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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.
"It is too easy to leave a hole which will compromise the overall security, and no amount of bits in the keys used will help that."
Such errors happens regularly even when the people involved do know what they are doing.
And as Andy notes, I would stay away from 8-bit or 16-bit processors if there is a need for decent cryptographic security.
I don't think I would go for any processor that can't run the OpenSSL code. Note that OpenSSL can be configured, so there is no need to include all algorithms.
There may be security holes in the OpenSSL package, but no home developer or "normal" company can hope to match OpenSSL when it comes to code quality or amount of security reviews.