Please tell me how to achieve 1024 bit and above Arithmetic operation using 8, 16, 32 bit microcontroller. The Arithmetic operation consist of Addition, Subtraction, Multiplication, Division, Modulo.
I don't know about any encryption algorithm that is safe at only 32 bits.
And if you did mean RSA, the page en.wikipedia.org/.../RSA notes that 300-bit RSA can be cracked within a couple of hours with a single PC.
Anything less than 1024 bits is a joke, and you would like to use 2048 bits to have a bit of safety margin.
If you let your customers select a RSA size between 32 and 1024 bits, then the customers will look at you and then they will turn their back and walk away.
The trick here is that RSA is too slow for encrypting real data. So you only use RSA for negotiating and transmitting a crypto key for a symmetric chiffer. Then you switch to something more efficient. But it doesn't matter how efficient or safe that second chiffer is, if you do the key negotiation with so weak encryption that people can break it with standard software you can download from the net.
If the hardware can't handle secure key sizes for RSA, then you only have two options. Find another processor or find another algorithm. Stepping down to ridiculous key sizes is not an option. You will only fool yourself and the customer into believing that you have a safe system. Customers don't like to be fooled! Customers may even decide to sue you if they feel that you have intentionally misinformed them, or shown grave unprofessionalism. If you can't do 1024-bit RSA - don't bother.
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