Connecting Symmetric and Asymmetric Cryptography for Leakage and Faults

Project Information

BRIDGE

Grant agreement ID: 101096871

DOI

10.3030/101096871

EC signature date 2 May 2023

Start date 1 September 2023

End date 31 August 2028

Funded under

• European Research Council (ERC)

Total cost

€ 2 499 560,00

EU contribution

€ 2 499 560,00

Coordinated by

UNIVERSITE CATHOLIQUE DE LOUVAIN
Belgium

Periodic Reporting for period 1 - BRIDGE (Connecting Symmetric and Asymmetric Cryptography for Leakage and Faults)

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

Summary of the context and overall objectives of the project

Symmetric & asymmetric cryptography offer the basic functionalities needed to communicate securely over a channel. Due to their different features and the different algebraic structures they exploit, the interaction between the design of these primitives and the security of their implementation against side-channel & fault attacks so far followed somewhat separated paths. Based on the observation that (i) many emerging challenges for the implementation security of symmetric & asymmetric primitives share similarities and would highly benefit from a more connected approach, and (ii) this is especially true when considering post-quantum asymmetric encryption schemes that include symmetric components and for which current designs are extremely challenging to protect against side-channel & faults attacks, the BRIDGE project aims to develop a unified treatment of symmetric & asymmetric cryptography by leveraging three innovative movements. First, we aim to export the concept of leveled implementation (where different parts of a primitive are protected with countermeasures of varying cost) from symmetric cryptography towards new post-quantum asymmetric schemes that inherently take implementation security as a design criteria. Second, we aim to export the use of larger (possibly prime) fields and more complex algebraic structures used in asymmetric cryptography to deliver advanced functionalities towards new symmetric schemes that guarantee security against side-channel & fault attacks in low-noise contexts that raise fundamental challenges for existing countermeasures. Third, we aim to exploit hard physical learning problems as radically new building blocks applicable to both types of primitives. By combining these movements, we aim to identify disruptive approaches to build new cryptographic schemes offering a better integration between symmetric & asymmetric designs and improvements of their implementation security by orders of magnitude.

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

The BRIDGE project has produced a suite of cryptographic primitives and evaluation tools that offer significant improvements in implementation security. Several bridges between symmetric cryptography and asymmetric cryptography have been investigated and it is expected that these progresses will be further amplified in the rest of the project. Most of these results have been published in the best venues for cryptographic research.

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)

Related to the aforementioned progresses, we introduced several novel methodologies that advance the state of the art in cryptographic design and evaluation, particularly in the context of physical security and post-quantum cryptography. We outline them next.
A key methodological innovation is the concept of levelled implementations that had been applied in symmetric cryptography in the past. It allows different parts of a cryptographic primitive to be protected with countermeasures of varying cost and strength. This approach was extended from symmetric to asymmetric designs, enabling more efficient and tailored protection strategies.
Another major contribution is the development of hard physical learning problems (e.g. Learning With Physical Rounding), which offer a new paradigm for building cryptographic primitives that inherently resist side-channel attacks. These methodologies bridge physical leakage models with mathematical hardness assumptions, opening new directions for secure design. Results on this topic is still in an early stage, but we expect reductions to standard problems by the end of the project.
In the domain of evaluation, we introduced the Training Information (TI) metric, which provides a fast-converging and reliable bound on the information leakage of an implementation. This metric supports extrapolation from small datasets and enables sound security claims even in constrained evaluation settings. It complements traditional metrics like Mutual Information and Perceived Information and has been validated both theoretically and empirically.
As for inter-disciplinary Developments, BRIDGE operates at the intersection of cryptography, hardware design, statistical learning, and formal verification. The project has leveraged techniques from machine learning (e.g. convergence analysis of profiling models), signal processing (e.g. leakage modelling), and microelectronics (e.g. hardware implementations) to inform cryptographic design. The project also explored connections with privacy-preserving technologies through a contribution on leakage-resilient garbled circuits.
Regarding knowledge and technology transfer finally, BRIDGE has primarily contributed to the broader cryptographic ecosystem through publications and collaborations with academic and industrial partners. Despite not yet completed, it is expected that several implementations developed during the project will be released as open-source prototypes and maintained through the SIMPLE-Crypto association (https://www.simple-crypto.org). This initiative will ensure long-term accessibility and usability of the project's outputs.

High-level vision and goals of the BRIDGE project