What is the weight of a 256 bit number ?

[gogismamero]

What is the weight of a 256 bit number.

is there a way to reduce its size ?

[Lauda]

"Weight"? Do you mean the size that it occupies (not that this question makes sense)? It's literally in its name: 256 bits or 32 bytes.

[Indighost]

what do you mean? bits and bytes are not physical and have therefore no weight

[Foxpup]

bits and bytes are not physical and have therefore no weight

Not true. Information storage requires a certain amount of entropy, which in turn requires energy in proportion to the temperature of the storage medium, and since energy produces gravity just as mass does, bits and bytes do in fact have weight, though far too little to be worth talking about normally. Specifically, a 256-bit number requires k_Bln(2²⁵⁶) = 2.45x10^-21J/K of entropy, which at room temperature corresponds to 7.35x10^-19J of energy or 8.17x10^-36kg of mass. For comparison, this is about 200 million times less than the mass of a proton.

This may not seem like much, but it does put a hard limit on the matter and energy requirements of computational processes. Iterating through all possible states of a 256-bit number requires 2²⁵⁶ times more energy than storing it once, which at 3 Kelvin (the average temperature of the Universe, and hence the best you can do as far as practical cooling is concerned) means 8.51x10⁵⁶J or 9.46x10³⁹kg, about 5 billion times the mass of the Sun. This makes brute-forcing 256-bit keys somewhat impractical.

(I hope I haven't screwed up my math as I'm prone to do at this hour, but the numbers seem about right.)