# Understanding Lattice based cryptosystem [closed]

I have heard that there is one paradigm of Public key cryptosystem, called Lattice based crytography. Further, its security claims are such that it will not be affected even if the quantum computers are available.

Would any one be kind enough to help me to understand the basic philosophy behind it, with examples?

EDIT As stated in comments, I don't any complete, state-of-the-art scenario of this system. I am only interested to know what are the basic pillars that constitute it. I mean, there has to be something like complicated non-linear operations, or finding prime factor(s) of a large number etc.

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## closed as too broad by e-sushi♦, Maarten Bodewes, DrLecter, hunter, Ricky DemerJul 27 '14 at 20:12

There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.If this question can be reworded to fit the rules in the help center, please edit the question.

I’m not really sure I get what you’re asking. You’re not asking us to explain lattice-based crypto from scratch, are you? That would be a bit too broad. But editing your question will probably help narrowing it down a bit… What research have you done, and what exactly are you having a hard time with or don’t you understand? – e-sushi Jul 27 '14 at 18:39
@e-sushi I don't want it from the scratch. I only want to know the idea behind it. I mean, public key cryptosystems are based on factorization, finding discrete log; private key cryptosystems are based on some random-looking permutations or complicated non-linear functions etc. Now, what makes lattice based system strong? – pushpen.paul Jul 28 '14 at 2:48
@pushpen.paul: It seems that the Wikipedia entry, or/and for this or that example it cites, is enough to answer what makes lattice based system strong? with: for many, the hardness of the Closest Vector Problem in some appropriate lattice. Perhaps, state this and ask for more, e.g. what the CVP is, or why it is believed to be secure even with quantum computers? – fgrieu Jul 28 '14 at 6:06