Improving ENUM-Sieve Reduction Algorithm for Prime Cyclotomic Lattices

Kazutaka Toda¹, Yuntao Wang^1,*, Hyungrok Jo², Yang Li¹
1 Graduate School of Informatics and Engineering, The University of Electro-Communications, Tokyo, Japan
2 Institute of Advanced Sciences, Yokohama National University, Yokohama, Kanagawa, Japan
* Corresponding Author: Yuntao Wang. Email: email
(This article belongs to the Special Issue: Advanced Security and Privacy for Future Mobile Internet and Convergence Applications: A Computer Modeling Approach)

Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2026.083407

Received 03 April 2026; Accepted 22 June 2026; Published online 16 July 2026

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Abstract

The rapid evolution of quantum computing poses a fundamental challenge to classical public-key cryptosystems, accelerating the adoption of lattice-based post-quantum cryptography in large-scale digital infrastructures, including Future Mobile Internet Technologies (FMIT) and their convergence applications (FMIT-CA). As lattice-based cryptography is expected to play an important role in such environments, accurate hardness estimation and parameter assessment of underlying lattice problems have become increasingly important. Since the security of these cryptographic schemes is closely related to the computational hardness of the Shortest Vector Problem (SVP), improving practical SVP-solving techniques contributes indirectly to the security evaluation of such systems. Among practical SVP solvers, sieve-based approaches such as the General Sieve Kernel (G6K) achieve state-of-the-art performance, yet their exponential complexity and resource demands constrain scalability in high-dimensional settings. In this work, we propose an improved version of the hybrid algorithm ENUM-Sieve Reduction (ESR) proposed by Toda et al. in ProvSec 2025. We refer to our proposal as ENUM-Sieve Reduction 2.0 (ESR 2.0). It integrates Block Korkine-Zolotarev 2.0 (BKZ 2.0) and extreme-pruning enumeration into the reduction pipeline and introduces a unimodular-matrix-based strategy for partial basis generation. Experimental results suggest that these enhancements enable stronger parameter configurations and more efficient execution in higher dimensions under realistic computational constraints. Experimental evaluations on prime cyclotomic ideal lattices demonstrate the practical usefulness of ESR 2.0 produces vectors equal to or shorter than those obtained by G6K in 75% of the tested instances for dimensions ranging from 96 to 130. Compared with ESR, ESR 2.0 achieves the same or shorter vectors in 62.5% of the tested instances. Although ESR 2.0 requires longer CPU time due to additional enumeration steps, GPU time and peak memory usage remain comparable to those of G6K and ESR. Furthermore, ESR 2.0 renewed record norms in the TU Darmstadt Ideal Lattice Challenge for dimensions 112, 126, 136, 148 and 156. These results indicate the usability of ESR 2.0, providing a competitive and practical framework for high-dimensional SVP solving. The proposed improvements contribute to a more accurate assessment of lattice hardness, which is essential for secure parameter selection in post-quantum cryptographic systems supporting future mobile and converged digital environments.