# Oblivious Encryption: Oblivious Transfer Based Encryption

I’m aware of a couple of OT protocols, most of which use Public Key Cryptography, Key Establishment (or similar constructs) as the base. I don’t really have specific knowledge on other OT protocols, however lately we’ve been discussing post-quantum OT, which actually inspired this approach on some “new(?)” type of asymmetric encryption. Which might potentially be useful, if an OT shows up which is not built on Public Key Cryptography or Key Establishment and proven to be post-quantum secure.

Here I would like to describe some form of encryption, humbly named “Oblivious Encryption”

Encryption: For each bit $b_i$ in Alice’s message, Bob creates two random numbers $r_{i_0}$ and $r_{i_1}$. By means of OT, Alice chooses one of these random values as $r_i$, based on the bit value of $b_i$. Alice sends all $r_i$ segments to Bob as the encrypted message.

Note: Bob is using a PRG with a seed (the seed acts as the key, and should not be reused)

Decryption: Bob initiates the PRG with the same seed. For each $r_i$ segment, Bob recreates the two random numbers $r_{i_0}$ and $r_{i_1}$ picks the value, that was associated with bit $0$ or $1$, constructing the $b_i$ values for message $m$

This, in essence, is a really silly symmetrical encryption scheme (probably akin to OTP); however with the touch of OT, it becomes somewhat asymmetrical, thus named Oblivious Encryption. First of all, does this make sense? Are there similar constructs, and what can you say about the security of this scheme?