Hardness of approximating the Minimum Solutions of Linear Diophantine Equations

Authors:
Wenbin Chen;Jiangtao Meng
Affiliations:
Department of Computer Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China;Department of Computer Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China
Venue:
Theoretical Computer Science
Year:
2007

Citing 6
Cited 2

Efficient probabilistically checkable proofs and applications to approximations

STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
The hardness of approximate optima in lattices, codes, and systems of linear equations

Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
A public-key cryptosystem with worst-case/average-case equivalence

STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Computers and Intractability; A Guide to the Theory of NP-Completeness

Computers and Intractability; A Guide to the Theory of NP-Completeness
Public-Key Cryptosystems from Lattice Reduction Problems

CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Approximating CVP to Within Almost-Polynomial Factors is NP-Hard

Combinatorica

An improved lower bound for approximating minimum GCD multiplier in l∞ norm (GCDM∞)

Theoretical Computer Science
On the resolution of the system of fuzzy Diophantine equations

Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology

Quantified Score

Hi-index	5.23

Visualization

Abstract

Let 1@?pNP, it is hard to approximate the Minimum Solutions of Linear Diophantine Equations in @?"p norm within any constant factor and it is also hard to approximate the Minimum Solutions of Linear Diophantine Equations in @?"p norm within the factor n^c^/^l^o^g^l^o^g^n for some constant c0 where n is the number of variables in the equations.