Let’s say I have a message $m$ of $n$ bits. And a predetermined pad of $k*n$ bits. And for every bit $b$ of this message $m$, I’m creating random sequence $s$ of $k$ bits.
I also have a predetermined boolean random function $f$ (imagine something like this: $f(s) = hash(s)\ mod\ 2$).
For each bit $b_i$, I choose a random value for $s_i$, so that $f(s_i)=b_i$.
So, I can construct a padded version of $m$ like this: $m_p= s_0 || s_1 || ... || s_n$, removing the padding is trivial.
The encryption is also straightforward XOR of the $m_p$ value with the predetermined pad of the same length ($k * n$)
Can this protocol justify/enable reusing of the same pad over and over again providing OTP-Like security?
Equivalent text-based formulation of the scheme:
One comes up with a fresh, random hash pre-image for each message bit that when hashed yields the message bit as the LSB. You then transmit the pre-images and encrypt them with the re-used OTP.