Good Gottesman-Kitaev-Preskill codes from the NTRU cryptosystem

作     者：Conrad, Jonathan Eisert, Jens Seifert, Jean Pierre 

作者机构：Dahlem Center for Complex Quantum Systems Physics Department Freie Universität Berlin Arnimallee 14 Berlin14195 Germany Helmholtz-Zentrum Berlin für Materialien und Energie Hahn-Meitner-Platz 1 Berlin14109 Germany Fraunhofer Heinrich Hertz Institute Einsteinufer 37 Berlin10587 Germany Electrical Engineering and Computer Science Department Technische Universität Berlin Straße des 17. Juni 135 Berlin10587 Germany Fraunhofer Institute for Secure Information Technology Rheinstraße 75 Darmstadt64295 Germany 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2023年

核心收录：

主　　题：Stochastic systems 

摘      要：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 ∆ ∝ √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. © 2023, CC BY.