Coursera

Here's my 2 cents:

Join the Coursera Cryptography online class.

The class is 6 six weeks. Each week there are several lecture videos, a graded quiz and an optional programming assignment. (And these assignments involve implementing crypto parts.)

At the end of the six weeks there is a test.

If you want to be challenged, then this is the right way to go. It is a lot of work. I suggest you plan 10+ hours each week. More if you want to do the programming assignment as well.

(Edit: Here's a table of contents for a previous run of this class.)

Start by breaking, not building your own. There's a worrisomely large number of stackexchange posts by people who've written their own algorithms. Take a look around and figure out what's wrong with them. (Don't look at the posted answers.)

Only when you've found issues in other people's work should you move to trying to implement other people's algorithms. (@stackzofztuff's comment about Coursera is not bad--if I recall, Dan Boneh starts out that way, with more structure than poking here.)

A good start would be to implement existing algorithms and learn how they work in depth. For example, the one-time pad algorithm is easy to learn and implement, and studying its strengths and weaknesses will get you started. It will also get you comfortable with the kind of bit-twiddling that's important in cryptography. Doing a search for "one-time pad" will get you started.

Bruce Schneier's Applied Cryptography is a must read if you want to start studying this field. I am surprised that nobody suggested it before.

And yes, you need to know a lot about crypto even before trying to roll your own algorithms for fun. Don't even think of using them for real-world problems, though -- there's already a lot of bad crypto around.

Concerning programming, avoid proprietary languages like the plague. I'd suggest C, or even C++.

You can implement already existing encryption algorithms, but designing your own encryption algorithm is one of the most complex matters you could deal with. For a general introduction I highly recommend this channel: https://www.youtube.com/channel/UC1usFRN4LCMcfIV7UjHNuQg/videos or the book "Understanding Cryptography" by Christoph Paar and Jan Pelzl (http://crypto-textbook.com/). I assume you are aiming at symmetric algorithms and I would recomment you to start reading a lot of theory about them, what is safe, was is unsafe (historicle) and explicitly how have current state of the art algorithms made their way to what they are (how was AES developed, chosen, etc).

You will encounter many mathematicle problems when you deal with different attacker models, even in the symmetric part. The asymmetric cryptography is manly based on mathematicle problems and there are some very tricky attacks which are very powerful against asymmetric cryptography.

Bottom line is do not develop your own algorithms, unless you have many years of experience and are very familiar with the topic (all parts of it). Implementing a few of them is nevertheless a good idea, but if you are looking for some kind of project why dont you write a program which uses already existing algorithms and decrypts some data for you. You will enough issues to deal with that, because a secure algorithm is not a guarantee at all for secure encryption. Different operation modes will be important on this matter and some other issues as well.

You could follow Scott Wilson's suggestion about the One-Time pad, but with real random data. You can e.g. consider the noise from the computer's webcam. Let the webcam take a few pictures of a static scene, convert the images to 32 bit floating point images, normalize the pictures to the same brightness, take the average and then subtract one of the pictures from the average. If you map negative pixels values to 0 and positive pixel values to 1, you almost have perfectly random bits, that are uncorrelated when the pixels are not too close. Applying von Neumann's algorithm to pairs of bits taken from distant pixels:

(0,1) ---> 0

(1,0)---> 1

(0,0) and (1,1) are discarded

will yield perfect random bits with 0 and 1 having exactly 50% probability.

Go ahead, write an algorithm but at the end give a task to one of your friends/fellows who regularly deal with cryptography; tell them to break your encryption if they can.

You will notice that they will be able to break it in a matter of minutes and you'll be left stunned thinking as to how many loopholes were there that gave the game away to people with extensive cryptography knowledge (to qoute your words)

This is exactly what happened to me when I was learning to program long ago and wanted to challenge some guys who were smart at such stuff and I failed miserably. So much so they could even decipher the message printed on a paper using just their mind and skills.

You certainly can write one and perfect it over the time but by no means it can be secure anytime soon against the people with that knowledge.

That will be a good starting point (or possibly even a stopping point) on your quest to write your own algorithm :)