public void BatchUnbatchPlaintextNET()
{
var parms = new EncryptionParameters();
parms.PolyModulus = "1x^64 + 1";
parms.CoeffModulus = new List <SmallModulus> {
DefaultParams.SmallMods60Bit(0)
};
parms.PlainModulus = 257;
var context = new SEALContext(parms);
Assert.IsTrue(context.Qualifiers.EnableBatching);
var crtbuilder = new PolyCRTBuilder(context);
Assert.AreEqual(64, crtbuilder.SlotCount);
var plain = new Plaintext(crtbuilder.SlotCount);
for (int i = 0; i < crtbuilder.SlotCount; i++)
{
plain[i] = (UInt64)i;
}
crtbuilder.Compose(plain);
crtbuilder.Decompose(plain);
for (int i = 0; i < crtbuilder.SlotCount; i++)
{
Assert.IsTrue(plain[i] == (UInt64)i);
}
for (int i = 0; i < crtbuilder.SlotCount; i++)
{
plain[i] = (UInt64)5;
}
crtbuilder.Compose(plain);
Assert.IsTrue(plain.ToString().Equals("5"));
crtbuilder.Decompose(plain);
for (int i = 0; i < crtbuilder.SlotCount; i++)
{
Assert.IsTrue(plain[i] == (UInt64)5);
}
var short_plain = new Plaintext(20);
for (int i = 0; i < 20; i++)
{
short_plain[i] = (UInt64)i;
}
crtbuilder.Compose(short_plain);
crtbuilder.Decompose(short_plain);
for (int i = 0; i < 20; i++)
{
Assert.IsTrue(short_plain[i] == (UInt64)i);
}
for (int i = 20; i < crtbuilder.SlotCount; i++)
{
Assert.IsTrue(short_plain[i] == 0UL);
}
}
public static void ExampleBatching()
{
PrintExampleBanner("Example: Batching using CRT");
// Create encryption parameters
var parms = new EncryptionParameters();
/*
* For PolyCRTBuilder it is necessary to have PlainModulus be a prime number congruent to 1 modulo
* 2*degree(PolyModulus). We can use for example the following parameters:
*/
parms.SetPolyModulus("1x^4096 + 1");
parms.SetCoeffModulus(ChooserEvaluator.DefaultParameterOptions[4096]);
parms.SetPlainModulus(40961);
parms.Validate();
// Create the PolyCRTBuilder
var crtbuilder = new PolyCRTBuilder(parms);
int slotCount = crtbuilder.SlotCount;
Console.WriteLine($"Encryption parameters allow {slotCount} slots.");
// Create a list of values that are to be stored in the slots. We initialize all values to 0 at this point.
var values = new List <BigUInt>(slotCount);
for (int i = 0; i < slotCount; ++i)
{
values.Add(new BigUInt(parms.PlainModulus.BitCount, 0));
}
// Set the first few entries of the values list to be non-zero
values[0].Set(2);
values[1].Set(3);
values[2].Set(5);
values[3].Set(7);
values[4].Set(11);
values[5].Set(13);
// Now compose these into one polynomial using PolyCRTBuilder
Console.Write("Plaintext slot contents (slot, value): ");
for (int i = 0; i < 6; ++i)
{
string toWrite = "(" + i.ToString() + ", " + values[i].ToDecimalString() + ")";
toWrite += (i != 5) ? ", " : "\n";
Console.Write(toWrite);
}
var plainComposedPoly = crtbuilder.Compose(values);
// Let's do some homomorphic operations now. First we need all the encryption tools.
// Generate keys.
Console.WriteLine("Generating keys ...");
var generator = new KeyGenerator(parms);
generator.Generate();
Console.WriteLine("... key generation completed");
var publicKey = generator.PublicKey;
var secretKey = generator.SecretKey;
// Create the encryption tools
var encryptor = new Encryptor(parms, publicKey);
var evaluator = new Evaluator(parms);
var decryptor = new Decryptor(parms, secretKey);
// Encrypt plainComposed_poly
Console.Write("Encrypting ... ");
var encryptedComposedPoly = encryptor.Encrypt(plainComposedPoly);
Console.WriteLine("done.");
// Let's square and then decrypt the encryptedComposedPoly
Console.Write("Squaring the encrypted polynomial ... ");
var encryptedSquare = evaluator.Square(encryptedComposedPoly);
Console.WriteLine("done.");
Console.Write("Decrypting the squared polynomial ... ");
var plainSquare = decryptor.Decrypt(encryptedSquare);
Console.WriteLine("done.");
// Print the squared slots
crtbuilder.Decompose(plainSquare, values);
Console.Write("Squared slot contents (slot, value): ");
for (int i = 0; i < 6; ++i)
{
string toWrite = "(" + i.ToString() + ", " + values[i].ToDecimalString() + ")";
toWrite += (i != 5) ? ", " : "\n";
Console.Write(toWrite);
}
// Now let's try to multiply the squares with the plaintext coefficients (3, 1, 4, 1, 5, 9, 0, 0, ..., 0).
// First create the coefficient list
var plainCoeffList = new List <BigUInt>(slotCount);
for (int i = 0; i < slotCount; ++i)
{
plainCoeffList.Add(new BigUInt(parms.PlainModulus.BitCount, 0));
}
plainCoeffList[0].Set(3);
plainCoeffList[1].Set(1);
plainCoeffList[2].Set(4);
plainCoeffList[3].Set(1);
plainCoeffList[4].Set(5);
plainCoeffList[5].Set(9);
// Use PolyCRTBuilder to compose plainCoeffList into a polynomial
var plainCoeffPoly = crtbuilder.Compose(plainCoeffList);
// Print the coefficient list
Console.Write("Coefficient slot contents (slot, value): ");
for (int i = 0; i < 6; ++i)
{
string toWrite = "(" + i.ToString() + ", " + plainCoeffList[i].ToDecimalString() + ")";
toWrite += (i != 5) ? ", " : "\n";
Console.Write(toWrite);
}
// Now use MultiplyPlain to multiply each encrypted slot with the corresponding coefficient
Console.Write("Multiplying squared slots with the coefficients ... ");
var encryptedScaledSquare = evaluator.MultiplyPlain(encryptedSquare, plainCoeffPoly);
Console.WriteLine(" done.");
// Decrypt it
Console.Write("Decrypting the scaled squared polynomial ... ");
var plainScaledSquare = decryptor.Decrypt(encryptedScaledSquare);
Console.WriteLine("done.");
// Print the scaled squared slots
crtbuilder.Decompose(plainScaledSquare, values);
Console.Write("Scaled squared slot contents (slot, value): ");
for (int i = 0; i < 6; ++i)
{
string toWrite = "(" + i.ToString() + ", " + values[i].ToDecimalString() + ")";
toWrite += (i != 5) ? ", " : "\n";
Console.Write(toWrite);
}
// How much noise budget are we left with?
Console.WriteLine("Noise budget in result: {0} bits", decryptor.InvariantNoiseBudget(encryptedScaledSquare));
}
public static void ExampleBatching()
{
PrintExampleBanner("Example: Batching using CRT");
// Create encryption parameters
var parms = new EncryptionParameters();
/*
* For PolyCRTBuilder we need to use a plain modulus congruent to 1 modulo 2*degree(PolyModulus), and
* preferably a prime number. We could for example use the following parameters:
*
* parms.PolyModulus.Set("1x^2048 + 1");
* parms.CoeffModulus.Set(ChooserEvaluator.DefaultParameterOptions[2048]);
* parms.PlainModulus.Set(12289);
*
* However, the primes suggested by ChooserEvaluator.DefaultParameterOptions are highly non-optimal in this
* case. The reason is that the noise growth in many homomorphic operations depends on the remainder
* CoeffModulus % PlainModulus, which is typically close to PlainModulus unless the parameters are carefully
* chosen. The primes in ChooserEvaluator.DefaultParameterOptions are chosen so that this remainder is 1
* when PlainModulus is a (not too large) power of 2, so in the earlier examples this was not an issue.
* However, here we are forced to take PlainModulus to be odd, and as a result the default parameters are no
* longer optimal at all in this sense.
*
* Thus, for improved performance when using PolyCRTBuilder, we recommend the user to use their own
* custom CoeffModulus. It should be a prime of the form 2^A - D, where D is as small as possible.
* The PlainModulus should be simultaneously chosen to be a prime congruent to 1 modulo 2*degree(PolyModulus),
* so that in addition CoeffModulus % PlainModulus is 1. Finally, CoeffModulus should be bounded by the
* same strict upper bounds that were mentioned in ExampleBasics():
* /------------------------------------\
| PolyModulus | CoeffModulus bound |
| -------------|---------------------|
| 1x^1024 + 1 | 48 bits |
| 1x^2048 + 1 | 96 bits |
| 1x^4096 + 1 | 192 bits |
| 1x^8192 + 1 | 384 bits |
| 1x^16384 + 1 | 768 bits |
\------------------------------------/
|
| One issue with using such custom primes, however, is that they are never NTT primes, i.e. not congruent
| to 1 modulo 2*degree(PolyModulus), and hence might not allow for certain optimizations to be used in
| polynomial arithmetic. Another issue is that the search-to-decision reduction of RLWE does not apply to
| non-NTT primes, but this is not known to result in any concrete reduction in the security level.
|
| In this example we use the prime 2^95 - 613077 as our coefficient modulus. The user should try switching
| between this and ChooserEvaluator.DefaultParameterOptions[2048] to observe the difference in the noise
| level at the end of the computation. This difference becomes significantly greater when using larger
| values for PlainModulus.
*/
parms.PolyModulus.Set("1x^2048 + 1");
parms.CoeffModulus.Set("7FFFFFFFFFFFFFFFFFF6A52B");
//parms.CoeffModulus.Set(ChooserEvaluator.DefaultParameterOptions[2048]);
parms.PlainModulus.Set(12289);
Console.WriteLine("Encryption parameters specify {0} coefficients with {1} bits per coefficient",
parms.PolyModulus.GetSignificantCoeffCount(), parms.CoeffModulus.GetSignificantBitCount());
// Create the PolyCRTBuilder
var crtbuilder = new PolyCRTBuilder(parms.PlainModulus, parms.PolyModulus);
int slotCount = crtbuilder.SlotCount;
// Create a list of values that are to be stored in the slots. We initialize all values to 0 at this point.
var values = new List <BigUInt>(slotCount);
for (int i = 0; i < slotCount; ++i)
{
values.Add(new BigUInt(parms.PlainModulus.BitCount, 0));
}
// Set the first few entries of the values list to be non-zero
values[0].Set(2);
values[1].Set(3);
values[2].Set(5);
values[3].Set(7);
values[4].Set(11);
values[5].Set(13);
// Now compose these into one polynomial using PolyCRTBuilder
Console.Write("Plaintext slot contents (slot, value): ");
for (int i = 0; i < 6; ++i)
{
string toWrite = "(" + i.ToString() + ", " + values[i].ToDecimalString() + ")";
toWrite += (i != 5) ? ", " : "\n";
Console.Write(toWrite);
}
var plainComposedPoly = crtbuilder.Compose(values);
// Let's do some homomorphic operations now. First we need all the encryption tools.
// Generate keys.
Console.WriteLine("Generating keys...");
var generator = new KeyGenerator(parms);
generator.Generate();
Console.WriteLine("... key generation completed");
var publicKey = generator.PublicKey;
var secretKey = generator.SecretKey;
// Create the encryption tools
var encryptor = new Encryptor(parms, publicKey);
var evaluator = new Evaluator(parms);
var decryptor = new Decryptor(parms, secretKey);
// Encrypt plainComposed_poly
Console.Write("Encrypting ... ");
var encryptedComposedPoly = encryptor.Encrypt(plainComposedPoly);
Console.WriteLine("done.");
// Let's square and then decrypt the encryptedComposedPoly
Console.Write("Squaring the encrypted polynomial ... ");
var encryptedSquare = evaluator.Exponentiate(encryptedComposedPoly, 2);
Console.WriteLine("done.");
Console.Write("Decrypting the squared polynomial ... ");
var plainSquare = decryptor.Decrypt(encryptedSquare);
Console.WriteLine("done.");
// Print the squared slots
Console.Write("Squared slot contents (slot, value): ");
for (int i = 0; i < 6; ++i)
{
string toWrite = "(" + i.ToString() + ", " + crtbuilder.GetSlot(plainSquare, i).ToDecimalString() + ")";
toWrite += (i != 5) ? ", " : "\n";
Console.Write(toWrite);
}
// Now let's try to multiply the squares with the plaintext coefficients (3, 1, 4, 1, 5, 9, 0, 0, ..., 0).
// First create the coefficient list
var plainCoeffList = new List <BigUInt>(slotCount);
for (int i = 0; i < slotCount; ++i)
{
plainCoeffList.Add(new BigUInt(parms.PlainModulus.BitCount, 0));
}
plainCoeffList[0].Set(3);
plainCoeffList[1].Set(1);
plainCoeffList[2].Set(4);
plainCoeffList[3].Set(1);
plainCoeffList[4].Set(5);
plainCoeffList[5].Set(9);
// Use PolyCRTBuilder to compose plainCoeffList into a polynomial
var plainCoeffPoly = crtbuilder.Compose(plainCoeffList);
// Print the coefficient list
Console.Write("Coefficient slot contents (slot, value): ");
for (int i = 0; i < 6; ++i)
{
string toWrite = "(" + i.ToString() + ", " + crtbuilder.GetSlot(plainCoeffPoly, i).ToDecimalString() + ")";
toWrite += (i != 5) ? ", " : "\n";
Console.Write(toWrite);
}
// Now use MultiplyPlain to multiply each encrypted slot with the corresponding coefficient
Console.Write("Multiplying squared slots with the coefficients ... ");
var encryptedScaledSquare = evaluator.MultiplyPlain(encryptedSquare, plainCoeffPoly);
Console.WriteLine(" done.");
// Decrypt it
Console.Write("Decrypting the scaled squared polynomial ... ");
var plainScaledSquare = decryptor.Decrypt(encryptedScaledSquare);
Console.WriteLine("done.");
// Print the scaled squared slots
Console.Write("Scaled squared slot contents (slot, value): ");
for (int i = 0; i < 6; ++i)
{
string toWrite = "(" + i.ToString() + ", " + crtbuilder.GetSlot(plainScaledSquare, i).ToDecimalString() + ")";
toWrite += (i != 5) ? ", " : "\n";
Console.Write(toWrite);
}
// How much noise did we end up with?
Console.WriteLine("Noise in the result: {0}/{1} bits", Utilities.InherentNoise(encryptedScaledSquare, parms, secretKey).GetSignificantBitCount(),
Utilities.InherentNoiseMax(parms).GetSignificantBitCount());
}
public void BatchUnbatchIntVectorNET()
{
var parms = new EncryptionParameters();
parms.PolyModulus = "1x^64 + 1";
parms.CoeffModulus = new List <SmallModulus> {
DefaultParams.SmallMods60Bit(0)
};
parms.PlainModulus = 257;
var context = new SEALContext(parms);
Assert.IsTrue(context.Qualifiers.EnableBatching);
var crtbuilder = new PolyCRTBuilder(context);
Assert.AreEqual(64, crtbuilder.SlotCount);
var plain_vec = new List <Int64>();
for (int i = 0; i < crtbuilder.SlotCount; i++)
{
plain_vec.Add((Int64)i * (1 - 2 * (i % 2)));
}
var plain = new Plaintext();
crtbuilder.Compose(plain_vec, plain);
var plain_vec2 = new List <Int64>();
crtbuilder.Decompose(plain, plain_vec2);
Assert.IsTrue(plain_vec.SequenceEqual(plain_vec2));
for (int i = 0; i < crtbuilder.SlotCount; i++)
{
plain_vec[i] = -5;
}
crtbuilder.Compose(plain_vec, plain);
Assert.IsTrue(plain.ToString().Equals("FC"));
crtbuilder.Decompose(plain, plain_vec2);
Assert.IsTrue(plain_vec.SequenceEqual(plain_vec2));
var short_plain_vec = new List <Int64>();
for (int i = 0; i < 20; i++)
{
short_plain_vec.Add((Int64)i * (1 - 2 * (i % 2)));
}
crtbuilder.Compose(short_plain_vec, plain);
var short_plain_vec2 = new List <Int64>();
crtbuilder.Decompose(plain, short_plain_vec2);
Assert.AreEqual(20, short_plain_vec.Count);
Assert.AreEqual(64, short_plain_vec2.Count);
for (int i = 0; i < 20; i++)
{
Assert.AreEqual(short_plain_vec[i], short_plain_vec2[i]);
}
for (int i = 20; i < crtbuilder.SlotCount; i++)
{
Assert.AreEqual(0L, short_plain_vec2[i]);
}
}