RELATE

Post-quantum cryptosystems are developed and standardized to be resistant against quantum computers. After a selection process that started in 2017, NIST unveiled in 2022 and 2025 its initial set of post-quantum standards, with three out of the five selected schemes being lattice-based. Hence, it is fair to say that lattice-based cryptography is among the leading mathematical families in the field of post-quantum cryptography. While the security foundations of lattice-based cryptography are well-explored, real-world deployments can introduce new vulnerabilities. Side-channel analysis (SCA) capitalizes on the physical characteristics of a device (e.g., power consumption, electromagnetic, or acoustic emissions) to compromise sensitive data. Fortunately, two complementary countermeasures bolster the resilience of deployed cryptography in adversarial settings. Masking distributes trust within a single device, while threshold cryptography extends trust across multiple devices. Masking shields cryptographic schemes from SCA, while thresholdization safeguards against complete device failure or compromise. Regrettably, the future standards have poor compatibility with these techniques: masking significantly increases their running time, and thresholdizing them ends up in extremely contrived and inefficient schemes. As a consequence, these standards are brittle when deployed in the wild. The goal of the RELATE project is to end this status quo by devising and implementing lattice-based schemes that can efficiently be masked and thresholdized. By making masking and thresholdizing friendliness a design criteria from the very beginning, we expect to obtain better security-efficiency trade-offs than adding them a-posteriori. Thanks to their mathematical proximity, these techniques will be studied together. In addition, solutions for one technique can often be transposed to the other. Finally, zero-knowledge proofs (ZKP) will be essential tools in our strategy. Indeed, ZKP can enforce some assumptions about the parties involved, which considerably simplifies masking and thresholdizing. Concrete outcomes will be efficient implementations of lattice cryptosystems with stronger side-channel countermeasures (masking), and implementations of lattice threshold cryptosystems. We will submit these innovative schemes to the upcoming NIST multi-party threshold cryptography (MPTC) call, with the aspiration of fortifying the future of lattice-based cryptographic standards. This industrial research project brings together theoretical cryptographers who seek to tackle challenging open research problems, and industrial experts who seek to increase the resilience, security and performance of their products. The academic partner is the LIRMM laboratory (Université de Montpellier). The industrial partners are PQShield SAS (Paris) and CryptoExperts (Paris).