BFV API¶

Data Structures¶

Poseidon supported parameter data structures, the following is specific to BFV：

1. BFV encoding and decoding class : BatchEncoder¶

Description：BatchEncoder is used to encode and decode message for BFV encryption scheme.

Functions：

BatchEncoder(const PoseidonContext &context);

context (const PoseidonContext &): The poseidon context.

Usage: Creates a BatchEncoder. It is necessary that the encryption parameters given through the PoseidonContext object support batching.

void encode(const vector<uint32_t> &src, Plaintext &plain);

src (const vector &): The source message is an array of integer elements.
plain (Plaintext &): The output plaintext .

Usage: Encoding a vector of integer numbers into a plaintext.

void decode(const Plaintext &plain,vector<uint32_t> &res);

plain const Plaintext &plain): The plaintext.
res (vector &): The result of message.

Usage: It is used to decode a plaintext into a vector of integer.

2. Plaintext matrix class : MatrixPlain ¶

Description: MatrixPlain is a class for storing plaintext matrix information.

c++ MatrixPlain() : log_slots(0), n1(0), level(0), scale(1.0), rot_index{}, plain_vec_pool{sz, std::map<int, Plaintext>()}, read_idx(0), write_idx(0), is_precompute(false)

Members:

LogSlots (uint32_t): Indicates the logarithm to 2 of the number of matrix elements.
N1 (uint32_t): Indicates the number of rows in a matrix.
level (uint32_t): Indicates the level of the ciphertext module chain in which the matrix resides.
scale (double): Indicates the scaling factor of the matrix.
rot_index (vector):Indicates the rotation index of a matrix element in a polynomial.
plain_vec (map):Indicates the polynomial corresponding to the matrix elements.

3. Evaluator class : EvaluatorBfvBase ¶

Description: EvaluatorBfvBase is a evaluator for homomorphic computation for BFV scheme.

Members: The member functions are listed in Chapter Evaluation Functions.

Evaluation Functions ¶

1. Addition of ciphertext and ciphertext: add¶

void add(Ciphertext &ciph1, Ciphertext &ciph2, Ciphertext &result);

ciph1 (Ciphertext): representing the addend.
ciph2 (Ciphertext): representing the other addend.
result (Ciphertext): storing the addition result.

Usage: add computes result = ciph1 + ciph2 .

2. Addition of ciphertext and plaintext: add_plain¶

void add_plain(Ciphertext &ciph, Plaintext &plain, Ciphertext &result);

ciph (Ciphertext): representing the addend.
plain (Plaintext): representing the other addend.
result (Ciphertext): storing the addition result.

Usage: add_plain computes result = ciph + plain .

3. Subtraction ciphertext from ciphertext: sub¶

void sub(Ciphertext &ciph1, Ciphertext &ciph2, Ciphertext &result);

ciph1 (Ciphertext): representing the minuend.
ciph2 (Ciphertext): representing the subtrahend
result (Ciphertext): storing the computation result.

Usage: sub computes result = ciph1 - ciph2.

4. Subtraction plaintext from ciphertext: sub_plain¶

void sub_plain(const Ciphertext &ciph, const Plaintext &plain, Ciphertext &result);

ciph (Ciphertext): representing the minuend.
plain (Plaintext): representing the subtrahend.
result (Ciphertext): storing the computation result.

Usage: sub_plain computes result = ciph - plain .

5. Multiplication between ciphertexts: multiply ( only software)¶

void multiply(const Ciphertext &ciph1, const Ciphertext &ciph2, Ciphertext &result);

ciph1 (Ciphertext): representing a ciphertext.
ciph2 (Ciphertext): representing the other ciphertext.
result (Ciphertext): storing the computation result.

Usage: multiply computes result = ciph1 * ciph2.

6. Multiplication between ciphertext and plaintext : multiply_plain¶

void multiply_plain(const Ciphertext &ciph, const Plaintext &plain, Ciphertext &result) const;

ciph (Ciphertext): representing a ciphertext.
plain (Plaintext): representing a plaintext.
result (Ciphertext): storing the computation result.

Usage: multiply_plain computes result = ciph * plain.

7. Multiplication with relinearization : multiply_relin¶

void multiply_relin(const Ciphertext &ciph1, const Ciphertext &ciph2, Ciphertext &result, const RelinKeys &relin_key) const;

ciph1 (Ciphertext): representing a ciphertext.
ciph2 (Ciphertext): representing the other ciphertext.
result (Ciphertext): storing the computation result.
relin_key (RelinKeys): A constant reference to a RelinKeys object, representing the relinearization key.

Usage: multiply_relin computes result = ciph1 * ciph2 and relinearize the ciphertext size of result.

8. Square inplace: square_inplace (only software)¶

void BFVEvaluator_S::square_inplace(Ciphertext &ciph) const;

ciph (Ciphertext): representing a ciphertext.

Usage: square_inplace computes ciph = ciph ^ 2 inplace.

9. Relinearization : relinearize (only software)¶

void relinearize(const Ciphertext &ciph, Ciphertext &result, const RelinKeys &relin_keys) const;

ciph (Ciphertext): representing a ciphertext.
relin_keys (RelinKeys): representing the relinearization key.
result (Ciphertext): storing the computation result.

Usage: relinearize function performs relinearization operation on the ciphertext.

10. Ciphertext row rotation : rotate_col¶

void rotate_col(const Ciphertext &ciph, Ciphertext &result, const GaloisKeys &galois_keys) const;

ciph (Ciphertext): representing a ciphertext.
galois_keys (GaloisKeys): representing the galois keys used for rotation.
result (Ciphertext): storing the ciphertext after column rotation.

Usage: rotate_col performs a column rotation operation on a ciphertext.

11. Ciphertext column rotation : rotate_row¶

void rotate_row(const Ciphertext &ciph, Ciphertext &result, int step, const GaloisKeys &galois_keys) const;

ciph (Ciphertext): representing a ciphertext.
result (Ciphertext): storing the ciphertext after row rotation.
step (int): An integer representing the rotation step length; a positive value indicates a left rotation while a negative value indicates a right rotation.
galois_keys (GaloisKeys): representing the galois keys used for row rotation.

Usage: rotate_row performs a row rotation operation on a ciphertext.

12. Modulo drop: drop_modulus¶

void drop_modulus(const Ciphertext &ciph, Ciphertext &result, uint32_t level) const;
void drop_modulus_to_next(const Ciphertext &ciph, Ciphertext &result) const;

ciph (Ciphertext): representing a ciphertext.
result (Ciphertext): storing the ciphertext after dropping the modulus.
level (uint32_t): The modulus level to switch into.

Usage: drop_modulus drops the modulus into a specific level. drop_modulus_to_next drops the modulus into the next level.

13. Number Theoretic Transform (forward) : ntt_fwd¶

void ntt_fwd(const Plaintext &plain, Plaintext &result, parms_id_type parms_id = parms_id_zero) const;
void ntt_fwd(const Ciphertext &ciph, Ciphertext &result) const;

plain (Plaintext): representing a plaintext.
ciph (Ciphertext): representing a ciphertext.
id (Ciphertext): target parms_id of plain(only used in BGV or BFV).
result (Ciphertext/Plaintext): storing the transformed plaintext or ciphertext.

Usage: ntt_fwd performs the Number Theoretic Transform(NTT) on a plaintext or a ciphertext.

14. Number Theoretic Transform (inverse) : ntt_inv¶

void ntt_inv(const Ciphertext &ciph, Ciphertext &result) const;

ciph (Ciphertext): representing a ciphertext.
result (Ciphertext or Plaintext): storing the inverse transformed ciphertext or plaintext.

Usage: ntt_inv performs the Inverse Number Theoretic Transform(INTT) on a plaintext or a ciphertext.

15. Matrix multiplication of ciphertext and plaintext matrix : multiplyByDiagMatrixBSGS¶

void multiply_by_diag_matrix_bsgs(const Ciphertext &ciph, const MatrixPlain &plain_mat, Ciphertext &result, const GaloisKeys &rot_key) const;

ciph (Ciphertext): representing a ciphertext.
plain_mat (MatrixPlain): representing a plaintext matrix.
result (Ciphertext): storing the computation result.
rot_key (GaloisKeys): representing the galois key for rotation.

Usage: multiply_by_diag_matrix_bsgs multiplies a ciphertext with a plaintext matrix, performing the linear transformation over the ciphertext with the Baby-Step-Giant-Step (BSGS) algorithm to accelerate the operations.

The BSGS algorithm can be performed with the following equation.

$\begin{aligned} A \cdot z & = \sum\limits_{0 \le j \le N_2} \sum\limits_{0 \le i \le N_1} (u_{N_i \cdot j + i} \odot \rho(z;N_1 \cdot j + i)) \\ & = \sum\limits_{0 \le j < N_2} \rho ( \sum\limits_{0 \le i < N_1} \rho(u_{N_1 \cdot j + i};-N_1 \cdot j) \odot \rho(z;i);N_1 \cdot j ) \end{aligned}$

notation:

$A$ denotes the plain matrix

$z$ denotes the ciphertext

$N_1$ is a divisor of $N/2$ and $N_2$ is $N/2N_1$

$\odot$ denotes the Hadamard (component-wise) multiplication between vectors.

$\rho(c;s)$ denotes the rotation of ciphertext $c$ , the rotation step is $s$ .