What Is The Definition Of The J-invariant Of An Elliptic Curve?

Elliptic Curve Cryptosystem-help?

• Hey guys, I hope everyone is doing well today. I'm urgently looking for some help with Elliptic Curve Cryptosystems(ECCs). Basically, I have to design a public-key cryptosystem using elliptic curve for email encryption(using C). It basically must have 3 basic functions: 1. Generate a key pair(public key and private key) 2. Must be able to encrypt and decrypt message 3. Keys must be protected So can anybody please help me, any advice or information on what I can do, where to start first. Any help will be greatly appreciated; websites, reviews, research papers, programs , etc.. Thanks in advance guys

• Answer:

  First off let me say that the math on this question is a tad out of my league, however I did attempt to read up on it and came up with a potential answer. you need to start by understanding completly the math behind the elliptic curve and identify a trap door function that you can use to encrypt your data blocks with. Elliptic functions section looks promising for finding such a trap door function, though it will be up to you to find it exactly. once found you need to identify the trap door part of the funciton that will allow you to decrypt a data block, the doubly periodic function looks promising as it has two variables w1 and w2 in an equality, if you use w1 as your public key and w2 as your private key.