Asymmetric Encryption: Overview & Techniques

[Krushnaraj Pandya]

Homework Statement

With a project I'm trying to demonstrate the key distribution problem on top of an Enigma machine encryption (I'm thinking about naming the project 'Enigmatic Encryption'). For that I'm trying to demonstrate asymmetric encryption, now it seems to me that the 'one-way' functions used in RSA encryption are too complex for me to demonstrate that. So I was thinking I'd have something like a quintic polynomial which takes in a value of x then goes through g(x)=x^5-x+1 and produces an encrypted message- which is sent to the person who has the inverse of this function (and the only person to know the inverse function since he's the only person who knows of g(x) in the first place) and gets back the original x by plugging in the encrypted x through the inverse.

I'm having two issues with this-

1) how would the function g(x) be hidden for the person who has the original message and wants to encrypt it? A key feature of asymmetric encryption is that even the person who encrypted the message can't decrypt it and so it becomes necessary that this function is hidden but can still be used- something like a magical vending machine where you put in something and get something out but have no idea how it works.

2) Another major problem seems to be that quintic functions don't have inverses which makes it impossible to reverse the encryption. Ideally I want a way so that, say, Joe has a function (in a sense his public key) and the inverse of a function (his private key) and he can distribute his public key for use without allowing people to know what the function is (so they can't find its inverse) but can still use that function. Do you know of any good functions I could use, which have an inverse and can be used in this sense.

Relevant Equations

NA

Outlined above

 

[pbuk]

For that I'm trying to demonstrate asymmetric encryption, now it seems to me that the 'one-way' functions used in RSA encryption are too complex for me to demonstrate that.

No, the RSA algorithm is remarkably simple, see this example on Wikipedia, so why not just use that?

 

[Krushnaraj Pandya]

No, the RSA algorithm is remarkably simple, see this example on Wikipedia, so why not just use that?

I was looking at the algorithm at earlier but got scared looking at modular multiplicative inverses; I still can't fully wrap my head around it but I'll try to learn more about it since you suggest that it's simple enough. Thank you very much.

 

[pbuk]

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