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I'm working on a 16-bit processor msp430 and I need to know what I need to study when it comes to key size efficiency of a public key cryptosystem.

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    $\begingroup$ Usually, efficiency is more of a concern than key size. A 2048-bit RSA private key in a standard form easily fits 1k bytes (and that can be reduced by a factor 10), the public key like 300 bytes (and that can be reduced by a factor of 2). ECDSA keys are even shorter. $\endgroup$ – fgrieu Feb 17 '17 at 16:31
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Every public-key system that I have seen in the constrained space was based on elliptical curves instead of the classic RSA scheme. This is primarily because cycle time is not as important as memory footprint and the 160-bits in ECC is believe to be roughly the same strength of 2048-bit RSA.

There seems to be some specific papers relevant to the MSP430 already. If you wanted to explore the space, you should start by looking at the cost in memory of storing the long binary words and the cost of each operation in memory. This will give you a good feel for the total memory, but not the calculation time. You also will find that things will be much smaller if you do it in assembly.

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    $\begingroup$ 160-bit ECC is the same strength of 1024-bit RSA: 80 bits. 2048-bit RSA has 112-bit strength. $\endgroup$ – user13741 Feb 19 '17 at 0:16

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