Classic McEliece Implementation with Low Memory Footprint

The Classic McEliece cryptosystem is one of the most trusted quantum-resistant cryptographic schemes. Deploying it in practical applications, however, is challenging due to the size of its public key. In this work, we bridge this gap. We present an implementation of Classic McEliece on an ARM Cortex-M4 processor, optimized to overcome memory constraints. To this end, we present an algorithm to retrieve the public key ad-hoc. This reduces memory and storage requirements and enables the generation of larger key pairs on the device. To further improve the implementation, we perform the public key operation by streaming the key to avoid storing it as a whole. This additionally reduces the risk of denial of service attacks. Finally, we use these results to implement and run TLS on the embedded device

Enhancing Code Based Zero-knowledge Proofs using Rank Metric

The advent of quantum computers is a threat to most currently deployed cryptographic primitives. Among these, zero-knowledge proofs play an important role, due to their numerous applications. The primitives and protocols presented in this work base their security on the difficulty of solving the Rank Syndrome Decoding (RSD) problem. This problem is believed to be hard even in the quantum model. We first present a perfectly binding commitment scheme. Using this scheme, we are able to build an interactive zero-knowledge proof to prove: the knowledge of a valid opening of a committed value, and that the valid openings of three committed values satisfy a given linear relation, and, more generally, any bitwise relation. With the above protocols it becomes possible to prove the relation of two committed values for an arbitrary circuit, with quasi-linear communication complexity and a soundness error of 2/3. To our knowledge, this is the first quantum resistant zero-knowledge protocol for arbitrary circuits based on the RSD problem. An important contribution of this work is the selection of a set of parameters, and an a full implementation, both for our proposal in the rank metric and for the original LPN based one by Jain et. al in the Hamming metric, from which we took the inspiration. Beside demonstrating the practicality of both constructions, we provide evidence of the convenience of rank metric, by reporting performance benchmarks and a detailed comparison