6_Rotation.cs

// Copyright (c) Microsoft Corporation. All rights reserved.
// Licensed under the MIT license.

using System;
using Microsoft.Research.SEAL;
using System.Collections.Generic;

namespace SEALNetExamples
{
    partial class Examples
    {
        /*
        Both the BFV and BGV schemes (with BatchEncoder) as well as the CKKS scheme support
        native vectorized computations on encrypted numbers. In addition to computing slot-wise,
        it is possible to rotate the encrypted vectors cyclically.

        Simply changing `SchemeType.BFV` to `SchemeType.BGV` will make this example work for
        the BGV scheme.
        */
        private static void ExampleRotationBFV()
        {
            Utilities.PrintExampleBanner("Example: Rotation / Rotation in BFV");

            using EncryptionParameters parms = new EncryptionParameters(SchemeType.BFV);

            ulong polyModulusDegree = 8192;
            parms.PolyModulusDegree = polyModulusDegree;
            parms.CoeffModulus = CoeffModulus.BFVDefault(polyModulusDegree);
            parms.PlainModulus = PlainModulus.Batching(polyModulusDegree, 20);

            using SEALContext context = new SEALContext(parms);
            Utilities.PrintParameters(context);
            Console.WriteLine();

            using KeyGenerator keygen = new KeyGenerator(context);
            using SecretKey secretKey = keygen.SecretKey;
            keygen.CreatePublicKey(out PublicKey publicKey);
            keygen.CreateRelinKeys(out RelinKeys relinKeys);
            using Encryptor encryptor = new Encryptor(context, publicKey);
            using Evaluator evaluator = new Evaluator(context);
            using Decryptor decryptor = new Decryptor(context, secretKey);

            using BatchEncoder batchEncoder = new BatchEncoder(context);
            ulong slotCount = batchEncoder.SlotCount;
            ulong rowSize = slotCount / 2;
            Console.WriteLine($"Plaintext matrix row size: {rowSize}");

            ulong[] podMatrix = new ulong[slotCount];
            podMatrix[0] = 0;
            podMatrix[1] = 1;
            podMatrix[2] = 2;
            podMatrix[3] = 3;
            podMatrix[rowSize] = 4;
            podMatrix[rowSize + 1] = 5;
            podMatrix[rowSize + 2] = 6;
            podMatrix[rowSize + 3] = 7;

            Console.WriteLine("Input plaintext matrix:");
            Utilities.PrintMatrix(podMatrix, (int)rowSize);
            Console.WriteLine();

            /*
            First we use BatchEncoder to encode the matrix into a plaintext. We encrypt
            the plaintext as usual.
            */
            Utilities.PrintLine();
            using Plaintext plainMatrix = new Plaintext();
            Console.WriteLine("Encode and encrypt.");
            batchEncoder.Encode(podMatrix, plainMatrix);
            using Ciphertext encryptedMatrix = new Ciphertext();
            encryptor.Encrypt(plainMatrix, encryptedMatrix);
            Console.WriteLine("    + Noise budget in fresh encryption: {0} bits",
                decryptor.InvariantNoiseBudget(encryptedMatrix));
            Console.WriteLine();

            /*
            Rotations require yet another type of special key called `Galois keys'. These
            are easily obtained from the KeyGenerator.
            */
            keygen.CreateGaloisKeys(out GaloisKeys galoisKeys);

            /*
            Now rotate both matrix rows 3 steps to the left, decrypt, decode, and print.
            */
            Utilities.PrintLine();
            Console.WriteLine("Rotate rows 3 steps left.");
            evaluator.RotateRowsInplace(encryptedMatrix, 3, galoisKeys);
            using Plaintext plainResult = new Plaintext();
            Console.WriteLine("    + Noise budget after rotation: {0} bits",
                decryptor.InvariantNoiseBudget(encryptedMatrix));
            Console.WriteLine("    + Decrypt and decode ...... Correct.");
            decryptor.Decrypt(encryptedMatrix, plainResult);
            List<ulong> podResult = new List<ulong>();
            batchEncoder.Decode(plainResult, podResult);
            Utilities.PrintMatrix(podResult, (int)rowSize);

            /*
            We can also rotate the columns, i.e., swap the rows.
            */
            Utilities.PrintLine();
            Console.WriteLine("Rotate columns.");
            evaluator.RotateColumnsInplace(encryptedMatrix, galoisKeys);
            Console.WriteLine("    + Noise budget after rotation: {0} bits",
                decryptor.InvariantNoiseBudget(encryptedMatrix));
            Console.WriteLine("    + Decrypt and decode ...... Correct.");
            decryptor.Decrypt(encryptedMatrix, plainResult);
            batchEncoder.Decode(plainResult, podResult);
            Utilities.PrintMatrix(podResult, (int)rowSize);

            /*
            Finally, we rotate the rows 4 steps to the right, decrypt, decode, and print.
            */
            Utilities.PrintLine();
            Console.WriteLine("Rotate rows 4 steps right.");
            evaluator.RotateRowsInplace(encryptedMatrix, -4, galoisKeys);
            Console.WriteLine("    + Noise budget after rotation: {0} bits",
                decryptor.InvariantNoiseBudget(encryptedMatrix));
            Console.WriteLine("    + Decrypt and decode ...... Correct.");
            decryptor.Decrypt(encryptedMatrix, plainResult);
            batchEncoder.Decode(plainResult, podResult);
            Utilities.PrintMatrix(podResult, (int)rowSize);

            /*
            Note that rotations do not consume any noise budget. However, this is only
            the case when the special prime is at least as large as the other primes. The
            same holds for relinearization. Microsoft SEAL does not require that the
            special prime is of any particular size, so ensuring this is the case is left
            for the user to do.
            */
        }

        private static void ExampleRotationCKKS()
        {
            Utilities.PrintExampleBanner("Example: Rotation / Rotation in CKKS");

            using EncryptionParameters parms = new EncryptionParameters(SchemeType.CKKS);

            ulong polyModulusDegree = 8192;
            parms.PolyModulusDegree = polyModulusDegree;
            parms.CoeffModulus = CoeffModulus.Create(
                polyModulusDegree, new int[] { 40, 40, 40, 40, 40 });

            using SEALContext context = new SEALContext(parms);
            Utilities.PrintParameters(context);
            Console.WriteLine();

            using KeyGenerator keygen = new KeyGenerator(context);
            using SecretKey secretKey = keygen.SecretKey;
            keygen.CreatePublicKey(out PublicKey publicKey);
            keygen.CreateRelinKeys(out RelinKeys relinKeys);
            keygen.CreateGaloisKeys(out GaloisKeys galoisKeys);
            using Encryptor encryptor = new Encryptor(context, publicKey);
            using Evaluator evaluator = new Evaluator(context);
            using Decryptor decryptor = new Decryptor(context, secretKey);

            using CKKSEncoder ckksEncoder = new CKKSEncoder(context);

            ulong slotCount = ckksEncoder.SlotCount;
            Console.WriteLine($"Number of slots: {slotCount}");

            List<double> input = new List<double>((int)slotCount);
            double currPoint = 0, stepSize = 1.0 / (slotCount - 1);
            for (ulong i = 0; i < slotCount; i++, currPoint += stepSize)
            {
                input.Add(currPoint);
            }
            Console.WriteLine("Input vector:");
            Utilities.PrintVector(input, 3, 7);

            double scale = Math.Pow(2.0, 50);

            Utilities.PrintLine();
            Console.WriteLine("Encode and encrypt.");
            using Plaintext plain = new Plaintext();
            ckksEncoder.Encode(input, scale, plain);
            using Ciphertext encrypted = new Ciphertext();
            encryptor.Encrypt(plain, encrypted);

            using Ciphertext rotated = new Ciphertext();
            Utilities.PrintLine();
            Console.WriteLine("Rotate 2 steps left.");
            evaluator.RotateVector(encrypted, 2, galoisKeys, rotated);
            Console.WriteLine("    + Decrypt and decode ...... Correct.");
            decryptor.Decrypt(encrypted, plain);
            List<double> result = new List<double>();
            ckksEncoder.Decode(plain, result);
            Utilities.PrintVector(result, 3, 7);

            /*
            With the CKKS scheme it is also possible to evaluate a complex conjugation on
            a vector of encrypted complex numbers, using Evaluator.ComplexConjugate. This
            is in fact a kind of rotation, and requires also Galois keys.
            */
        }

        private static void ExampleRotation()
        {
            Utilities.PrintExampleBanner("Example: Rotation");

            /*
            Run all rotation examples.
            */
            ExampleRotationBFV();
            ExampleRotationCKKS();
        }
    }
}