Master Thesis
Analysis of a Threshold Variant of the HQC Cryptosystem
The development of quantum computers threatens classical public-key cryptosystems such as RSA and elliptic-curve systems. To address this issue, the National Institute of Standards and Technology (NIST) has initiated a standardization project for post-quantum cryptography (PQC) [1] to evaluate candidates that are resistant to attacks supported by both classical and quantum computers. One of the selected schemes is the Hamming Quasi-Cyclic (HQC) [2] cryptosystem, whose security is based on the Quasi-Cyclic Syndrome Decoding (QCSD) problem.
In parallel, there is an increasing interest in threshold cryptography for PQC schemes. Threshold cryptography adds security and reliability to conventional cryptographic primitives by eliminating any single points of failure and by distributing trust among multiple parties. Due to such advantages of threshold techniques, NIST has initiated a Threshold Cryptography Project [3].
In a threshold public key encryption scheme, a secret key is distributed among multiple parties so that at least a threshold number t of participants are needed to cooperate for decrypting a given ciphertext. The theoretical foundation of such distributed systems is provided by Multi-Party Computation (MPC). MPC enables multiple parties, each with their own private data, to jointly perform a computation without disclosing their individual private data. Recently, Giorgi et al. [4] have combined these ideas by applying secure distributed decoding techniques to HQC, enabling threshold decryption without revealing the secret key.
As a first step of this thesis, the goal is to understand the basics of coding theory, MPC, and the HQC system. Based on this, the goal is to develop a technical understanding of threshold decryption for HQC based on the literature.
References
[1] Post-Quantum Cryptography Project
[2] Hamming Quasi-Cyclic (HQC)
[3] NIST First Call for Multi-Party Threshold Schemes
[4] Constant-Round Secure Distributed Decoding and HQC Threshold Decryption