Recent progress on the elliptic curve discrete logarithm problem

SD Galbraith, P Gaudry - Designs, Codes and Cryptography, 2016 - Springer
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Complementary dual algebraic geometry codes

S Mesnager, C Tang, Y Qi - IEEE Transactions on Information …, 2017 - ieeexplore.ieee.org
Linear complementary dual (LCD) codes are a class of linear codes introduced by Massey
in 1964. LCD codes have been extensively studied in literature recently. In addition to their …

New constructions of MDS symbol-pair codes

B Ding, G Ge, J Zhang, T Zhang, Y Zhang - Designs, Codes and …, 2018 - Springer
Motivated by the application of high-density data storage technologies, symbol-pair codes
are proposed to protect against pair-errors in symbol-pair channels, whose outputs are …

ECC2: Error correcting code and elliptic curve based cryptosystem

F Zhang, Z Zhang, P Guan - Information Sciences, 2020 - Elsevier
Code-based cryptography has aroused wide public concern as one of the main candidates
for post quantum cryptography to resist attacks against cryptosystems from quantum …

[PDF][PDF] Counting subset sums of finite abelian groups

J Li, D Wan - Journal of Combinatorial Theory, Series A, 2012 - core.ac.uk
Counting subset sums of finite abelian groups Page 1 Journal of Combinatorial Theory, Series A
119 (2012) 170–182 Contents lists available at ScienceDirect Journal of Combinatorial Theory …

On the equivalence of two post-quantum cryptographic families

A Meneghetti, A Pellegrini, M Sala - Annali di Matematica Pura ed …, 2023 - Springer
The maximum likelihood decoding problem (MLD) is known to be NP-hard and its
complexity is strictly related to the security of some post-quantum cryptosystems, that is, the …

[PDF][PDF] A post-quantum digital signature scheme from QC-LDPC codes

A Meneghetti, C Picozzi, G Tognolini - IACR Cryptology ePrint …, 2022 - iacr.steepath.eu
We propose a novel post-quantum code-based digital signature algorithm whose security is
based on the difficulty of decoding Quasi-Cyclic codes in systematic form, and whose …

NP-Hardness of Reed--Solomon Decoding, and the Prouhet--Tarry--Escott Problem

V Gandikota, B Ghazi, E Grigorescu - SIAM Journal on Computing, 2018 - SIAM
Establishing the complexity of bounded distance decoding for Reed--Solomon codes is a
fundamental open problem in coding theory, explicitly asked by Guruswami and Vardy IEEE …

Improved Lower Bounds for Approximating Parameterized Nearest Codeword and Related Problems under ETH

S Li, B Lin, Y Liu - arxiv preprint arxiv:2402.09825, 2024 - arxiv.org
In this paper we present a new gap-creating randomized self-reduction for parameterized
Maximum Likelihood Decoding problem over $\mathbb {F} _p $($ k $-MLD $ _p $). The …

On Deep Holes of Elliptic Curve Codes

J Zhang, D Wan - IEEE Transactions on Information Theory, 2023 - ieeexplore.ieee.org
We give a method to construct deep holes for elliptic curve codes. For long elliptic curve
codes, we conjecture that our construction is complete in the sense that it gives all deep …