I am currently exploring the concept of multimedia encryption and have come across the use of the finite field π2 for cryptographic purposes, particularly in the context of homomorphic encryption. I am interested in understanding how to practically implement encryption using this field. this is the paper

subframes in a frame are encrypted with plaintexts β Z2, wherein addition and multiplication are equivalent to binary XOR and AND operations, respectively. For b β Z2, its ciphertext is denoted as [b]. For an integer n, [n] denotes its binary encryption, i.e., encryption of each bit in its binary representation. In our work, BGV is used as the homomorphic encryption.

βYes, I can utilize binary Fully Homomorphic Encryption (binFHE). However, I am concerned that binFHE might not support SIMD operations, which allow for the packing of multiple plaintexts into a single ciphertext. Therefore, I am seeking alternative methods to achieve the desired functionality in Z2.β
the paper DOIοΌ(Decoding Homomorphically Encrypted Flac Audio without Decryption | IEEE Conference Publication | IEEE Xplore)γthis paper use HElib to implement something.

The Z2 arithmetic can also be supported in BGV and BFV, but this requires the use of non-power-of-two cyclotomics (to support CRT batching). Helib supports this plaintext algebra. OpenFHE currently does not support non-power-of-two cyclotomics at the level of crypto schemes (it only supports it at a lower lattice layer).

I have not had a chance to look at this work in more detail yet. I am also not aware of an OpenFHE implementation of it at the moment. We will look into this work a little bit later. If someone has already implemented it in OpenFHE, please chime in