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I have experienced a little with lattice in my master thesis, but I didn't had time to get the perspectives about it nor any open problem, does lattice based cryptography has open problems or perspectives to be a topic of Ph.D ???

My background is in Algebra, abstract algebra and algebraic number theory and the master thesis topic.

any advices I will be thankful

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It does, but it is difficult to write an answer at this level of abstraction (properly explaining the open problems of lattice-based cryptography could easily be a decently-long survey article).

That being said, Chris Peikert wrote such a survey here, and its last section is devoted to open problems in the field. The survey is from 2016, so the open problems may be mildly out of date, but in general it is still a good resource for someone in your position.

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