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Paper 1

Post-Quantum and Code-Based Cryptography—Some Prospective Research Directions

Chithralekha Balamurugan, Kalpana Singh, Ganeshvani Ganesan, Muttukrishnan Rajarajan

Year

2021

Journal

Cryptography

DOI

10.3390/cryptography5040038

arXiv

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Cryptography has been used from time immemorial for preserving the confidentiality of data/information in storage or transit. Thus, cryptography research has also been evolving from the classical Caesar cipher to the modern cryptosystems, based on modular arithmetic to the contemporary cryptosystems based on quantum computing. The emergence of quantum computing poses a major threat to the modern cryptosystems based on modular arithmetic, whereby even the computationally hard problems which constitute the strength of the modular arithmetic ciphers could be solved in polynomial time. This threat triggered post-quantum cryptography research to design and develop post-quantum algorithms that can withstand quantum computing attacks. This paper provides an overview of the various research directions that have been explored in post-quantum cryptography and, specifically, the various code-based cryptography research dimensions that have been explored. Some potential research directions that are yet to be explored in code-based cryptography research from the perspective of codes is a key contribution of this paper.

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Paper 2

Qubit-oscillator concatenated codes: decoding formalism & code comparison

Yijia Xu, Yixu Wang, En-Jui Kuo, Victor V. Albert

Year

2022

Journal

arXiv preprint

DOI

arXiv:2209.04573

arXiv

2209.04573

Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given there are several bosonic codes and concatenation schemes to choose from, including the recently discovered GKP-stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)}] that allow protection of a logical bosonic mode from fluctuations of the mode's conjugate variables. We develop efficient maximum-likelihood decoders for and analyze the performance of three different concatenations of codes taken from the following set: qubit stabilizer codes, analog/Gaussian stabilizer codes, GKP codes, and GKP-stabilizer codes. We benchmark decoder performance against additive Gaussian white noise, corroborating our numerics with analytical calculations. We observe that the concatenation involving GKP-stabilizer codes outperforms the more conventional concatenation of a qubit stabilizer code with a GKP code in some cases. We also propose a GKP-stabilizer code that suppresses fluctuations in both conjugate variables without extra quadrature squeezing, and formulate qudit versions of GKP-stabilizer codes.

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