Post Quantum Computing Cryptography Key Generation: An Lenstra-Lenstra-Lovasz (LLL) Approach

Authors: Subramanian, J Harihara, Nagaraja, K.V., Belwal, Meena

Source: 2025 International Conference on Advancements in Smart, Secure and Intelligent Computing (ASSIC) Advancements in Smart, Secure and Intelligent Computing (ASSIC), 2025 International Conference on. :1-6 May, 2025

Relation: 2025 International Conference on Advancements in Smart, Secure and Intelligent Computing (ASSIC)

Correctly Rounded Evaluation of a Function: Why, How, and at What Cost?

Authors: Brisebarre, Nicolas, Hanrot, Guillaume, Muller, Jean-Michel, Zimmermann, Paul

Contributors: Muller, Jean-Michel

Source: ACM Computing Surveys. 58:1-34

Subject Terms: algorithmic number theory, standardization, elementary functions, floating-point arithmetic, LLL algorithm, lattice basis reduction, [INFO.INFO-AO] Computer Science [cs]/Computer Arithmetic, approximation theory, Computer arithmetic, Correct rounding, Table maker's dilemma

File Description: application/pdf

On the Feasibility of 256-Bit Prime Field Arithmetic via PMNS on 8-Bit Architectures

Authors: Aoki, Daichi^{Aff9, Aff10}, Takagi, Tsuyoshi^Aff10

Contributors: Hartmanis, Juris, Founding Editor^Aff1, Goos, Gerhard, Founding Editor^Aff2, Bertino, Elisa, Series Editor^Aff3, Gao, Wen, Series Editor^Aff4, Steffen, Bernhard, Series Editor^Aff5, Yung, Moti, Series Editor^Aff6, Batina, Lejla, editor^Aff7, Özbudak, Ferruh, editor^Aff8

Source: Arithmetic of Finite Fields : 11th International Workshop, WAIFI 2026, Santander, Spain, June 3–5, 2026, Revised Selected Papers. 16611:284-299

An LLL algorithm with symmetries

Authors: Beth Romano, Jack A. Thorne

Source: International Journal of Number Theory. 21:1361-1393

Subject Terms: explicit methods in number theory, Mathematics - Number Theory, LLL algorithm, symmetric spaces, 49 Mathematical Sciences, FOS: Mathematics, 4904 Pure Mathematics, Quadratic forms (reduction theory, extreme forms, etc.), Number Theory (math.NT), Number-theoretic algorithms, complexity, reduction theory

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Access URL: http://arxiv.org/abs/2408.07012
https://zbmath.org/8054361
https://doi.org/10.1142/s1793042125500708

Revisiting Modular Inversion Hidden Number Problem and Its Applications

Authors: Xu, J., Sarkar, S., Hu, L., Wang, H., Pan, Y.

Source: IEEE Transactions on Information Theory IEEE Trans. Inform. Theory Information Theory, IEEE Transactions on. 69(8):5337-5356 Aug, 2023

Investigating Vulnerabilities in RSA-like Cryptosystems Through Lattice-based Attacks on Small Exponent Keys

Authors: Kumagai, Sou, Kanzawa, Shota, Huda, Samsul, Kodera, Yuta, Nogami, Yasuyuki

Source: 2024 International Conference on Consumer Electronics - Taiwan (ICCE-Taiwan) Consumer Electronics - Taiwan (ICCE-Taiwan), 2024 International Conference on. :585-586 Jul, 2024

Relation: 2024 International Conference on Consumer Electronics - Taiwan (ICCE-Taiwan)

A generalized partial exposure lattice attack against an RSA variant based on cubic Pell curves

Authors: Seck, Michel ^{a, ⁎}, Tchapgnouo, Hortense Boudjou ^b

Source: In Discrete Applied Mathematics 15 June 2026 386:334-344

On the largest value of the solutions of Erdős’ last equation: On the largest value of the solutions of Erdős' last equation

Authors: Florian Luca, István Pink, Csaba Sándor

Source: International Journal of Number Theory. 21:1281-1295

Subject Terms: Baker's method, Counting solutions of Diophantine equations, LLL algorithm, Erdős's last equation, Diophantine equations in many variables

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Access URL: https://zbmath.org/8054357
https://doi.org/10.1142/s1793042125500666

Security Analysis of Hybrid Attack for NTRU-Class Encryption Schemes

Authors: Levina, A., Kadykov, V., Valluri, M.R.

Source: IEEE Access Access, IEEE. 11:109939-109952 2023

Message recovery attack on NTRU using a lattice independent from the public key

Authors: Marios Adamoudis, Konstantinos A. Draziotis

Source: Advances in Mathematics of Communications. 19:109-125

Subject Terms: FOS: Computer and information sciences, Computer Science - Cryptography and Security, closest vector problem, Algebraic coding theory, cryptography (number-theoretic aspects), General topics of discrete mathematics in relation to computer science, Babai's nearest plane algorithm, 0102 computer and information sciences, 02 engineering and technology, public key cryptography, 01 natural sciences, lattices, Cryptography, Lattices and convex bodies (number-theoretic aspects), LLL algorithm, 0202 electrical engineering, electronic engineering, information engineering, NTRU cryptosystem, Cryptography and Security (cs.CR), 94A60

File Description: application/xml

Access URL: http://arxiv.org/abs/2203.09620

Algorithms and Bounds for Complex and Quaternionic Lattices With Application to MIMO Transmission

Authors: Stern, S., Ling, C., Fischer, R.F.H.

Source: IEEE Transactions on Information Theory IEEE Trans. Inform. Theory Information Theory, IEEE Transactions on. 68(7):4491-4517 Jul, 2022

Powers of two-classes in generalized Fibonacci and Pell sequences

Authors: Bravo, Jhon J.^Aff1, Herrera, Jose L.^{Aff1, IDs40590025007704_cor1}, Ruiz, Julieth F.^Aff1

Source: Boletín de la Sociedad Matemática Mexicana: Third Series. 31(3)

Towards Message Recovery in NTRU Encryption with Auxiliary Data

Authors: Adamoudis, Marios^Aff10, Draziotis, Konstantinos A.^Aff10, Poimenidou, Eirini^{Aff10, Aff11}

Contributors: Goos, Gerhard, Series Editor^Aff1, Hartmanis, Juris, Founding Editor^Aff2, Bertino, Elisa, Editorial Board Member^Aff3, Gao, Wen, Editorial Board Member^Aff4, Steffen, Bernhard, Editorial Board Member^Aff5, Yung, Moti, Editorial Board Member^Aff6, Dąbrowski, Andrzej, editor^Aff7, Pieprzyk, Josef, editor^Aff8, Pomykała, Jacek, editor^Aff9

Source: Number-Theoretic Methods in Cryptology : 4th International Conference, NuTMiC 2024, Szczecin, Poland, June 24–26, 2024, Revised Selected Papers. 14966:314-329

Deep LLL on Module Lattices

Authors: Zhou, Yang^{Aff9, Aff10}, Cao, Heyang^{Aff9, Aff10}, Wang, Mingsheng^{Aff9, Aff10}

Contributors: Goos, Gerhard, Series Editor^Aff1, Hartmanis, Juris, Founding Editor^Aff2, Bertino, Elisa, Editorial Board Member^Aff3, Gao, Wen, Editorial Board Member^Aff4, Steffen, Bernhard, Editorial Board Member^Aff5, Yung, Moti, Editorial Board Member^Aff6, Mouha, Nicky, editor^Aff7, Nikiforakis, Nick, editor^Aff8

Source: Information Security : 27th International Conference, ISC 2024, Arlington, VA, USA, October 23–25, 2024, Proceedings, Part II. 15258:24-40

Precoder Design for Communication-Efficient Distributed MIMO Receivers With Controlled Peak-Average Power Ratio

Authors: Vaishampayan, V.A.

Source: IEEE Transactions on Communications IEEE Trans. Commun. Communications, IEEE Transactions on. 69(7):4704-4716 Jul, 2021

NTRU-Like Random Congruential Public-Key Cryptosystem for Wireless Sensor Networks

Authors: Ibrahim, Anas, Chefranov, Alexander, Hamad, Nagham, Daraghmi, Yousef-Awwad, Al-Khasawneh, Ahmad, Rodrigues, Joel J. P. C.

Subject Terms: wireless sensor network, random congruential public-key cryptosystem, lattice, NTRU, polynomial, lattice basis reduction attack, LLL algorithm, Gaussian lattice reduction, IND-CCA2 security

Relation: Sensors; Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı; https://doi.org/10.3390/s20164632; https://hdl.handle.net/11129/10127; 20; 16; Q1; WOS:000565675100001; Q2

Availability: https://hdl.handle.net/11129/10127
https://doi.org/10.3390/s20164632

On the Properties of Reduced Basis Related to Lattice-Reduced Algorithm: On the properties of reduced basis related to lattice-reduced algorithm

Authors: Salleh, N., Kamarulhaili, H.

Source: Malaysian Journal of Mathematical Sciences. 18:287-300

Subject Terms: Quantum theory, LLL algorithm, lattice-based cryptography, 0102 computer and information sciences, 0101 mathematics, reduced basis, 01 natural sciences, Numerical analysis

File Description: application/xml

NTRU-Like Secure and Effective Congruential Public-Key Cryptosystem Using Big Numbers

Authors: Ibrahim, Anas, Chefranov, Alexander, Hamad, Nagham

Source: 2019 2nd International Conference on new Trends in Computing Sciences (ICTCS) Trends in Computing Sciences (ICTCS), 2019 2nd International Conference on new. :1-7 Oct, 2019

Relation: 2019 2nd International Conference on new Trends in Computing Sciences (ICTCS)

Lenstra Lenstra Lovász (LLL) Assisted Likelihood Ascent Search (LAS) Algorithm for Signal Detection in Massive MIMO

Authors: Menon, U.V., Challa, N.R., Bagadi, K.

Source: 2019 International Conference on Vision Towards Emerging Trends in Communication and Networking (ViTECoN) Vision Towards Emerging Trends in Communication and Networking (ViTECoN), 2019 International Conference on. :1-4 Mar, 2019

Relation: 2019 International Conference on Vision Towards Emerging Trends in Communication and Networking (ViTECoN)

Improving BDD Enumeration for LWE Problem Using GPU

Authors: Esseissah, M.S., Bhery, A., Bahig, H.M.

Source: IEEE Access Access, IEEE. 8:19737-19749 2020