fhe-study

Implementations from scratch done while studying some FHE papers; do not use in production.

• arith: contains $\mathbb{Z}_q$, $R_q=\mathbb{Z}_q/(X^N+1)$, $R=\mathbb{Z}/(X^N+1)$, $\mathbb{T}_q/(X^N +1)$ arithmetic implementations, together with the NTT implementation.
• gfhe: (gfhe=generalized-fhe) contains the structs and logic for RLWE, GLWE, GLev, GGSW, RGSW cryptosystems, and modulus switching and key switching methods, which can be used by concrete FHE schemes.
• bfv: https://eprint.iacr.org/2012/144.pdf scheme implementation
• ckks: https://eprint.iacr.org/2016/421.pdf scheme implementation
• tfhe: https://eprint.iacr.org/2018/421.pdf scheme implementation

Run tests

cargo test --release

Example of usage

the repo is a work in progress, interfaces will change.

This example shows usage of TFHE, but the idea is that the same interface would work for using CKKS & BFV, the only thing to be changed would be the parameters and the line type S = TWLE<K> to use CKKS<Q, N> or BFV<Q, N, T>.

let param = Param {
    err_sigma: crate::ERR_SIGMA,
    ring: RingParam { q: u64::MAX, n: 1 },
    k: 256,
    t: 128, // plaintext modulus
};

let mut rng = rand::thread_rng();
let msg_dist = Uniform::new(0_u64, param.t);

let (sk, pk) = TLWE::new_key(&mut rng, &param)?;

// get two random msgs in Z_t
let m1 = Rq::rand_u64(&mut rng, msg_dist, &param.pt())?;
let m2 = Rq::rand_u64(&mut rng, msg_dist, &param.pt())?;
let m3 = Rq::rand_u64(&mut rng, msg_dist, &param.pt())?;

// encode the msgs into the plaintext space
let p1 = TLWE::encode(&param, &m1); // plaintext
let p2 = TLWE::encode(&param, &m2); // plaintext
let c3_const: T64 = T64(m3.coeffs()[0].v); // encode it as constant

let c1 = TLWE::encrypt(&mut rng, &param, &pk, &p1)?;
let c2 = TLWE::encrypt(&mut rng, &param, &pk, &p2)?;

// now we can do encrypted operations (notice that we do them using simple
// operation notation by rust's operator overloading):
let c_12 = c1 + c2;
let c4 = c_12 * c3_const;

// decrypt & decode
let p4_recovered = c4.decrypt(&sk);
let m4 = TLWE::decode(&param, &p4_recovered);

// m4 is equal to (m1+m2)*m3
assert_eq!(((m1 + m2).to_r() * m3.to_r()).to_rq(param.t), m4);

Status of the implementation

• TFHE
  • {TLWE, TGLWE, TLev, TGLev, TGSW, TGGSW} encryption & decryption
  • addition of ciphertexts, addition & multiplication of ciphertext by a plaintext
  • external products of ciphertexts
    • TGSW x TLWE
    • TGGSW x TGLWE
  • {TGSW, TGGSW} CMux gate
  • blind rotation, key switching, mod switching
  • bootstrapping
• CKKS
  • encoding & decoding
  • encryption & decryption
  • addition & substraction of ciphertexts
• BFV
  • encryption & decryption
  • addition & substraction of ciphertexts
  • addition & multiplication of ciphertext by a plaintext
  • multiplication of ciphertexts with relinearization
• GFHE (generalized FHE)
  • {GLWE & GLev} encryption & decryption
  • key switching, mod switching
  • addition & substraction of ciphertexts
  • addition & multiplication of ciphertext by a plaintext
• arith
  • base arithmetic for $\mathbb{Z}_q,~~ R_q=\mathbb{Z}_q/(X^N+1),~~ R=\mathbb{Z}/(X^N+1),~~ \mathbb{T}_q/(X^N +1)$
  • NTT implementation (negacyclic convolution)