static ZInt RandPrime(int k)
{
if (k < 2)
{
throw new ArgumentException();
}
ZInt min = ZInt.One << (k - 1);
ZInt max = ZInt.One << k;
for (;;)
{
ZInt p = ZInt.MakeRand(min, max) | 1;
if (p.IsPrime)
{
return(p);
}
}
}
internal static void TestModInt()
{
Console.Write("Test ModInt: ");
for (int k = 2; k <= 128; k++)
{
for (int i = 0; i < 10; i++)
{
int kwlen = (k + 30) / 31;
int kwb = 31 * kwlen;
ZInt p;
if (k >= 9)
{
p = ZInt.DecodeUnsignedBE(
BigInt.RandPrime(k));
if (p.BitLength != k)
{
throw new Exception(
"wrong prime size");
}
if (!p.IsPrime)
{
throw new Exception(
"not prime");
}
}
else
{
p = RandPrime(k);
}
ZInt a = ZInt.MakeRand(p);
ZInt b = ZInt.MakeRand(p);
ZInt v = ZInt.MakeRand(k + 60);
if (b == ZInt.Zero)
{
b = ZInt.One;
}
byte[] ea = a.ToBytesBE();
byte[] eb = b.ToBytesBE();
byte[] ev = v.ToBytesBE();
ModInt mz = new ModInt(p.ToBytesBE());
ModInt ma = mz.Dup();
ModInt mb = mz.Dup();
ma.Decode(ea);
CheckEq(ma, a);
ma.Decode(ea);
mb.Decode(eb);
ma.Add(mb);
CheckEq(ma, (a + b).Mod(p));
ma.Decode(ea);
mb.Decode(eb);
ma.Sub(mb);
CheckEq(ma, (a - b).Mod(p));
ma.Decode(ea);
ma.Negate();
CheckEq(ma, (-a).Mod(p));
ma.Decode(ea);
mb.Decode(eb);
ma.MontyMul(mb);
CheckEq((ZInt.DecodeUnsignedBE(ma.Encode())
<< kwb).Mod(p), (a * b).Mod(p));
ma.Decode(ea);
ma.ToMonty();
CheckEq(ma, (a << kwb).Mod(p));
ma.FromMonty();
CheckEq(ma, a);
ma.Decode(ea);
mb.Decode(eb);
ma.ToMonty();
mb.ToMonty();
ma.MontyMul(mb);
ma.FromMonty();
CheckEq(ma, (a * b).Mod(p));
mb.Decode(eb);
mb.Invert();
ZInt r = ZInt.DecodeUnsignedBE(mb.Encode());
CheckEq(ZInt.One, (r * b).Mod(p));
ma.Decode(ea);
ma.Pow(ev);
CheckEq(ma, ZInt.ModPow(a, v, p));
ma.DecodeReduce(ev);
CheckEq(ma, v.Mod(p));
mb.Decode(eb);
ma.Set(mb);
CheckEq(ma, b);
ModInt mv = new ModInt(
((p << 61) + 1).ToBytesBE());
mv.Decode(ev);
ma.Set(mv);
CheckEq(ma, v.Mod(p));
if (k >= 9)
{
ma.Decode(ea);
mb.Set(ma);
mb.ToMonty();
mb.MontyMul(ma);
if ((int)mb.SqrtBlum() != -1)
{
throw new CryptoException(
"square root failed");
}
if (!mb.Eq(ma))
{
mb.Negate();
}
CheckEq(mb, a);
mb.Decode(eb);
mb.ToMonty();
mb.MontySquare();
mb.FromMonty();
mb.Negate();
if (mb.SqrtBlum() != 0)
{
throw new CryptoException(
"square root should"
+ " have failed");
}
}
}
Console.Write(".");
}
Console.WriteLine(" done.");
}