Mod 1 is intended to drop the whole number part and only yield the irrational fractional component
i don't think it's a trapboor function but rather a form of asymmetric cipher, it's not too distantly different from an elliptic curve.
https://wikimedia.org/api/rest_v1/media/math/render/svg/3dbe6cab1bc2c7f1c99757dc6e5d7a517cf9b4f8
y^2=x^3+a*x+b
your equation is:
p1^2 = (p1*p2)%x)
mod 1 is um... 1. i'm using the simple modulo notation % meaning "remainder", which is sorta like one step of a modulo, more or less the same operation, at least, one cycle of a clockwork arithmetic system. that mod value tells you the potential number of values that could be valid for y, relative to how p2 relates to it.
i'm used to working with these things in code not so much in math. the finite field is a different shape to the field of real numbers.
Discussion
i'm pretty sure anything mod one is the whole number part and to remove it you then need to subtract this from the result, so you'd have to repeat the formula with a subtract
p1^2 = (p1*p2)-((p1*p2) mod 1)
i forget what the precedence of mod is, i think it's commutative to multiply/divide thus the braces. also, mod(dividend, divisor) is programming function notation, i'm pretty sure in math notation you use mod as an infix.
i'm pretty foggy on all these things to be honest, i rarely have to decipher math notation to write algorithms, usually someone else already did that and i just copy/adapt it.
or have i got that backwards. lol! i'm alwaays getting things backwards and off-by-one.