Draft:Hamming Quasi-Cyclic
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Comment: Please do not use Wikipedia to advertise research results. The topic appears to have been introduced in 2018 but I do not believe that sufficient time has passed to ensure that the topic is generally notable and has been more broadly reported on. Caleb Stanford (talk) 02:03, 5 June 2025 (UTC)
HQC (Hamming Quasi-Cyclic) is a key encapsulation mechanism (KEM) designed to be resistant to cryptanalytic attacks with future powerful quantum computers. It is used to establish a shared secret between two communicating parties without an (IND-CCA2) attacker in the transmission system being able to decrypt it. This asymmetric cryptosystem is based on code-based cryptography. More specifically, HQC was created in 2016 in the continuity of Alekhnovich's idea of 2003 [1]
. It was chosen as an alternative to Kyber alternative in the NIST competition for post-quantum cryptography standard.[2]
Scheme definition
[edit]HQC consists of four polynomial-time algorithms: a setup which ouputs the global parameters, a key generation algorithm, the encryption algorithm and the decryption algorithm.[3]
Roughly, the idea behind this public-key cryptosystem is to encode a message to a codeword, and use the public key to add errors such that it can't be decoded easily. The secret key is thus applied to remove enough error such that it can be decoded.
As opposed to cryptosystems like RSA or ECC, the decoding of the ciphertext is correct with a certain probability named DFR (Decoding Failure Rate). In the general case, HQC uses two codes, the first one being a random quasi-cyclic code while the second one can be any code.[4] However, the choice of the codes used greatly changes the DFR and the length of the ciphertext.[5]
The submission to the NIST competition is using a concatenated error correction code of an internal code, a Reed-Muller code and an external code, a duplicated Reed–Solomon error correction.
References
[edit]- ^ Efficient Encryption from Random Quasi-Cyclic Codes
- ^ "NIST Selects HQC as Fifth Algorithm for Post-Quantum Encryption", NIST, 11 March 2025
- ^ HQC specification
- ^ Aguilar-Melchor, Carlos; Blazy, Olivier; Deneuville, Jean-Christophe; Gaborit, Philippe; Zemor, Gilles (2018), "Efficient Encryption from Random Quasi-Cyclic Codes", IEEE Transactions on Information Theory, 64 (5): 3927–3943, arXiv:1612.05572, doi:10.1109/TIT.2018.2804444
- ^ Aguilar-Melchor, Carlos; Aragon, Nicolas; Deneuville, Jean-Christophe; Gaborit, Philippe; Lacan, Jérôme; Zémor, Gilles (2024), "Efficient error-correcting codes for the HQC post-quantum cryptosystem", Designs, Codes and Cryptography, 92 (12): 4511–4530, doi:10.1007/s10623-024-01507-6