Current browse context:
quant-ph
Change to browse by:
References & Citations
Quantum Physics
Title: Good Gottesman-Kitaev-Preskill codes from the NTRU cryptosystem
(Submitted on 4 Mar 2023 (v1), last revised 26 Apr 2024 (this version, v3))
Abstract: We introduce a new class of random Gottesman-Kitaev-Preskill (GKP) codes derived from the cryptanalysis of the so-called NTRU cryptosystem. The derived codes are good in that they exhibit constant rate and average distance scaling $\Delta \propto \sqrt{n}$ with high probability, where $n$ is the number of bosonic modes, which is a distance scaling equivalent to that of a GKP code obtained by concatenating single mode GKP codes into a qubit-quantum error correcting code with linear distance. The derived class of NTRU-GKP codes has the additional property that decoding for a stochastic displacement noise model is equivalent to decrypting the NTRU cryptosystem, such that every random instance of the code naturally comes with an efficient decoder. This construction highlights how the GKP code bridges aspects of classical error correction, quantum error correction as well as post-quantum cryptography. We underscore this connection by discussing the computational hardness of decoding GKP codes and propose, as a new application, a simple public key quantum communication protocol with security inherited from the NTRU cryptosystem.
Submission history
From: Jonathan Conrad [view email][v1] Sat, 4 Mar 2023 14:39:20 GMT (951kb,D)
[v2] Mon, 10 Apr 2023 15:14:38 GMT (908kb,D)
[v3] Fri, 26 Apr 2024 10:33:04 GMT (911kb,D)
Link back to: arXiv, form interface, contact.