rabin.cpp

// rabin.cpp - originally written and placed in the public domain by Wei Dai
 
#include "pch.h"
#include "rabin.h"
#include "integer.h"
#include "nbtheory.h"
#include "modarith.h"
#include "asn.h"
#include "sha.h"
#include "trap.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;
    CRYPTOPP_ASSERT(pass);
    pass = pass && m_r > Integer::One() && m_r < m_n;
    CRYPTOPP_ASSERT(pass);
    pass = pass && m_s > Integer::One() && m_s < m_n;
    CRYPTOPP_ASSERT(pass);
    if (level >= 1)
    {
        pass = pass && Jacobi(m_r, m_n) == -1 && Jacobi(m_s, m_n) == -1;
        CRYPTOPP_ASSERT(pass);
    }
    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();
 
    CRYPTOPP_ASSERT(IsPrime(m_p));
    CRYPTOPP_ASSERT(IsPrime(m_q));
}
 
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
{
    CRYPTOPP_ASSERT(IsPrime(m_p));
    CRYPTOPP_ASSERT(IsPrime(m_q));
 
    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);
    CRYPTOPP_ASSERT(pass);
    pass = pass && m_p > Integer::One() && m_p%4 == 3 && m_p < m_n;
    CRYPTOPP_ASSERT(pass);
    pass = pass && m_q > Integer::One() && m_q%4 == 3 && m_q < m_n;
    CRYPTOPP_ASSERT(pass);
    pass = pass && m_u.IsPositive() && m_u < m_p;
    CRYPTOPP_ASSERT(pass);
    if (level >= 1)
    {
        pass = pass && m_p * m_q == m_n;
        CRYPTOPP_ASSERT(pass);
        pass = pass && m_u * m_q % m_p == 1;
        CRYPTOPP_ASSERT(pass);
        pass = pass && Jacobi(m_r, m_p) == 1;
        CRYPTOPP_ASSERT(pass);
        pass = pass && Jacobi(m_r, m_q) == -1;
        CRYPTOPP_ASSERT(pass);
        pass = pass && Jacobi(m_s, m_p) == -1;
        CRYPTOPP_ASSERT(pass);
        pass = pass && Jacobi(m_s, m_q) == 1;
        CRYPTOPP_ASSERT(pass);
    }
    if (level >= 2)
    {
        pass = pass && VerifyPrime(rng, m_p, level-2) && VerifyPrime(rng, m_q, level-2);
        CRYPTOPP_ASSERT(pass);
    }
    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