I can compute something in milliseconds that you cannot reverse in a billion years...
This asymmetry between forward computation and reverse computation is the foundation of all public-key cryptography.
The Impossible Reversal Challenge
I computed 5^x mod 23 = 17 in microseconds. Can you find my secret value of x?
The Forward Direction (Easy)
5
base (g)
^
?
secret (x)
mod
23
modulus (p)
=
17
result
With small numbers, you could try all values of x (1, 2, 3...) until you find the answer. But imagine if the modulus was a 2048-bit number with 617 digits!
Try to find x:
With only 22 possibilities (1-22), brute force works. With 2^2048 possibilities, it does not.
