I have a question about division operation.
There are two entities, Alice and Bob.
Bob randomly selects a finite set of numbers (set K). (about 10K or 100K)
Alice randomly generates one big number $x_1$ and chooses one element $y_1$ (from Bob's set K).
Alice makes $X$ ($X=x_1*y_1 \bmod n$) and sends $X$ to Bob.
In this case, can Bob figure out what Alice chooses from the set K?
Small number example: 3 ($x_1$) * 5 ($y_1$) mod 7 = 1 ($X$).
Bob knows that there is '5' in the set K, but I think that 1 divided by 5 (mod 7) equals 1.
So I don't think that Bob can figure out what Alice chooses from the set K.
Am I right?
Sorry for my bad English.