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It (or rather, the software running on it) will use arbitrary-precision ("bignum") arithmetic. The way this works is basically the same way in which you (probably) learned to do arithmetic on paper at school. The arithmetic taught to us humans at school is base-10 arithmetic — that is, we represent numbers as strings made up of ten different digits, ...


7

Of course the processor cannot process such large numbers directly; this is done though a library such as GMP. See Wikipedia for a list of such libraries, and a good textbook such as that of Gerhard and von zur Gathen for the underlying ideas. The freely available Handbook of Applied Cryptography also talks about this, especially in Chapter 14.


3

While other answers approach the problem from the simpler question, "How do computer handle large number computation" the specific question is how computers handle large modulus numbers, and the answer is that there are algorithms and techniques specifically for handling large modulus calculations. Wikipedia provides a short list of terms and algorithms one ...


3

As others have noted, you typically use some sort of arbitrary precision integer library. I feel obliged to point out, however, that extending multiplication to large integers is decidedly non-trivial compared to addition. With addition, you have a single bit of carry from one word to the next, and on a typical processor you even have an instruction ...


1

If I understood well, you have two issues: About the $2\beta$ values of $x$ "generating" $\beta^2$ values About your the bugs in your code. So, answering (1): Notice that in the summation (and in your first for loop) for each $x_{i,0}$ you have $\beta$ different values of $x_{1,j}$, which means $\beta^2$ combinations of those $2\beta$ values. You are ...


1

Since this is still open and the issue keeps coming up: TLDR: There are lots of things in OpenSSL that implement standards including AES, but the key derivation part of enc is partly nonstandard First, OpenSSL has several commandline operations it calls commands (although they usually aren't separate programs, as typical commands are on Unix), and a whole ...



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