text: // rabin.cpp - written and placed in the public domain by Wei Dai
  
  #include "pch.h"
  #include "rabin.h"
  #include "nbtheory.h"
  #include "asn.h"
  #include "sha.h"
  #include "modarith.h"
  
  NAMESPACE_BEGIN(CryptoPP)
  
  void RabinFunction::BERDecode(BufferedTransformation &bt)
  {
  	BERSequenceDecoder seq(bt);
  	m_n.BERDecode(seq);
  	m_r.BERDecode(seq);
  	m_s.BERDecode(seq);
  	seq.MessageEnd();
  }
  
  void RabinFunction::DEREncode(BufferedTransformation &bt) const
  {
  	DERSequenceEncoder seq(bt);
  	m_n.DEREncode(seq);
  	m_r.DEREncode(seq);
  	m_s.DEREncode(seq);
  	seq.MessageEnd();
  }
  
  Integer RabinFunction::ApplyFunction(const Integer &in) const
  {
  	DoQuickSanityCheck();
  
  	Integer out = in.Squared()%m_n;
  	if (in.IsOdd())
  		out = out*m_r%m_n;
  	if (Jacobi(in, m_n)==-1)
  		out = out*m_s%m_n;
  	return out;
  }
  
  bool RabinFunction::Validate(RandomNumberGenerator &rng, unsigned int level) const
  {
  	bool pass = true;
  	pass = pass && m_n > Integer::One() && m_n%4 == 1;
  	pass = pass && m_r > Integer::One() && m_r < m_n;
  	pass = pass && m_s > Integer::One() && m_s < m_n;
  	if (level >= 1)
  		pass = pass && Jacobi(m_r, m_n) == -1 && Jacobi(m_s, m_n) == -1;
  	return pass;
  }
  
  bool RabinFunction::GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
  {
  	return GetValueHelper(this, name, valueType, pValue).Assignable()
  		CRYPTOPP_GET_FUNCTION_ENTRY(Modulus)
  		CRYPTOPP_GET_FUNCTION_ENTRY(QuadraticResidueModPrime1)
  		CRYPTOPP_GET_FUNCTION_ENTRY(QuadraticResidueModPrime2)
  		;
  }
  
  void RabinFunction::AssignFrom(const NameValuePairs &source)
  {
  	AssignFromHelper(this, source)
  		CRYPTOPP_SET_FUNCTION_ENTRY(Modulus)
  		CRYPTOPP_SET_FUNCTION_ENTRY(QuadraticResidueModPrime1)
  		CRYPTOPP_SET_FUNCTION_ENTRY(QuadraticResidueModPrime2)
  		;
  }
  
  // *****************************************************************************
  // private key operations:
  
  // generate a random private key
  void InvertibleRabinFunction::GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &alg)
  {
  	int modulusSize = 2048;
  	alg.GetIntValue("ModulusSize", modulusSize) || alg.GetIntValue("KeySize", modulusSize);
  
  	if (modulusSize < 16)
  		throw InvalidArgument("InvertibleRabinFunction: specified modulus size is too small");
  
  	// VC70 workaround: putting these after primeParam causes overlapped stack allocation
  	bool rFound=false, sFound=false;
  	Integer t=2;
  
  	AlgorithmParameters primeParam = MakeParametersForTwoPrimesOfEqualSize(modulusSize)
  		("EquivalentTo", 3)("Mod", 4);
  	m_p.GenerateRandom(rng, primeParam);
  	m_q.GenerateRandom(rng, primeParam);
  
  	while (!(rFound && sFound))
  	{
  		int jp = Jacobi(t, m_p);
  		int jq = Jacobi(t, m_q);
  
  		if (!rFound && jp==1 && jq==-1)
  		{
  			m_r = t;
  			rFound = true;
  		}
  
  		if (!sFound && jp==-1 && jq==1)
  		{
  			m_s = t;
  			sFound = true;
  		}
  
  		++t;
  	}
  
  	m_n = m_p * m_q;
  	m_u = m_q.InverseMod(m_p);
  }
  
  void InvertibleRabinFunction::BERDecode(BufferedTransformation &bt)
  {
  	BERSequenceDecoder seq(bt);
  	m_n.BERDecode(seq);
  	m_r.BERDecode(seq);
  	m_s.BERDecode(seq);
  	m_p.BERDecode(seq);
  	m_q.BERDecode(seq);
  	m_u.BERDecode(seq);
  	seq.MessageEnd();
  }
  
  void InvertibleRabinFunction::DEREncode(BufferedTransformation &bt) const
  {
  	DERSequenceEncoder seq(bt);
  	m_n.DEREncode(seq);
  	m_r.DEREncode(seq);
  	m_s.DEREncode(seq);
  	m_p.DEREncode(seq);
  	m_q.DEREncode(seq);
  	m_u.DEREncode(seq);
  	seq.MessageEnd();
  }
  
  Integer InvertibleRabinFunction::CalculateInverse(RandomNumberGenerator &rng, const Integer &in) const
  {
  	DoQuickSanityCheck();
  
  	ModularArithmetic modn(m_n);
  	Integer r(rng, Integer::One(), m_n - Integer::One());
  	r = modn.Square(r);
  	Integer r2 = modn.Square(r);
  	Integer c = modn.Multiply(in, r2);		// blind
  
  	Integer cp=c%m_p, cq=c%m_q;
  
  	int jp = Jacobi(cp, m_p);
  	int jq = Jacobi(cq, m_q);
  
  	if (jq==-1)
  	{
  		cp = cp*EuclideanMultiplicativeInverse(m_r, m_p)%m_p;
  		cq = cq*EuclideanMultiplicativeInverse(m_r, m_q)%m_q;
  	}
  
  	if (jp==-1)
  	{
  		cp = cp*EuclideanMultiplicativeInverse(m_s, m_p)%m_p;
  		cq = cq*EuclideanMultiplicativeInverse(m_s, m_q)%m_q;
  	}
  
  	cp = ModularSquareRoot(cp, m_p);
  	cq = ModularSquareRoot(cq, m_q);
  
  	if (jp==-1)
  		cp = m_p-cp;
  
  	Integer out = CRT(cq, m_q, cp, m_p, m_u);
  
  	out = modn.Divide(out, r);	// unblind
  
  	if ((jq==-1 && out.IsEven()) || (jq==1 && out.IsOdd()))
  		out = m_n-out;
  
  	return out;
  }
  
  bool InvertibleRabinFunction::Validate(RandomNumberGenerator &rng, unsigned int level) const
  {
  	bool pass = RabinFunction::Validate(rng, level);
  	pass = pass && m_p > Integer::One() && m_p%4 == 3 && m_p < m_n;
  	pass = pass && m_q > Integer::One() && m_q%4 == 3 && m_q < m_n;
  	pass = pass && m_u.IsPositive() && m_u < m_p;
  	if (level >= 1)
  	{
  		pass = pass && m_p * m_q == m_n;
  		pass = pass && m_u * m_q % m_p == 1;
  		pass = pass && Jacobi(m_r, m_p) == 1;
  		pass = pass && Jacobi(m_r, m_q) == -1;
  		pass = pass && Jacobi(m_s, m_p) == -1;
  		pass = pass && Jacobi(m_s, m_q) == 1;
  	}
  	if (level >= 2)
  		pass = pass && VerifyPrime(rng, m_p, level-2) && VerifyPrime(rng, m_q, level-2);
  	return pass;
  }
  
  bool InvertibleRabinFunction::GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
  {
  	return GetValueHelper<RabinFunction>(this, name, valueType, pValue).Assignable()
  		CRYPTOPP_GET_FUNCTION_ENTRY(Prime1)
  		CRYPTOPP_GET_FUNCTION_ENTRY(Prime2)
  		CRYPTOPP_GET_FUNCTION_ENTRY(MultiplicativeInverseOfPrime2ModPrime1)
  		;
  }
  
  void InvertibleRabinFunction::AssignFrom(const NameValuePairs &source)
  {
  	AssignFromHelper<RabinFunction>(this, source)
  		CRYPTOPP_SET_FUNCTION_ENTRY(Prime1)
  		CRYPTOPP_SET_FUNCTION_ENTRY(Prime2)
  		CRYPTOPP_SET_FUNCTION_ENTRY(MultiplicativeInverseOfPrime2ModPrime1)
  		;
  }
  
  NAMESPACE_END
  