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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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