settings of secure computation.