Fully Homomorphic Encryption (FHE), the ‘holy grail’ of cryptography, is a form of encryption that allows arbitrary computations on encrypted data.

Alice, the data owner, encrypts data with her key and sends it to an untrusted machine for storage and processing.

Ursula performs arbitrary computations on the encrypted data without learning anything about the plaintext.

Alice decrypts the results of Ursula's computations using her original key, retaining confidentiality of data in-use.

NuFHE is a proof-of-concept that implements Fully Homomorphic Encryption over the Torus. Unlike TFHE, where FFT is used internally to speed up polynomial multiplication, NuFHE can use either FFT or purely integer NTT (DFT-like transform on a finite field). The latter is based on the arithmetic operations and NTT scheme from cuFHE.