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I have taken a course in my undergraduate on the theory part of abstract algebra.Now am interested to know how can abstract algebra be applied to cryptography.Thanks

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closed as too broad by e-sushi, mikeazo Apr 24 '14 at 18:11

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'd suggest reading an introductory book on crypto then trying to ask more specific questions. As is, the question is to broad. – mikeazo Apr 24 '14 at 18:11
up vote 3 down vote accepted

Wow that's a broad question. The shortest answer is that lots of Public Key Cryptography is based around a collection of mathematical problems that we believe are hard to solve. Why do we believe they're hard to solve? Because they're age-old Algebra (well, normally Number Theory actually but still) problems that mathematicians and computer scientists have been trying to find efficient solutions to for a long time.

The first two examples you're likely to come across are the Diffie-Hellman key exchange and the RSA scheme. In the case of D-H, the mathematical problem underlying it is a group theory issue, known as the DHP, and for RSA it's a number theoretical assumption known (unsurprisingly) as the RSA assumption

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