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I'm pretty sure that "64" and "128" are in base 10 not binary. I'm also pretty sure that 64*2=128. Now 2^64 is much less than 2^128. But it's also true that 10^64 is much less than 10^128. In short the problem is not the base.
It doesn't matter which system you use. I'm in the US I use cups and feet and fahrenheit and feet and inches and gallons and liters and meters and volts and amps and seconds and (ooo there's lots of time units I use.) Probably some more. Oh and I can multiply as well.
As far as I know, there is nothing that is reasonable to use that is proven to be secure. Lots of things are very likely to be secure. Often you are trying to balance the convience of a protocol with its security.