Anyone here who has some experience in Cryptography? From where should I start this? I'm asking this from research point of view

Depending on where your focus is i recommend the "handbook of applied cryptography". It's free, but not easy to read.

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You need to be a little more specific, do you want to start from the bottom ("how do crypto-algorithms work and how are they combined (if needed)?") Or from the top ("how does the secure connection in my browser work etc.?") Cryptography is a big topic.

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@YouAreAPIRate Actually I wanted to apply for Research Intern for the summer. So for that purpose I wanted to know with what all things should I begin with so that the professor knows I'm genuinely interested in it and I can improve my prospects of getting selected

I'd say look at basic encryption, how prime numbers are used, more advanced encryption, then go from there

@bravoMike then i'd recommend you to learn about the "everyday use" of cryptography. I don't know what will impress your teacher, but this will bring you the knowledge.

Start with hashes, learn why passwords must be hashed, why hashes are salted and sometimes peppered and why bcrypt is more secure than a simple hash.
Then dive into public and private keys, those have many applications. Learn how they are created, why you cant get the private key from the public key, how they are used for a login instead of a password and learn about digital signatures based on private keys.
When you got this learn about the pki and website certificates in general. Learn how a website certificate is validated and why it's game over when you accept a rougue certificate.
In the end you can learn a bit about tls, how it works and why it is secure and fast (in general) and what the latest attacks on tls were. Poodle, beast, etc.

Gotta come, i'll write more later

@YouAreAPIRate Yeah I'll start looking at the things mentioned by you. Apart from this is there any good course online on platforms like Coursera etc? I was thinking once I'm done with the basics I'll start reading some research papers related to cryptography.

@bravoMike i'm not sure about online-courses, i am self-tought via security- and crypto-stackexchange. Maybe there are some good ted talks or presentations on media.ccc.de on this topic. Other devrant members should add to this list as well, please.

And once again i recommend the "handbook of cryptography", it's a good start even though it brings all the maths with it.

Cryptography borrows a lot of it's fundamentals from Discrete Mathematics. Try this notes ( the end chapters will provide you strong fundamentals ) : https://google.co.in/url/..._ - Lecture notes by Prof. Laszlo Lovasz