Abstract
AbstractLattice reduction is a powerful concept for solving diverse problems involving point lattices. Lattice reduction has been successfully utilizing in Number Theory, Linear algebra and Cryptology. Not only the existence of lattice based cryptosystems of hard in nature, but also has vulnerabilities by lattice reduction techniques. In this survey paper, we are focusing on point lattices and then describing an introduction to the theoretical and practical aspects of lattice reduction. Finally, we describe the applications of lattice reduction in cryptanalysis like subset sum problem of low density, modular equations, Attacking RSA with small e by knowing parts of the message and Diophantine Approximation using LLL algorithm.KeywordsatticesLattice ReductionRSACoppersmithSubset SumSimultaneous DiophantineMerkle-Hellman
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