2021SC@SDUSC PALISADE开源库（二）CKKS讲解系列（六）旋转（rotation）

2021SC@SDUSC

目录

介绍

rotation

了解

两种基本操作

旋转列

 运行结果

 旋转行

运行结果

源代码

---

介绍

        由于之前我的疏忽，在进行CKKS讲解代码的过程中，忘记介绍rotation（旋转）的部分，所以，现在在这篇博客中。我们将进一步走近有关CKKS旋转的部分，进行进一步的学习。

rotation

了解

        CKKS中的旋转大多就是进行对于矩阵的旋转，通俗一点讲就是，对于矩阵来说，旋转列可能就是将一列元素进行向左或者是向右进行平移。旋转行可能就是将矩阵的每两行进行对调，从而实现旋转的操作。

        旋转是不消耗任何的噪音预算的。

两种基本操作

旋转列

steps 为正 向左移动

steps 为负 向右移动

Ciphertext rotated;
print_line(__LINE__);
cout << "Rotate the first two elements of the column" << endl;
evaluator.rotate_vector(encrypted, 2, galois_keys, rotated);
cout << "     Decrypt and decode" << endl;
decryptor.decrypt(rotated, plain);
vector result;
ckks_encoder.decode(plain, result);
print_vector(result, 3, 7);

 运行结果

 旋转行

print_line(__LINE__);
cout << "Rotate columns." << endl;
evaluator.rotate_columns_inplace(encrypted_matrix, galois_keys);
cout << "    + Decrypt and decode" << endl;
decryptor.decrypt(encrypted_matrix, plain_result);
batch_encoder.decode(plain_result, pod_matrix);
print_matrix(pod_matrix, row_size);

运行结果

源代码

#include "examples.h"

using namespace std;
using namespace seal;

void example_rotation_bfv()
{
    print_example_banner("Example: Rotation / Rotation in BFV");
    EncryptionParameters parms(scheme_type::bfv);

    size_t poly_modulus_degree = 8192;
    parms.set_poly_modulus_degree(poly_modulus_degree);
    parms.set_coeff_modulus(CoeffModulus::BFVDefault(poly_modulus_degree));
    parms.set_plain_modulus(PlainModulus::Batching(poly_modulus_degree, 20));
    
    SEALContext context(parms);
    print_parameters(context);
    cout << endl;

    KeyGenerator keygen(context);
    SecretKey secret_key = keygen.secret_key();
    PublicKey public_key;
    keygen.create_public_key(public_key);
    RelinKeys relin_key;
    keygen.create_relin_keys(relin_key);

    Encryptor encryptor(context, public_key);
    Evaluator evaluator(context);
    Decryptor decryptor(context, secret_key);

    BatchEncoder batch_encoder(context);

    size_t slot_count = batch_encoder.slot_count();
    size_t row_size = slot_count / 2;
    cout << "Plaintext matrix row size: " << row_size << endl;
    

    vector pod_matrix(slot_count, 0ULL);
    pod_matrix[0] = 0ULL;
    pod_matrix[1] = 1ULL;
    pod_matrix[2] = 2ULL;
    pod_matrix[3] = 3ULL;
    pod_matrix[row_size] = 4ULL;
    pod_matrix[row_size + 1] = 5ULL;
    pod_matrix[row_size + 2] = 6ULL;
    pod_matrix[row_size + 3] = 7ULL;

    cout << "Input plaintext matrix:" << endl;
    print_matrix(pod_matrix, row_size);

    Plaintext plain_matrix;
    print_line(__LINE__);
    cout << "Encode and encrypt." << endl;
    batch_encoder.encode(pod_matrix, plain_matrix);
    Ciphertext encrypted_matrix;
    encryptor.encrypt(plain_matrix, encrypted_matrix);
    
    cout << "    + Noise budget in fresh encryption: " << decryptor.invariant_noise_budget(encrypted_matrix) << " bits"
    << endl;
    cout << endl;

    /* 
    * 旋转还需要另一种类型的特殊键 Galois keys
    */
    GaloisKeys galois_keys;
    keygen.create_galois_keys(galois_keys);

    /*
    现在将矩阵行向左循环移动3步, 解密、解码和打印
    */
    print_line(__LINE__);
    cout << "Rotate rows 3 steps left." << endl;
    evaluator.rotate_rows_inplace(encrypted_matrix, 3, galois_keys);
    Plaintext plain_result;
    cout << "    + Noise budget after rotation: " << decryptor.invariant_noise_budget(encrypted_matrix) << " bits"
        << endl;
    cout << "    + Decrypt and decode ...... Correct." << endl;
    decryptor.decrypt(encrypted_matrix, plain_result);
    batch_encoder.decode(plain_result, pod_matrix);
    print_matrix(pod_matrix, row_size);

    /*
    我们也可以旋转列, i.e., 交换行.
    */
    print_line(__LINE__);
    cout << "Rotate columns." << endl;
    evaluator.rotate_columns_inplace(encrypted_matrix, galois_keys);
    cout << "    + Noise budget after rotation: " << decryptor.invariant_noise_budget(encrypted_matrix) << " bits"
        << endl;
    cout << "    + Decrypt and decode ...... Correct." << endl;
    decryptor.decrypt(encrypted_matrix, plain_result);
    batch_encoder.decode(plain_result, pod_matrix);
    print_matrix(pod_matrix, row_size);

    /*
    最后，我们将这些行向右旋转4步, decrypt, decode, and print.
    */
    print_line(__LINE__);
    cout << "Rotate rows 4 steps right." << endl;
    evaluator.rotate_rows_inplace(encrypted_matrix, -4, galois_keys);
    cout << "    + Noise budget after rotation: " << decryptor.invariant_noise_budget(encrypted_matrix) << " bits"
        << endl;
    cout << "    + Decrypt and decode ...... Correct." << endl;
    decryptor.decrypt(encrypted_matrix, plain_result);
    batch_encoder.decode(plain_result, pod_matrix);
    print_matrix(pod_matrix, row_size);
}
void example_rotation_ckks() {
    print_example_banner("Example: Rotation / Rotation in CKKS");

    /*
    Rotations in the CKKS scheme work very similarly to rotations in BFV.
    */
    EncryptionParameters parms(scheme_type::ckks);

    size_t poly_modulus_degree = 8192;
    parms.set_poly_modulus_degree(poly_modulus_degree);
    parms.set_coeff_modulus(CoeffModulus::Create(poly_modulus_degree, { 40, 40, 40, 40, 40 }));

    SEALContext context(parms);
    print_parameters(context);
    cout << endl;

    KeyGenerator keygen(context);
    SecretKey secret_key = keygen.secret_key();
    PublicKey public_key;
    keygen.create_public_key(public_key);
    RelinKeys relin_keys;
    keygen.create_relin_keys(relin_keys);
    GaloisKeys galois_keys;
    keygen.create_galois_keys(galois_keys);

    Encryptor encryptor(context, public_key);
    Evaluator evaluator(context);
    Decryptor decryptor(context, secret_key);

    CKKSEncoder ckks_encoder(context);

    size_t slot_count = ckks_encoder.slot_count();
    cout << "Number of slots: " << slot_count << endl;

    vector input;
    input.reserve(slot_count);
    double curr_point = 0;
    double step_size = 1.0 / (static_cast(slot_count) - 1);
    for (size_t i = 0; i < slot_count; i++, curr_point += step_size)
    {
        input.push_back(curr_point);
    }
    cout << "Input vector:" << endl;
    print_vector(input, 3, 7);
    auto scale = pow(2.0, 50);

    print_line(__LINE__);
    cout << "Encode and encrypt." << endl;
    Plaintext plain;
    ckks_encoder.encode(input, scale, plain);
    Ciphertext encrypted;
    encryptor.encrypt(plain, encrypted);

    Ciphertext rotated;
    print_line(__LINE__);
    cout << "Rotate 2 steps left." << endl;
    evaluator.rotate_vector(encrypted, 2, galois_keys, rotated);
    cout << "    + Decrypt and decode ...... Correct." << endl;
    decryptor.decrypt(rotated, plain);
    vector result;
    ckks_encoder.decode(plain, result);
    print_vector(result, 3, 7);

    print_line(__LINE__);
    cout << "Rotate 2 steps right." << endl;
    evaluator.rotate_vector(encrypted, -2, galois_keys, rotated);
    cout << "    + Decrypt and decode ...... Correct." << endl;
    decryptor.decrypt(rotated, plain);
    
    ckks_encoder.decode(plain, result);
    print_vector(result, 3, 7);

}

void example_rotation()
{
    print_example_banner("Example: Rotation");

    /*
    Run all rotation examples.
    */
    example_rotation_bfv();
    example_rotation_ckks();
}

        对于源代码，我就不作过多的分析了，希望大家能够深入的看下去，一起努力吧。