private List <BigInteger> FractiontoContinuedFraction(BigFraction _fraction)
{
List <BigInteger> _lstCF = new List <BigInteger>();
List <BigFraction> _lstFraction = new List <BigFraction>();
BigInteger _remainder;
BigInteger _qi;
_qi = BigInteger.DivRem(_fraction.Numerator, _fraction.Denominator, out _remainder);
_lstCF.Add(_qi);
BigFraction _bfrac = new BigFraction(_remainder, _fraction.Denominator);
_lstFraction.Add(_bfrac);
int i = 0;
while (true)
{
i++;
_qi = BigInteger.DivRem(_lstFraction[i - 1].Denominator, _lstFraction[i - 1].Numerator, out _remainder);
_lstCF.Add(_qi);
_bfrac = new BigFraction(_remainder, _lstFraction[i - 1].Numerator);
_lstFraction.Add(_bfrac);
if (_remainder <= BigInteger.Zero)
{
break;
}
}
return(_lstCF);
}
private BigFraction ContinuedFractiontoFraction(List <BigInteger> _contfraction)
{
BigFraction _bfraction = new BigFraction();
List <BigInteger> _lstNumerator = new List <BigInteger>();
List <BigInteger> _lstDenominator = new List <BigInteger>();
int _iCount = _contfraction.Count;
_lstNumerator.Add(_contfraction[0]);
_lstDenominator.Add(1);
if (_iCount > 1)
{
_lstNumerator.Add(_contfraction[0] * _contfraction[1] + 1);
_lstDenominator.Add(_contfraction[1]);
for (int i = 2; i < _iCount; i++)
{
_lstNumerator.Add(_contfraction[i] * _lstNumerator[i - 1] + _lstNumerator[i - 2]);
_lstDenominator.Add(_contfraction[i] * _lstDenominator[i - 1] + _lstDenominator[i - 2]);
}
}
_bfraction.Numerator = _lstNumerator.Last();
_bfraction.Denominator = _lstDenominator.Last();
return(_bfraction);
}
public BigInteger WienerAlgorithm()
{
m_form.UpdateListbox("Calculating continued fraction from e/N");
BigFraction _bfraction = new BigFraction(m_rsaKey.Public_exponent, m_rsaKey.Modulus);
m_lstContinuedFraction = FractiontoContinuedFraction(_bfraction);
List <BigInteger> tmp_lstContFraction = new List <BigInteger>();
tmp_lstContFraction = m_lstContinuedFraction.Clone().ToList();
int iCount = m_lstContinuedFraction.Count;
m_form.UpdateListbox("Continued fraction from e/N is:");
string _strContFraction = null;
for (int i = 0; i < iCount; i++)
{
if (i == 0)
{
_strContFraction = "< ";
}
_strContFraction += m_lstContinuedFraction[i];
if (i == iCount - 1)
{
_strContFraction += " >";
}
else
{
_strContFraction += ", ";
}
}
m_form.UpdateListbox(_strContFraction);
for (int i = 0; i < iCount; i++)
{
BigFraction _bfrK_DG = new BigFraction();
BigFraction _bfrEulerToitient;
tmp_lstContFraction = m_lstContinuedFraction.Take(i + 1).ToList();
if (0 == i % 2)
{
tmp_lstContFraction[i] = tmp_lstContFraction[i] + 1;
}
_bfrK_DG = ContinuedFractiontoFraction(tmp_lstContFraction);
_bfrEulerToitient = new BigFraction(_bfrK_DG.Denominator * m_rsaKey.Public_exponent - 1, _bfrK_DG.Numerator);
BigInteger _iEulerToitient = _bfrEulerToitient.Floor();
var result = SolveQuadraticEquation(1, -1 * (m_rsaKey.Modulus - _iEulerToitient + 1), m_rsaKey.Modulus);
BigInteger _iG = BigInteger.Remainder(_bfrEulerToitient.Numerator, _bfrEulerToitient.Denominator);
if (result.Item1 * result.Item2 == m_rsaKey.Modulus)
{
m_rsaKey.Private_exponent = _bfrK_DG.Denominator;
m_lstD.Add(m_rsaKey.Private_exponent);
if (m_rsaKey.TestKey())
{
return(m_rsaKey.Private_exponent);
}
}
}
return(BigInteger.Zero);
}
