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Thank you for your time on writing this. You mentioned some maths' phrases like discrete logarithm or Taylor Series that are unknown to me. You said, though, that in order to reverse the result of a public key we need the discrete logarithm. A computer calculates only in real numbers, so it cannot reverse it. Here's my question. Can a human do it? Or is it mathematically impossible?
Also, I'm not fully sure why a computer calculates only in real numbers since it can calculate
x * G on an elliptic curve shape. For example, how all these incredibly many bounces are calculated on the axis within 1 second?
Sorry for the terms, I talk about it on my day-by-day and missuppose that everyone know it!
Discrete logarithm are logarithms function with discrete numbers (integers are discrete, for example)
Series are not more then a sum of simple terms with a former rule: like x+x²+x³+x⁴... is formed from sum (x
n) where sum() is just the sum of all terms.
Taylor Series are some special ones that gives the same (or close to) the result of another. For exemplo, how carry out in a CPU that only knows basic math (sum, subtract...) functions like sin(x). We use this Series to get the result, like this:
https://wikimedia.org/api/rest_v1/media/math/render/svg/3e8311bbbeac9364f73b437929aa85c71715a7a8Here's my question. Can a human do it? Or is it mathematically impossible?
Yes! What is the log of 4 in base 2; two, of course. But, why? I know that 2² is 4, and I also know that the log
2(4) is a number
n, that when I take 2
a it returns 4. This method is called "imediate" or "intuitive", and works for small number. But for big numbers, the process becomes hard. Imagine hand-calculate log
12334434343(34234325654767454)? So, isn't mathematically impossible (there is methods to solve then) but is HARD.
Also, I'm not fully sure why a computer calculates only in real numbers since it can calculate x * G on an elliptic curve shape. For example, how all these incredibly many bounces are calculated on the axis within 1 second?
Because taking the process on the "right" direction (private -> public) not involves DLs. Is basically ordinary math, but to go backwards you should solve a DL, hence this function is so called "an one way function". This is the point you should keep in mind (sorry if I'm being boring) in one way: ordinary math, in the other way: DLs.