/*
* (non-Javadoc)
*
* @see org.bouncycastle.crypto.AsymmetricCipherKeyPairGenerator#generateKeyPair()
*/
public IAsymmetricCipherKeyPair GenerateKeyPair()
{
int strength = param.Strength;
ISecureRandom rand = param.Random;
int certainty = param.Certainty;
bool debug = param.IsDebug;
#if !NETFX_CORE
if (debug)
{
Console.WriteLine("Fetching first " + param.CountSmallPrimes + " primes.");
}
#endif
IList smallPrimes = findFirstPrimes(param.CountSmallPrimes);
smallPrimes = PermuteList(smallPrimes, rand);
IBigInteger u = BigInteger.One;
IBigInteger v = BigInteger.One;
for (int i = 0; i < smallPrimes.Count / 2; i++)
{
u = u.Multiply((BigInteger)smallPrimes[i]);
}
for (int i = smallPrimes.Count / 2; i < smallPrimes.Count; i++)
{
v = v.Multiply((BigInteger)smallPrimes[i]);
}
IBigInteger sigma = u.Multiply(v);
// n = (2 a u _p + 1 ) ( 2 b v _q + 1)
// -> |n| = strength
// |2| = 1 in bits
// -> |a| * |b| = |n| - |u| - |v| - |_p| - |_q| - |2| -|2|
// remainingStrength = strength - sigma.bitLength() - _p.bitLength() -
// _q.bitLength() - 1 -1
int remainingStrength = strength - sigma.BitLength - 48;
IBigInteger a = GeneratePrime(remainingStrength / 2 + 1, certainty, rand);
IBigInteger b = GeneratePrime(remainingStrength / 2 + 1, certainty, rand);
IBigInteger _p;
IBigInteger _q;
IBigInteger p;
IBigInteger q;
long tries = 0;
#if !NETFX_CORE
if (debug)
{
Console.WriteLine("generating p and q");
}
#endif
IBigInteger _2au = a.Multiply(u).ShiftLeft(1);
IBigInteger _2bv = b.Multiply(v).ShiftLeft(1);
for (; ;)
{
tries++;
_p = GeneratePrime(24, certainty, rand);
p = _p.Multiply(_2au).Add(BigInteger.One);
if (!p.IsProbablePrime(certainty))
{
continue;
}
for (; ;)
{
_q = GeneratePrime(24, certainty, rand);
if (_p.Equals(_q))
{
continue;
}
q = _q.Multiply(_2bv).Add(BigInteger.One);
if (q.IsProbablePrime(certainty))
{
break;
}
}
if (!sigma.Gcd(_p.Multiply(_q)).Equals(BigInteger.One))
{
#if !NETFX_CORE
Console.WriteLine("sigma.gcd(_p.mult(_q)) != 1!\n _p: " + _p + "\n _q: " + _q);
#endif
continue;
}
if (p.Multiply(q).BitLength < strength)
{
#if !NETFX_CORE
if (debug)
{
Console.WriteLine("key size too small. Should be " + strength + " but is actually "
+ p.Multiply(q).BitLength);
}
#endif
continue;
}
break;
}
#if !NETFX_CORE
if (debug)
{
Console.WriteLine("needed " + tries + " tries to generate p and q.");
}
#endif
IBigInteger n = p.Multiply(q);
IBigInteger phi_n = p.Subtract(BigInteger.One).Multiply(q.Subtract(BigInteger.One));
IBigInteger g;
tries = 0;
#if !NETFX_CORE
if (debug)
{
Console.WriteLine("generating g");
}
#endif
for (; ;)
{
// TODO After the first loop, just regenerate one randomly-selected gPart each time?
IList gParts = Platform.CreateArrayList();
for (int ind = 0; ind != smallPrimes.Count; ind++)
{
IBigInteger i = (BigInteger)smallPrimes[ind];
IBigInteger e = phi_n.Divide(i);
for (; ;)
{
tries++;
g = GeneratePrime(strength, certainty, rand);
if (!g.ModPow(e, n).Equals(BigInteger.One))
{
gParts.Add(g);
break;
}
}
}
g = BigInteger.One;
for (int i = 0; i < smallPrimes.Count; i++)
{
IBigInteger gPart = (BigInteger)gParts[i];
IBigInteger smallPrime = (BigInteger)smallPrimes[i];
g = g.Multiply(gPart.ModPow(sigma.Divide(smallPrime), n)).Mod(n);
}
// make sure that g is not divisible by p_i or q_i
bool divisible = false;
for (int i = 0; i < smallPrimes.Count; i++)
{
if (g.ModPow(phi_n.Divide((BigInteger)smallPrimes[i]), n).Equals(BigInteger.One))
{
#if !NETFX_CORE
if (debug)
{
Console.WriteLine("g has order phi(n)/" + smallPrimes[i] + "\n g: " + g);
}
#endif
divisible = true;
break;
}
}
if (divisible)
{
continue;
}
// make sure that g has order > phi_n/4
//if (g.ModPow(phi_n.Divide(BigInteger.ValueOf(4)), n).Equals(BigInteger.One))
if (g.ModPow(phi_n.ShiftRight(2), n).Equals(BigInteger.One))
{
#if !NETFX_CORE
if (debug)
{
Console.WriteLine("g has order phi(n)/4\n g:" + g);
}
#endif
continue;
}
if (g.ModPow(phi_n.Divide(_p), n).Equals(BigInteger.One))
{
#if !NETFX_CORE
if (debug)
{
Console.WriteLine("g has order phi(n)/p'\n g: " + g);
}
#endif
continue;
}
if (g.ModPow(phi_n.Divide(_q), n).Equals(BigInteger.One))
{
#if !NETFX_CORE
if (debug)
{
Console.WriteLine("g has order phi(n)/q'\n g: " + g);
}
#endif
continue;
}
if (g.ModPow(phi_n.Divide(a), n).Equals(BigInteger.One))
{
#if !NETFX_CORE
if (debug)
{
Console.WriteLine("g has order phi(n)/a\n g: " + g);
}
#endif
continue;
}
if (g.ModPow(phi_n.Divide(b), n).Equals(BigInteger.One))
{
#if !NETFX_CORE
if (debug)
{
Console.WriteLine("g has order phi(n)/b\n g: " + g);
}
#endif
continue;
}
break;
}
#if !NETFX_CORE
if (debug)
{
Console.WriteLine("needed " + tries + " tries to generate g");
Console.WriteLine();
Console.WriteLine("found new NaccacheStern cipher variables:");
Console.WriteLine("smallPrimes: " + CollectionUtilities.ToString(smallPrimes));
Console.WriteLine("sigma:...... " + sigma + " (" + sigma.BitLength + " bits)");
Console.WriteLine("a:.......... " + a);
Console.WriteLine("b:.......... " + b);
Console.WriteLine("p':......... " + _p);
Console.WriteLine("q':......... " + _q);
Console.WriteLine("p:.......... " + p);
Console.WriteLine("q:.......... " + q);
Console.WriteLine("n:.......... " + n);
Console.WriteLine("phi(n):..... " + phi_n);
Console.WriteLine("g:.......... " + g);
Console.WriteLine();
}
#endif
return(new AsymmetricCipherKeyPair(new NaccacheSternKeyParameters(false, g, n, sigma.BitLength),
new NaccacheSternPrivateKeyParameters(g, n, sigma.BitLength, smallPrimes, phi_n)));
}
