public void PrimesGeneratorTestMethod()
{
var pluginInstance = TestHelpers.GetPluginInstance("PrimesGenerator");
var scenario = new PluginTestScenario(pluginInstance, new[] { "n", ".Mode" }, new[] { "OutputString" });
foreach (TestVector vector in testvectors)
{
if (vector.mode <= 2)
{
for (int i = 0; i < vector.count; i++)
{
object[] output = scenario.GetOutputs(new object[] { vector.input, vector.mode });
Assert.IsTrue(BigIntegerHelper.IsProbablePrime((BigInteger)output[0]), (BigInteger)output[0] + " is not a prime number in test #" + vector.n + ".");
}
}
else
{
object[] output = scenario.GetOutputs(new object[] { vector.input, vector.mode });
Assert.AreEqual(vector.output, output[0], "Unexpected value in test #" + vector.n + ".");
}
}
}
private void DoCalculateGoldbach(object o)
{
if (o == null || o.GetType() != typeof(PrimesBigInteger))
{
return;
}
PrimesBigInteger value = o as PrimesBigInteger;
if (value.Mod(PrimesBigInteger.Two).Equals(PrimesBigInteger.One)) // value is odd
{
ControlHandler.SetPropertyValue(lblGoldbachInfoCalc, "Text", string.Format(Distribution.numberline_isodd, value));
ControlHandler.SetPropertyValue(gbGoldbach, "Visibility", Visibility.Collapsed);
}
else if (value.Equals(PrimesBigInteger.Two)) // value = 2
{
ControlHandler.SetPropertyValue(lblGoldbachInfoCalc, "Text", Distribution.numberline_istwo);
ControlHandler.SetPropertyValue(gbGoldbach, "Visibility", Visibility.Collapsed);
}
else // value is even and not prime
{
int counter = 0;
int maxlines = 1000;
if (!value.IsProbablePrime(10))
{
long x = value.LongValue;
int i = 0;
long sum1 = PrimeNumbers.primes[i];
while (sum1 <= x / 2)
{
long sum2 = x - sum1;
if (BigIntegerHelper.IsProbablePrime(sum2))
//if (PrimeNumbers.isprime.Contains(sum2))
{
counter++;
if (counter < maxlines)
{
logGoldbach.Info(string.Format("{0} + {1} ", sum1, sum2));
}
else if (counter == maxlines)
{
logGoldbach.Info(string.Format(Distribution.numberline_goldbachmaxlines, maxlines));
}
if (counter % 50 == 0)
{
string fmt = (counter == 1) ? Distribution.numberline_goldbachfoundsum : Distribution.numberline_goldbachfoundsums;
ControlHandler.SetPropertyValue(lblGoldbachInfoCalc, "Text", string.Format(fmt, counter, value));
}
}
sum1 = (++i < PrimeNumbers.primes.Length) ? PrimeNumbers.primes[i] : (long)BigIntegerHelper.NextProbablePrime(sum1 + 1);
}
string fmt1 = (counter == 1) ? Distribution.numberline_goldbachfoundsum : Distribution.numberline_goldbachfoundsums;
ControlHandler.SetPropertyValue(lblGoldbachInfoCalc, "Text", string.Format(fmt1, counter, value));
ControlHandler.SetPropertyValue(gbGoldbach, "Visibility", goldbachIsOpen ? Visibility.Visible : Visibility.Collapsed);
}
}
if (GoldbachDone != null)
{
GoldbachDone();
}
}
/// <summary>
/// Called by the environment to start generating of public/private keys
/// </summary>
public void Execute()
{
BigInteger p;
BigInteger q;
BigInteger n;
BigInteger e;
BigInteger d;
ProgressChanged(0.0, 1.0);
switch (settings.Source)
{
// manual
case 0:
try
{
p = BigIntegerHelper.ParseExpression(settings.P);
q = BigIntegerHelper.ParseExpression(settings.Q);
e = BigIntegerHelper.ParseExpression(settings.E);
if (!BigIntegerHelper.IsProbablePrime(p))
{
GuiLogMessage(p.ToString() + " is not prime!", NotificationLevel.Error);
return;
}
if (!BigIntegerHelper.IsProbablePrime(q))
{
GuiLogMessage(q.ToString() + " is not prime!", NotificationLevel.Error);
return;
}
if (p == q)
{
GuiLogMessage("The primes P and Q can not be equal!", NotificationLevel.Error);
return;
}
}
catch (Exception ex)
{
GuiLogMessage("Invalid Big Number input: " + ex.Message, NotificationLevel.Error);
return;
}
try
{
D = BigIntegerHelper.ModInverse(e, (p - 1) * (q - 1));
}
catch (Exception)
{
GuiLogMessage("RSAKeyGenerator Error: E (" + e + ") can not be inverted.", NotificationLevel.Error);
return;
}
try
{
N = p * q;
E = e;
}
catch (Exception ex)
{
GuiLogMessage("Big Number fail: " + ex.Message, NotificationLevel.Error);
return;
}
break;
case 1:
try
{
n = BigIntegerHelper.ParseExpression(settings.N);
d = BigIntegerHelper.ParseExpression(settings.D);
e = BigIntegerHelper.ParseExpression(settings.E);
}
catch (Exception ex)
{
GuiLogMessage("Invalid Big Number input: " + ex.Message, NotificationLevel.Error);
return;
}
try
{
N = n;
E = e;
D = d;
}
catch (Exception ex)
{
GuiLogMessage("Big Number fail: " + ex.Message, NotificationLevel.Error);
return;
}
break;
//randomly generated
case 2:
try
{
n = BigInteger.Parse(this.settings.Range);
switch (this.settings.RangeType)
{
case 0: // n = number of bits for primes
if ((int)n <= 2)
{
GuiLogMessage("Value for n has to be greater than 2.", NotificationLevel.Error);
return;
}
if (n >= 1024)
{
GuiLogMessage("Please note that the generation of prime numbers with " + n + " bits may take some time...", NotificationLevel.Warning);
}
// calculate the number of expected tries for the indeterministic prime number generation using the density of primes in the given region
BigInteger limit = ((BigInteger)1) << (int)n;
limittries = (int)(BigInteger.Log(limit) / 6);
expectedtries = 2 * limittries;
tries = 0;
p = this.RandomPrimeBits((int)n);
tries = limittries; limittries = expectedtries;
do
{
q = this.RandomPrimeBits((int)n);
} while (p == q);
break;
case 1: // n = upper limit for primes
default:
if (n <= 4)
{
GuiLogMessage("Value for n has to be greater than 4", NotificationLevel.Error);
return;
}
p = BigIntegerHelper.RandomPrimeLimit(n + 1);
ProgressChanged(0.5, 1.0);
do
{
q = BigIntegerHelper.RandomPrimeLimit(n + 1);
} while (p == q);
break;
}
}
catch
{
GuiLogMessage("Please enter an integer value for n.", NotificationLevel.Error);
return;
}
BigInteger phi = (p - 1) * (q - 1);
// generate E for the given values of p and q
bool found = false;
foreach (var ee in new BigInteger[] { 3, 5, 7, 11, 17, 65537 })
{
if (ee < phi && ee.GCD(phi) == 1)
{
E = ee; found = true; break;
}
}
if (!found)
{
for (int i = 0; i < 1000; i++)
{
e = BigIntegerHelper.RandomIntLimit(phi);
if (e >= 2 && e.GCD(phi) == 1)
{
E = e; found = true; break;
}
}
}
if (!found)
{
GuiLogMessage("Could not generate a valid E for p=" + p + " and q=" + q + ".", NotificationLevel.Error);
return;
}
N = p * q;
D = BigIntegerHelper.ModInverse(E, phi);
break;
//using x509 certificate
case 3:
try
{
X509Certificate2 cert;
RSAParameters par;
if (this.settings.Password != "")
{
GuiLogMessage("Password entered. Try getting public and private key", NotificationLevel.Info);
cert = new X509Certificate2(settings.CertificateFile, settings.Password, X509KeyStorageFlags.Exportable);
if (cert == null || cert.PrivateKey == null)
{
throw new Exception("Private Key of X509Certificate could not be fetched");
}
RSACryptoServiceProvider provider = (RSACryptoServiceProvider)cert.PrivateKey;
par = provider.ExportParameters(true);
}
else
{
GuiLogMessage("No Password entered. Try loading public key only", NotificationLevel.Info);
cert = new X509Certificate2(settings.CertificateFile);
if (cert == null || cert.PublicKey == null || cert.PublicKey.Key == null)
{
throw new Exception("Private Key of X509Certificate could not be fetched");
}
RSACryptoServiceProvider provider = (RSACryptoServiceProvider)cert.PublicKey.Key;
par = provider.ExportParameters(false);
}
try
{
N = new BigInteger(par.Modulus);
}
catch (Exception ex)
{
GuiLogMessage("Could not get N from certificate: " + ex.Message, NotificationLevel.Warning);
}
try
{
E = new BigInteger(par.Exponent);
}
catch (Exception ex)
{
GuiLogMessage("Could not get E from certificate: " + ex.Message, NotificationLevel.Warning);
}
try
{
if (this.settings.Password != "")
{
D = new BigInteger(par.D);
}
else
{
D = 0;
}
}
catch (Exception ex)
{
GuiLogMessage("Could not get D from certificate: " + ex.Message, NotificationLevel.Warning);
}
}
catch (Exception ex)
{
GuiLogMessage("Could not load the selected certificate: " + ex.Message, NotificationLevel.Error);
}
break;
}
ProgressChanged(1.0, 1.0);
}
/// <summary>
/// Called by the environment to start generating of public/private keys
/// </summary>
public void Execute()
{
BigInteger p = 1, q = 1;
ProgressChanged(0, 1);
switch (settings.Source)
{
// manually enter primes
case 0:
try
{
p = BigIntegerHelper.ParseExpression(settings.P);
q = BigIntegerHelper.ParseExpression(settings.Q);
if (!BigIntegerHelper.IsProbablePrime(p))
{
GuiLogMessage(p.ToString() + " is not prime!", NotificationLevel.Error);
return;
}
if (!BigIntegerHelper.IsProbablePrime(q))
{
GuiLogMessage(q.ToString() + " is not prime!", NotificationLevel.Error);
return;
}
if (p == q)
{
GuiLogMessage("The primes P and Q can not be equal!", NotificationLevel.Error);
return;
}
}
catch (Exception ex)
{
GuiLogMessage("Invalid Big Number input: " + ex.Message, NotificationLevel.Error);
return;
}
break;
//randomly generated primes
case 1:
try
{
int keyBitLength = Convert.ToInt32(settings.KeyBitLength);
if (keyBitLength < 4)
{
GuiLogMessage("The keylength must be greater than 3.", NotificationLevel.Error);
return;
}
int i, maxtries = 10;
for (i = 0; i < maxtries; i++)
{
p = BigIntegerHelper.RandomPrimeMSBSet(keyBitLength - (keyBitLength / 2));
q = BigIntegerHelper.RandomPrimeMSBSet(keyBitLength / 2);
//GuiLogMessage("p = " + p.ToString(), NotificationLevel.Info);
//GuiLogMessage("q = " + q.ToString(), NotificationLevel.Info);
if (p != q)
{
break;
}
}
if (i == maxtries)
{
throw new Exception("Could not create two differing primes");
}
}
catch (Exception ex)
{
GuiLogMessage(ex.Message, NotificationLevel.Error);
return;
}
break;
default:
throw new Exception("Illegal Key Generation Mode");
}
N = p * q;
G = N + 1;
Lambda = (p - 1) * (q - 1);
ProgressChanged(1, 1);
}
private void generateKeys(int k, int t, int l, BigInteger ownu)
{
if (l < 8 || l > 16)
{
throw new Exception("Choose parameter l from the interval 8<=l<=16 !");
}
if (t <= l)
{
throw new Exception("Parameter t must be greater than l.");
}
if (k <= t)
{
throw new Exception("Parameter k must be greater than t.");
}
if (k % 2 != 0)
{
throw new Exception("Parameter k has to be an even number!");
}
//if ((k / 2 < (l + 5)) || (k / 2 < t + 2))
// throw new Exception("Parameter k has to be specified by the rules k/2 > l+4 and k/2 > t+1!");
if (k / 2 < l + t + 10)
{
throw new Exception("Choose parameters k,l,t so that k/2 >= l+t+10 !");
}
// generate u the minimal prime number greater than l+2
//Workaround, TODO:
//u = (l == 0) ? ownu : BigIntegerHelper.NextProbablePrime(l + l + 2);
u = BigIntegerHelper.NextProbablePrime((1 << l) + 2);
// generate vp, vq as a random t bit prime number
vp = BigIntegerHelper.RandomPrimeBits(t);
vq = BigIntegerHelper.RandomPrimeBits(t);
// store the product vp*vq
vpvq = vp * vq;
// DGK style to generate p and q from u and v:
// p is chosen as rp * u * vp + 1 where r_p is randomly chosen such that p has roughly k/2 bits
BigInteger rp, rq, tmp;
int needed_bits;
tmp = u * vp;
needed_bits = k / 2 - (int)Math.Ceiling(BigInteger.Log(tmp, 2));
//int needed_bits = k / 2 - mpz_sizeinbase(tmp1, 2);
do
{
rp = BigIntegerHelper.RandomIntMSBSet(needed_bits - 1) * 2;
p = rp * tmp + 1;
} while (!BigIntegerHelper.IsProbablePrime(p));
// q is chosen as rq * u*vq + 1 where rq is randomly chosen such that q has roughly k/2 bits
tmp = u * vq;
needed_bits = k / 2 - (int)Math.Ceiling(BigInteger.Log(tmp, 2));
do
{
rq = BigIntegerHelper.RandomIntMSBSet(needed_bits - 1) * 2;
q = rq * tmp + 1;
} while (!BigIntegerHelper.IsProbablePrime(q));
// RSA modulus n
N = p * q;
/*
* h must be random in Zn* and have order vp*vq. We
* choose it by setting
*
* h = h' ^{rp * rq * u}.
*
* Seeing h as (hp, hq) and h' as (h'p, h'q) in Zp* x Zq*, we
* then have
*
* (hp^vpvq, hq^vpvq) = (h'p^{rp*u*vp}^(rq*vq), h'q^{rq*u*vq}^(rp*vp))
* = (1^(rq*vq), 1^(rp*vp)) = (1, 1)
*
* which means that h^(vpvq) = 1 in Zn*.
*
* So we only need to check that h is not 1 and that it really
* is in Zn*.
*/
BigInteger r;
tmp = rp * rq * u;
while (true)
{
r = BigIntegerHelper.RandomIntLimit(n);
h = BigInteger.ModPow(r, tmp, n);
if (h == 1)
{
continue;
}
if (BigInteger.GreatestCommonDivisor(h, n) == 1)
{
break;
}
}
/*
* g is chosen at random in Zn* such that it has order uv. This
* is done in much the same way as for h, but the order of
* power of the random number might be u, v or uv. We therefore
* also check that g^u and g^v are different from 1.
*/
BigInteger rprq = rp * rq;
while (true)
{
r = BigIntegerHelper.RandomIntLimit(n);
g = BigInteger.ModPow(r, rprq, n);
// test if g is "good":
if (g == 1)
{
continue;
}
if (BigInteger.GreatestCommonDivisor(g, n) != 1)
{
continue;
}
if (BigInteger.ModPow(g, u, n) == 1)
{
continue; // test if ord(g) == u
}
if (BigInteger.ModPow(g, vp, n) == 1)
{
continue; // test if ord(g) == vp
}
if (BigInteger.ModPow(g, vq, n) == 1)
{
continue; // test if ord(g) == vq
}
if (BigInteger.ModPow(g, u * vp, n) == 1)
{
continue; // test if ord(g) == u*vp
}
if (BigInteger.ModPow(g, u * vq, n) == 1)
{
continue; // test if ord(g) == u*vq
}
if (BigInteger.ModPow(g, vpvq, n) == 1)
{
continue; // test if ord(g) == vp*vq
}
break; // g has passed all tests
}
}
