Cryptographic Foundation for Secure and Scalable Distributed Systems

Project Information

CRYPTOSYSTEMS

Grant agreement ID: 101116713

DOI

10.3030/101116713

EC signature date 22 August 2023

Start date 1 September 2023

End date 31 August 2028

Funded under

• European Research Council (ERC)

Total cost

€ 1 416 204,00

EU contribution

€ 1 416 204,00

Coordinated by

RUHR-UNIVERSITAET BOCHUM
Germany

Periodic Reporting for period 1 - CRYPTOSYSTEMS (Cryptographic Foundation for Secure and Scalable Distributed Systems)

Reporting period: 2023-09-01 to 2026-02-28

Summary of the context and overall objectives of the project

Many of today’s critical infrastructures, such as power grids or cellular networks, are distributed systems which are
comprised of autonomous nodes connected over a peer-to-peer network. A central goal in distributed computing is
to implement such systems in a fault-tolerant manner to avoid single points of failure. Fault-tolerant systems remain
secure and available even if some minority of nodes crashes or spreads incorrect information.
Distributed systems frequently rely on cryptography, which has proven a powerful tool for robustness and scalability.
However, despite its benefits, cryptography can incur performance penalties or lead to vulnerabilities when not
used cautiously. Both of these aspects significantly complicate its use in practice. As a result, many real-world
systems use cryptography sparingly, thus lacking robustness and scalability. Using cutting-edge cryptography,
CRYPTOSYSTEMS will significantly advance the resilience and efficiency of distributed algorithms at the heart
of many distributed systems. The objectives are as follows: (i) Develop and explore formal security models for
cryptographic distributed algorithms that accurately reflect real-world threats. (ii) Apply cryptography to design robust
and scalable distributed algorithms that tolerate the theoretical limits of faults. (iii) Develop novel cryptography, such
as compact signatures and communication-efficient distributed randomness generation routines to boost the efficiency
and security of distributed algorithms.
These innovations will provide a major step toward the wide-scale deployment of secure and scalable distributed
infrastructures.

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

CRYPTOSYSTEMS addresses three main challenges that revolve around improving the robustness and scalability of distributed systems using cutting-edge cryptography: (i) laying theoretical foundations for distributed algorithms using cryptography. This includes refining classical models used in the are of distributed algorithm as well as proposing entirely new ones in order to capture unaddressed issues in existing models. These challenges are addressed in WP1. (ii) designing novel algorithms for important distributed tasks such as consensus and clock synchronisation with improved scalability and robustness by leveraging cryptography. These challenges are addressed in WP2. (iii) designing novel cryptographic tools such as threshold signatures and threshold secret sharing schemes that can be used in distributed algorithms for various important tasks, in particular for generating shared randomness. These challenges are addressed in WP3.
In the following, I will summarise the progress made so far for each of these objectives.
Objective 1: New Formal Models. I have made significant progress in exploring feasibility of distributed algorithms in new fault models. Importantly, I have published two papers dealing with a generalised fault model that distinguishes two important types of benign faults from fully malicious ones. In more detail, my works consider so-called omission faults for which an attacker can selectively delete incoming or outgoing messages. These faults are simultaneously very realistic and hard to deal with, as they may keep participating with faulty behaviour in an algorithm over an extended period of time. In two works, I present algorithms with optimal fault tolerance in a model where both benign and fully malicious faults may appear. These works have appeared at TCC 2023 and TCC 2024, respectively.
Objective 2: Efficient and Robust Distributed Algorithms. Several works of mine have improved on the efficiency and robustness of distributed algorithms for variants of consensus. On one hand, I have published several works (1x FC 2024, 2x CRYPTO 2025) that significantly improve the communication, i.e. the number of bits that parties need to exchange in order to reach consensus. w in protocols for consensus. I have also shown how to improve the time complexity, i.e. the number of communication steps of consensus algorithms for the challenging setting where a majority of the parties can be corrupted. These works have appeared at EUROCRYPT 2024 and SODA 2025, respectively.
Objective 3: Cryptography for Scalable Shared Randomness. Several of my works have improved the state of the art in efficiency and robustness for important cryptographic tools related to consensus such as randomness generation (CCS 2023, CCS 2024) and jointly computing a compact signature on a message (EUROCRYPT 2024, CCS 2024, ASIACRYPT 2024, EUROCRYPT 2025, CRYPTO 2025). These works have advanced the field significantly and have produced several followup works by other researchers, as well as ongoing follow up projects that I am currently working on.

The results listed under Objective 1 required novel insights relating to self detection of omission faulty nodes. Thereafter, such a node can discontinue participating in the protocol so as to not cause further harm to parties that remain honest in the protocol.
The results listed under Objective 2 related to communication complexity involve novel techniques that are based on expander graphs as well as improved algorithms for gossiping information efficiently. Moreover, the results related to round efficiency under dishonest majority involved a translation of techniques of the honest majority setting that required novel technical insights into the problem.
For the results listed under Objective 3, several new techniques were developed to deal with an adaptive adversary that dynamically corrupts participating protocol parties based on the flow of the protocol execution. Moreover, the results related to shared randomness generation required novel definitions and proof techniques for Publicly Verifiable Secret Sharing (PVSS) that may be of independent interest.

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 five most significant achievements are the following publications: (a) Early stopping for any number of Corruptions (EUROCRYPT 2024), (b) GRandLine: Adaptively Secure DKG and Randomness Beacon with (Log-)Quadratic Communication Complexity (CCS 2024), (c) Sublinear-Round Broadcast without Trusted Setup (SODA 2025), (d) Nearly Optimal Parallel Broadcast in the Plain Public Key Model (CRYPTO 2025), (e) Leader Election with Poly-Logarithmic Communication Per Party (CRYPTO 2025).
I consider (a) and (b) breakthroughs, as they both solve long-standing open questions in their respective domains. (a) gives the first consensus protocol that terminates in a number of rounds proportional to the actual number of byzantine parties in a given execution. Prior works achieving this guarantee (called early stopping) only existed for up to half of parties being faulty. (b) also achieves a major breakthrough for the problem of distributed key generation (DKG). DKG is the problem of multiple parties agreeing on a shared key so that only a sufficiently large subset of share holders can reconstruct it. My paper shows, for the first time, how DKG can be obtained within a quadratic number of bits in the number of parties even against an adaptive adversary.

Taken together, the work I have achieved so far already has pushed the state of the field forward considerably. I believe that given the remainder of the duration of the project, even more high-impact and pivotal results like the above will be likely.