Selected work

Representative Papers

Constant-time decoding of Gabidulin codes and their generalizations with application to RQC

Jul 22, 2026

This work addresses a critical gap in rank-metric cryptography: the absence of constant-time decoding implementations for Gabidulin codes, which renders schemes like RQC vulnerable to side-channel attacks. The paper presents the first constant-time decoding algorithm for augmented Gabidulin (AG) codes, achieving quadratic time complexity by introducing zero-column-extended Gabidulin codes and a constant-time q-polynomial left division technique. This approach is integrated into a new variant, RQC-Block-MS-AG, which maintains ciphertext and key sizes approximately one-quarter those of HQC while outperforming the original RQC in efficiency. Although roughly four times slower than HQC, the proposed scheme significantly improves the trade-off between security and practicality, thereby filling a key void in secure implementations of rank-metric cryptosystems.

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Advancing RT Core-Accelerated Fixed-Radius Nearest Neighbor Search

Jan 22, 2026

This work addresses the challenges posed by dynamic scenes, memory constraints, and periodic boundary conditions in fixed-radius nearest neighbor (FRNN) searches for particle physics simulations. To overcome these limitations, the authors propose an efficient RT Core–accelerated FRNN method that incorporates real-time BVH update and reconstruction strategies, eliminates reliance on traditional neighbor lists, and introduces novel support for periodic boundary conditions directly within the RT Core pipeline. This approach significantly broadens the applicability and energy efficiency of hardware-accelerated FRNN. Experimental results on the Lennard-Jones model demonstrate up to a 3.4× speedup in the RT Core pipeline and a 1.3–2.0× improvement in per-step simulation performance, while successfully enabling large-scale, non-uniform particle systems that previously failed due to insufficient memory.

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(2,2)-GB Codes: Classification and Comparison with weight-4 Surface Codes

Jul 28, 2025

This work addresses the systematic classification and quantum error-correcting performance evaluation of (2,2)-generalized bicycle (GB) codes. Challenging the conventional belief that even-distance (2,2)-GB codes cannot exist, we propose an algebraic construction framework based on binary circulant matrix pairs and Cayley graphs, and introduce a CSS-structure-preserving equivalence relation to enable precise code-family partitioning. We construct, for the first time, three optimal infinite families: [[2n², 2, n]], [[4r², 2, 2r]], and [[(2t+1)²+1, 2, 2t+1]], all achieving the theoretical distance bound. Additionally, we complete the full classification of extremal non-equivalent (2,2)-GB codes of length less than 200. A systematic comparison with weight-4 surface codes demonstrates that our new families significantly outperform existing constructions in the encoding rate–distance trade-off, thereby overcoming longstanding construction bottlenecks.

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Computing in complete local equicharacteristic Noetherian rings via topological rewriting on commutative formal power series

Jul 05, 2025

This paper addresses computational challenges concerning non-finitely generated ideals in complete local equicharacteristic Noetherian rings—particularly formal power series rings—where classical Gröbner basis theory fails. Method: It introduces, for the first time, purely topological rewriting tools into standard basis theory, integrating generalized confluence analysis, standard basis algorithms over formal power series rings, and algebraic techniques including the Cohen Structure Theorem. Contribution/Results: The work rigorously reconstructs and proves a generalized confluence characterization of standard bases; establishes, for the first time, logical equivalence between two distinct notions of generalized confluence in formal power series rings; and thereby constructs a unified computational framework applicable to non-finitely generated ideals. This significantly extends both the scope and theoretical depth of Gröbner-type theories, bridging standard basis theory with topological rewriting theory through a profound structural analogy.

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On the Generalization of Kitaev Codes as Generalized Bicycle Codes

Apr 25, 2025

This work addresses the high physical resource overhead and low encoding efficiency in quantum error correction by proposing a novel class of generalized bicycle (GB) codes. Methodologically, it introduces a unified framework based on pairs of binary circulant matrices with exactly two non-zero entries per row/column, systematically generalizing both standard and optimized Kitaev toric codes; this enables the first rigorous construction and analysis of such codes, establishing a strict lower bound of minimum distance ≥ √n. The approach yields 21 GB codes of length < 200, including 14 previously unknown constructions; among these, three new codes achieve distances 4, 8, and 12—surpassing all known weight-4 GB codes and setting new records. Results demonstrate that the proposed GB codes simultaneously attain higher code rates, stronger fault-tolerance capabilities, and reduced physical qubit requirements, thereby significantly improving quantum hardware resource efficiency.

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Recent publications

Latest Papers

Constant-time decoding of Gabidulin codes and their generalizations with application to RQC

Jul 22, 2026

This work addresses a critical gap in rank-metric cryptography: the absence of constant-time decoding implementations for Gabidulin codes, which renders schemes like RQC vulnerable to side-channel attacks. The paper presents the first constant-time decoding algorithm for augmented Gabidulin (AG) codes, achieving quadratic time complexity by introducing zero-column-extended Gabidulin codes and a constant-time q-polynomial left division technique. This approach is integrated into a new variant, RQC-Block-MS-AG, which maintains ciphertext and key sizes approximately one-quarter those of HQC while outperforming the original RQC in efficiency. Although roughly four times slower than HQC, the proposed scheme significantly improves the trade-off between security and practicality, thereby filling a key void in secure implementations of rank-metric cryptosystems.

0 citationsRead paper

Advancing RT Core-Accelerated Fixed-Radius Nearest Neighbor Search

Jan 22, 2026

This work addresses the challenges posed by dynamic scenes, memory constraints, and periodic boundary conditions in fixed-radius nearest neighbor (FRNN) searches for particle physics simulations. To overcome these limitations, the authors propose an efficient RT Core–accelerated FRNN method that incorporates real-time BVH update and reconstruction strategies, eliminates reliance on traditional neighbor lists, and introduces novel support for periodic boundary conditions directly within the RT Core pipeline. This approach significantly broadens the applicability and energy efficiency of hardware-accelerated FRNN. Experimental results on the Lennard-Jones model demonstrate up to a 3.4× speedup in the RT Core pipeline and a 1.3–2.0× improvement in per-step simulation performance, while successfully enabling large-scale, non-uniform particle systems that previously failed due to insufficient memory.

0 citationsRead paper

(2,2)-GB Codes: Classification and Comparison with weight-4 Surface Codes

Jul 28, 2025

This work addresses the systematic classification and quantum error-correcting performance evaluation of (2,2)-generalized bicycle (GB) codes. Challenging the conventional belief that even-distance (2,2)-GB codes cannot exist, we propose an algebraic construction framework based on binary circulant matrix pairs and Cayley graphs, and introduce a CSS-structure-preserving equivalence relation to enable precise code-family partitioning. We construct, for the first time, three optimal infinite families: [[2n², 2, n]], [[4r², 2, 2r]], and [[(2t+1)²+1, 2, 2t+1]], all achieving the theoretical distance bound. Additionally, we complete the full classification of extremal non-equivalent (2,2)-GB codes of length less than 200. A systematic comparison with weight-4 surface codes demonstrates that our new families significantly outperform existing constructions in the encoding rate–distance trade-off, thereby overcoming longstanding construction bottlenecks.

0 citationsRead paper

Computing in complete local equicharacteristic Noetherian rings via topological rewriting on commutative formal power series

Jul 05, 2025

This paper addresses computational challenges concerning non-finitely generated ideals in complete local equicharacteristic Noetherian rings—particularly formal power series rings—where classical Gröbner basis theory fails. Method: It introduces, for the first time, purely topological rewriting tools into standard basis theory, integrating generalized confluence analysis, standard basis algorithms over formal power series rings, and algebraic techniques including the Cohen Structure Theorem. Contribution/Results: The work rigorously reconstructs and proves a generalized confluence characterization of standard bases; establishes, for the first time, logical equivalence between two distinct notions of generalized confluence in formal power series rings; and thereby constructs a unified computational framework applicable to non-finitely generated ideals. This significantly extends both the scope and theoretical depth of Gröbner-type theories, bridging standard basis theory with topological rewriting theory through a profound structural analogy.

0 citationsRead paper

On the Generalization of Kitaev Codes as Generalized Bicycle Codes

Apr 25, 2025

This work addresses the high physical resource overhead and low encoding efficiency in quantum error correction by proposing a novel class of generalized bicycle (GB) codes. Methodologically, it introduces a unified framework based on pairs of binary circulant matrices with exactly two non-zero entries per row/column, systematically generalizing both standard and optimized Kitaev toric codes; this enables the first rigorous construction and analysis of such codes, establishing a strict lower bound of minimum distance ≥ √n. The approach yields 21 GB codes of length < 200, including 14 previously unknown constructions; among these, three new codes achieve distances 4, 8, and 12—surpassing all known weight-4 GB codes and setting new records. Results demonstrate that the proposed GB codes simultaneously attain higher code rates, stronger fault-tolerance capabilities, and reduced physical qubit requirements, thereby significantly improving quantum hardware resource efficiency.

0 citationsRead paper