ON THE TERMINATION OF QUASI LLL LATTICE BASIS REDUCTION ALGORITHM OVER GAUSSIAN NUMBER FIELDS

2018 ◽  
Vol 109 (1) ◽  
pp. 175-184
Author(s):  
Koichi Arimoto
Keyword(s):  
Number Fields ◽  
Reduction Algorithm ◽  
Lattice Basis Reduction ◽  
Basis Reduction ◽  
Lattice Basis Reduction Algorithm

scholarly journals Factoring the Modulus of Type N = p2q by Finding Small Solutions of the Equation er − (Ns + t) = αp2 + βq2

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2931
Author(s):  
Muhammad Asyraf Asbullah ◽  
Normahirah Nek Abd Rahman ◽  
Muhammad Rezal Kamel Ariffin ◽  
Nur Raidah Salim
Keyword(s):  
Mobile Applications ◽  
Security Analysis ◽  
Public Key ◽  
Lattice Basis Reduction ◽  
Unknown Parameters ◽  
Simultaneous Diophantine Approximation ◽  
Basis Reduction ◽  
Single User ◽  
The Internet Of Things ◽  
Lattice Basis Reduction Algorithm

The modulus of type N=p2q is often used in many variants of factoring-based cryptosystems due to its ability to fasten the decryption process. Faster decryption is suitable for securing small devices in the Internet of Things (IoT) environment or securing fast-forwarding encryption services used in mobile applications. Taking this into account, the security analysis of such modulus is indeed paramount. This paper presents two cryptanalyses that use new enabling conditions to factor the modulus N=p2q of the factoring-based cryptosystem. The first cryptanalysis considers a single user with a public key pair (e,N) related via an arbitrary relation to equation er−(Ns+t)=αp2+βq2, where r,s,t are unknown parameters. The second cryptanalysis considers two distinct cases in the situation of k-users (i.e., multiple users) for k≥2, given the instances of (Ni,ei) where i=1,…,k. By using the lattice basis reduction algorithm for solving simultaneous Diophantine approximation, the k-instances of (Ni,ei) can be successfully factored in polynomial time.

Solving the FCSR synthesis problem for multi-sequences by lattice basis reduction

2017 ◽  
Vol 86 (5) ◽  
pp. 1023-1038 ◽  
Author(s):  
Weihua Liu ◽  
Andrew Klapper ◽  
Zhixiong Chen
Keyword(s):  
Synthesis Problem ◽  
Lattice Basis Reduction ◽  
Basis Reduction

scholarly journals Perturbation Analysis of the QR factor R in the context of LLL lattice basis reduction

2012 ◽  
Vol 81 (279) ◽  
pp. 1487-1511 ◽  
Author(s):  
Xiao-Wen Chang ◽  
Damien Stehlé ◽  
Gilles Villard
Keyword(s):  
Perturbation Analysis ◽  
Lattice Basis Reduction ◽  
Basis Reduction
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