public void BalancedEncodeDecodeInt64NET()
{
var modulus = new SmallModulus(0x10000);
var encoder = new BalancedEncoder(modulus, 3, MemoryPoolHandle.New());
var poly = encoder.Encode(0L);
Assert.AreEqual(0, poly.SignificantCoeffCount());
Assert.IsTrue(poly.IsZero);
Assert.AreEqual(0L, encoder.DecodeInt64(poly));
var poly1 = encoder.Encode(1L);
Assert.AreEqual(1, poly1.SignificantCoeffCount());
Assert.AreEqual("1", poly1.ToString());
Assert.AreEqual(1L, encoder.DecodeInt64(poly1));
var poly2 = encoder.Encode(2L);
Assert.AreEqual(2, poly2.SignificantCoeffCount());
Assert.AreEqual("1x^1 + FFFF", poly2.ToString());
Assert.AreEqual(2L, encoder.DecodeInt64(poly2));
var poly3 = encoder.Encode(3L);
Assert.AreEqual(2, poly3.SignificantCoeffCount());
Assert.AreEqual("1x^1", poly3.ToString());
Assert.AreEqual(3L, encoder.DecodeInt64(poly3));
var poly4 = encoder.Encode(-1L);
Assert.AreEqual(1, poly4.SignificantCoeffCount());
Assert.AreEqual("FFFF", poly4.ToString());
Assert.AreEqual(-1L, encoder.DecodeInt64(poly4));
var poly5 = encoder.Encode(-2L);
Assert.AreEqual(2, poly5.SignificantCoeffCount());
Assert.AreEqual("FFFFx^1 + 1", poly5.ToString());
Assert.AreEqual(-2L, encoder.DecodeInt64(poly5));
var poly6 = encoder.Encode(-3L);
Assert.AreEqual(2, poly6.SignificantCoeffCount());
Assert.AreEqual("FFFFx^1", poly6.ToString());
Assert.AreEqual(-3L, encoder.DecodeInt64(poly6));
var poly7 = encoder.Encode(-0x2671L);
Assert.AreEqual(9, poly7.SignificantCoeffCount());
for (int i = 0; i < 9; ++i)
{
Assert.AreEqual(0xFFFFUL, poly7[i]);
}
Assert.AreEqual(-0x2671L, encoder.DecodeInt64(poly7));
var poly8 = encoder.Encode(-4374L);
Assert.AreEqual(9, poly8.SignificantCoeffCount());
Assert.AreEqual(0xFFFFUL, poly8[8]);
Assert.AreEqual(1UL, poly8[7]);
for (int i = 0; i < 7; ++i)
{
Assert.IsTrue(poly8[i] == 0);
}
Assert.AreEqual(-4374L, encoder.DecodeInt64(poly8));
var poly9 = encoder.Encode(-0xD4EBL);
Assert.AreEqual(11, poly9.SignificantCoeffCount());
for (int i = 0; i < 11; ++i)
{
if (i % 3 == 1)
{
Assert.AreEqual(0xFFFFUL, poly9[i]);
}
else if (i % 3 == 0)
{
Assert.IsTrue(poly9[i] == 0);
}
else
{
Assert.AreEqual(1UL, poly9[i]);
}
}
Assert.AreEqual(-0xD4EBL, encoder.DecodeInt64(poly9));
var poly10 = encoder.Encode(-30724L);
Assert.AreEqual(11, poly10.SignificantCoeffCount());
Assert.AreEqual(0xFFFFUL, poly10[10]);
Assert.AreEqual(1UL, poly10[9]);
Assert.AreEqual(1UL, poly10[8]);
Assert.AreEqual(1UL, poly10[7]);
Assert.IsTrue(poly10[6] == 0);
Assert.IsTrue(poly10[5] == 0);
Assert.AreEqual(0xFFFFUL, poly10[4]);
Assert.AreEqual(0xFFFFUL, poly10[3]);
Assert.IsTrue(poly10[2] == 0);
Assert.AreEqual(1UL, poly10[1]);
Assert.AreEqual(0xFFFFUL, poly10[0]);
Assert.AreEqual(-30724L, encoder.DecodeInt64(poly10));
var encoder2 = new BalancedEncoder(modulus, 13, MemoryPoolHandle.New());
var poly11 = encoder2.Encode(-126375543984L);
Assert.AreEqual(11, poly11.SignificantCoeffCount());
Assert.AreEqual(0xFFFFUL, poly11[10]);
Assert.AreEqual(1UL, poly11[9]);
Assert.AreEqual(1UL, poly11[8]);
Assert.AreEqual(1UL, poly11[7]);
Assert.IsTrue(poly11[6] == 0);
Assert.IsTrue(poly11[5] == 0);
Assert.AreEqual(0xFFFFUL, poly11[4]);
Assert.AreEqual(0xFFFFUL, poly11[3]);
Assert.IsTrue(poly11[2] == 0);
Assert.AreEqual(1UL, poly11[1]);
Assert.AreEqual(0xFFFFUL, poly11[0]);
Assert.AreEqual(-126375543984L, encoder2.DecodeInt64(poly11));
modulus.Set(0xFFFF);
var encoder3 = new BalancedEncoder(modulus, 7, MemoryPoolHandle.New());
var poly12 = new Plaintext(6);
poly12[0] = 1;
poly12[1] = 0xFFFE; // -1
poly12[2] = 0xFFFD; // -2
poly12[3] = 0x8000; // -32767
poly12[4] = 0x7FFF; // 32767
poly12[5] = 0x7FFE; // 32766
Assert.AreEqual(1L + -1 * 7 + -2 * 49 + -32767 * 343 + 32767 * 2401 + 32766 * 16807, encoder3.DecodeInt64(poly12));
var encoder4 = new BalancedEncoder(modulus, 6, MemoryPoolHandle.New());
poly8 = new Plaintext(4);
poly8[0] = 5;
poly8[1] = 4;
poly8[2] = 3;
poly8[3] = (modulus.Value - 2);
Int64 value = 5 + 4 * 6 + 3 * 36 - 2 * 216;
Assert.AreEqual(value, encoder4.DecodeInt64(poly8));
var encoder5 = new BalancedEncoder(modulus, 10, MemoryPoolHandle.New());
poly9 = new Plaintext(4);
poly9[0] = 1;
poly9[1] = 2;
poly9[2] = 3;
poly9[3] = 4;
value = 4321;
Assert.AreEqual(value, encoder5.DecodeInt64(poly9));
value = -1234;
poly10.Set(encoder3.Encode(value));
Assert.AreEqual(5, poly10.SignificantCoeffCount());
Assert.IsTrue(value.Equals(encoder3.DecodeInt64(poly10)));
value = -1234;
poly11.Set(encoder4.Encode(value));
Assert.AreEqual(5, poly11.SignificantCoeffCount());
Assert.IsTrue(value.Equals(encoder4.DecodeInt64(poly11)));
value = -1234;
poly12.Set(encoder5.Encode(value));
Assert.AreEqual(4, poly12.SignificantCoeffCount());
Assert.IsTrue(value.Equals(encoder5.DecodeInt64(poly12)));
}
public void BalancedEncodeDecodeInt64NET()
{
var modulus = new BigUInt("10000");
var encoder = new BalancedEncoder(modulus, 3);
var poly = encoder.Encode(0L);
Assert.AreEqual(0, poly.GetSignificantCoeffCount());
Assert.IsTrue(poly.IsZero);
Assert.AreEqual(0L, encoder.DecodeInt64(poly));
var poly1 = encoder.Encode(1L);
Assert.AreEqual(1, poly1.GetSignificantCoeffCount());
Assert.AreEqual(modulus.BitCount, poly1.CoeffBitCount);
Assert.AreEqual("1", poly1.ToString());
Assert.AreEqual(1L, encoder.DecodeInt64(poly1));
var poly2 = encoder.Encode(2L);
Assert.AreEqual(2, poly2.GetSignificantCoeffCount());
Assert.AreEqual(modulus.BitCount, poly2.CoeffBitCount);
Assert.AreEqual("1x^1 + FFFF", poly2.ToString());
Assert.AreEqual(2L, encoder.DecodeInt64(poly2));
var poly3 = encoder.Encode(3L);
Assert.AreEqual(2, poly3.GetSignificantCoeffCount());
Assert.AreEqual(modulus.BitCount, poly3.CoeffBitCount);
Assert.AreEqual("1x^1", poly3.ToString());
Assert.AreEqual(3L, encoder.DecodeInt64(poly3));
var poly4 = encoder.Encode(-1L);
Assert.AreEqual(1, poly4.GetSignificantCoeffCount());
Assert.AreEqual(modulus.BitCount, poly4.CoeffBitCount);
Assert.AreEqual("FFFF", poly4.ToString());
Assert.AreEqual(-1L, encoder.DecodeInt64(poly4));
var poly5 = encoder.Encode(-2L);
Assert.AreEqual(2, poly5.GetSignificantCoeffCount());
Assert.AreEqual(modulus.BitCount, poly5.CoeffBitCount);
Assert.AreEqual("FFFFx^1 + 1", poly5.ToString());
Assert.AreEqual(-2L, encoder.DecodeInt64(poly5));
var poly6 = encoder.Encode(-3L);
Assert.AreEqual(2, poly6.GetSignificantCoeffCount());
Assert.AreEqual(modulus.BitCount, poly6.CoeffBitCount);
Assert.AreEqual("FFFFx^1", poly6.ToString());
Assert.AreEqual(-3L, encoder.DecodeInt64(poly6));
var poly7 = encoder.Encode(-0x2671L);
Assert.AreEqual(9, poly7.GetSignificantCoeffCount());
Assert.AreEqual(modulus.BitCount, poly7.CoeffBitCount);
for (int i = 0; i < 9; ++i)
{
Assert.AreEqual("FFFF", poly7[i].ToString());
}
Assert.AreEqual(-0x2671L, encoder.DecodeInt64(poly7));
var poly8 = encoder.Encode(-4374L);
Assert.AreEqual(9, poly8.GetSignificantCoeffCount());
Assert.AreEqual(modulus.BitCount, poly8.CoeffBitCount);
Assert.AreEqual("FFFF", poly8[8].ToString());
Assert.AreEqual("1", poly8[7].ToString());
for (int i = 0; i < 7; ++i)
{
Assert.IsTrue(poly8[i].IsZero);
}
Assert.AreEqual(-4374L, encoder.DecodeInt64(poly8));
var poly9 = encoder.Encode(-0xD4EBL);
Assert.AreEqual(11, poly9.GetSignificantCoeffCount());
Assert.AreEqual(modulus.BitCount, poly9.CoeffBitCount);
for (int i = 0; i < 11; ++i)
{
if (i % 3 == 1)
{
Assert.AreEqual("FFFF", poly9[i].ToString());
}
else if (i % 3 == 0)
{
Assert.IsTrue(poly9[i].IsZero);
}
else
{
Assert.AreEqual("1", poly9[i].ToString());
}
}
Assert.AreEqual(-0xD4EBL, encoder.DecodeInt64(poly9));
var poly10 = encoder.Encode(-30724L);
Assert.AreEqual(11, poly10.GetSignificantCoeffCount());
Assert.AreEqual(modulus.BitCount, poly10.CoeffBitCount);
Assert.AreEqual("FFFF", poly10[10].ToString());
Assert.AreEqual("1", poly10[9].ToString());
Assert.AreEqual("1", poly10[8].ToString());
Assert.AreEqual("1", poly10[7].ToString());
Assert.IsTrue(poly10[6].IsZero);
Assert.IsTrue(poly10[5].IsZero);
Assert.AreEqual("FFFF", poly10[4].ToString());
Assert.AreEqual("FFFF", poly10[3].ToString());
Assert.IsTrue(poly10[2].IsZero);
Assert.AreEqual("1", poly10[1].ToString());
Assert.AreEqual("FFFF", poly10[0].ToString());
Assert.AreEqual(-30724L, encoder.DecodeInt64(poly10));
var encoder2 = new BalancedEncoder(modulus, 13);
var poly11 = encoder2.Encode(-126375543984L);
Assert.AreEqual(11, poly11.GetSignificantCoeffCount());
Assert.AreEqual(modulus.BitCount, poly11.CoeffBitCount);
Assert.AreEqual("FFFF", poly11[10].ToString());
Assert.AreEqual("1", poly11[9].ToString());
Assert.AreEqual("1", poly11[8].ToString());
Assert.AreEqual("1", poly11[7].ToString());
Assert.IsTrue(poly11[6].IsZero);
Assert.IsTrue(poly11[5].IsZero);
Assert.AreEqual("FFFF", poly11[4].ToString());
Assert.AreEqual("FFFF", poly11[3].ToString());
Assert.IsTrue(poly11[2].IsZero);
Assert.AreEqual("1", poly11[1].ToString());
Assert.AreEqual("FFFF", poly11[0].ToString());
Assert.AreEqual(-126375543984L, encoder2.DecodeInt64(poly11));
modulus.Set("FFFF");
var encoder3 = new BalancedEncoder(modulus, 7);
var poly12 = new BigPoly(6, 16);
poly12[0].Set(1);
poly12[1].Set("FFFE"); // -1
poly12[2].Set("FFFD"); // -2
poly12[3].Set("8000"); // -32767
poly12[4].Set("7FFF"); // 32767
poly12[5].Set("7FFE"); // 32766
Assert.AreEqual(1L + -1 * 7 + -2 * 49 + -32767 * 343 + 32767 * 2401 + 32766 * 16807, encoder3.DecodeInt64(poly12));
}
public static void ExampleParameterSelection()
{
PrintExampleBanner("Example: Automatic Parameter Selection");
/*
* Here we demonstrate the automatic parameter selection tool. Suppose we want to find parameters
* that are optimized in a way that allows us to evaluate the polynomial 42x^3-27x+1. We need to know
* the size of the input data, so let's assume that x is an integer with base-3 representation of length
* at most 10.
*/
Console.Write("Finding optimized parameters for computing 42x^3-27x+1 ... ");
var chooserEncoder = new ChooserEncoder();
var chooserEvaluator = new ChooserEvaluator();
/*
* First create a ChooserPoly representing the input data. You can think of this modeling a freshly
* encrypted cipheretext of a plaintext polynomial with length at most 10 coefficients, where the
* coefficients have absolute value at most 1.
*/
var cinput = new ChooserPoly(10, 1);
// Compute the first term
var ccubedInput = chooserEvaluator.Exponentiate(cinput, 3);
var cterm1 = chooserEvaluator.MultiplyPlain(ccubedInput, chooserEncoder.Encode(42));
// Compute the second term
var cterm2 = chooserEvaluator.MultiplyPlain(cinput, chooserEncoder.Encode(27));
// Subtract the first two terms
var csum12 = chooserEvaluator.Sub(cterm1, cterm2);
// Add the constant term 1
var cresult = chooserEvaluator.AddPlain(csum12, chooserEncoder.Encode(1));
// To find an optimized set of parameters, we use ChooserEvaluator::select_parameters(...).
var optimalParms = new EncryptionParameters();
chooserEvaluator.SelectParameters(cresult, optimalParms);
Console.WriteLine("done.");
// Let's print these to see what was recommended
Console.WriteLine("Selected parameters:");
Console.WriteLine("{{ poly_modulus: {0}", optimalParms.PolyModulus);
Console.WriteLine("{{ coeff_modulus: {0}", optimalParms.CoeffModulus);
Console.WriteLine("{{ plain_modulus: {0}", optimalParms.PlainModulus.ToDecimalString());
Console.WriteLine("{{ decomposition_bit_count: {0}", optimalParms.DecompositionBitCount);
Console.WriteLine("{{ noise_standard_deviation: {0}", optimalParms.NoiseStandardDeviation);
Console.WriteLine("{{ noise_max_deviation: {0}", optimalParms.NoiseMaxDeviation);
// Let's try to actually perform the homomorphic computation using the recommended parameters.
// Generate keys.
Console.WriteLine("Generating keys...");
var generator = new KeyGenerator(optimalParms);
generator.Generate();
Console.WriteLine("... key generation completed");
var publicKey = generator.PublicKey;
var secretKey = generator.SecretKey;
// Create the encoding/encryption tools
var encoder = new BalancedEncoder(optimalParms.PlainModulus);
var encryptor = new Encryptor(optimalParms, publicKey);
var evaluator = new Evaluator(optimalParms);
var decryptor = new Decryptor(optimalParms, secretKey);
// Now perform the computations on real encrypted data.
const int inputValue = 12345;
var plainInput = encoder.Encode(inputValue);
Console.WriteLine("Encoded {0} as polynomial {1}", inputValue, plainInput);
Console.Write("Encrypting ... ");
var input = encryptor.Encrypt(plainInput);
Console.WriteLine("done.");
// Compute the first term
Console.Write("Computing first term ... ");
var cubedInput = evaluator.Exponentiate(input, 3);
var term1 = evaluator.MultiplyPlain(cubedInput, encoder.Encode(42));
Console.WriteLine("done.");
// Compute the second term
Console.Write("Computing second term ... ");
var term2 = evaluator.MultiplyPlain(input, encoder.Encode(27));
Console.WriteLine("done.");
// Subtract the first two terms
Console.Write("Subtracting first two terms ... ");
var sum12 = evaluator.Sub(term1, term2);
Console.WriteLine("done.");
// Add the constant term 1
Console.Write("Adding one ... ");
var result = evaluator.AddPlain(sum12, encoder.Encode(1));
Console.WriteLine("done.");
// Decrypt and decode
Console.Write("Decrypting ... ");
var plainResult = decryptor.Decrypt(result);
Console.WriteLine("done.");
// Finally print the result
Console.WriteLine("Polynomial 42x^3-27x+1 evaluated at x=12345: {0}", encoder.DecodeInt64(plainResult));
// How much noise did we end up with?
Console.WriteLine("Noise in the result: {0}/{1} bits", Utilities.InherentNoise(result, optimalParms, secretKey).GetSignificantBitCount(),
Utilities.InherentNoiseMax(optimalParms).GetSignificantBitCount());
}