rw.cpp

// rw.cpp - originally written and placed in the public domain by Wei Dai

#include "pch.h"

#include "rw.h"
#include "asn.h"
#include "integer.h"
#include "nbtheory.h"
#include "modarith.h"
#include "asn.h"

#ifndef CRYPTOPP_IMPORTS

#if defined(_OPENMP)
# define CRYPTOPP_RW_USE_OMP 1
#else
# define CRYPTOPP_RW_USE_OMP 0
#endif

NAMESPACE_BEGIN(CryptoPP)

void RWFunction::BERDecode(BufferedTransformation &bt)
{
    BERSequenceDecoder seq(bt);
    m_n.BERDecode(seq);
    seq.MessageEnd();
}

void RWFunction::DEREncode(BufferedTransformation &bt) const
{
    DERSequenceEncoder seq(bt);
    m_n.DEREncode(seq);
    seq.MessageEnd();
}

Integer RWFunction::ApplyFunction(const Integer &in) const
{
    DoQuickSanityCheck();

    Integer out = in.Squared()%m_n;
    const word r = 12;
    // this code was written to handle both r = 6 and r = 12,
    // but now only r = 12 is used in P1363
    const word r2 = r/2;
    const word r3a = (16 + 5 - r) % 16; // n%16 could be 5 or 13
    const word r3b = (16 + 13 - r) % 16;
    const word r4 = (8 + 5 - r/2) % 8;  // n%8 == 5
    switch (out % 16)
    {
    case r:
        break;
    case r2:
    case r2+8:
        out <<= 1;
        break;
    case r3a:
    case r3b:
        out.Negate();
        out += m_n;
        break;
    case r4:
    case r4+8:
        out.Negate();
        out += m_n;
        out <<= 1;
        break;
    default:
        out = Integer::Zero();
    }
    return out;
}

bool RWFunction::Validate(RandomNumberGenerator &rng, unsigned int level) const
{
    CRYPTOPP_UNUSED(rng), CRYPTOPP_UNUSED(level);
    bool pass = true;
    pass = pass && m_n > Integer::One() && m_n%8 == 5;
    CRYPTOPP_ASSERT(pass);
    return pass;
}

bool RWFunction::GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
{
    return GetValueHelper(this, name, valueType, pValue).Assignable()
        CRYPTOPP_GET_FUNCTION_ENTRY(Modulus)
        ;
}

void RWFunction::AssignFrom(const NameValuePairs &source)
{
    AssignFromHelper(this, source)
        CRYPTOPP_SET_FUNCTION_ENTRY(Modulus)
        ;
}

// *****************************************************************************
// private key operations:

// generate a random private key
void InvertibleRWFunction::GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &alg)
{
    int modulusSize = 2048;
    alg.GetIntValue("ModulusSize", modulusSize) || alg.GetIntValue("KeySize", modulusSize);

    if (modulusSize < 16)
        throw InvalidArgument("InvertibleRWFunction: specified modulus length is too small");

    AlgorithmParameters primeParam = MakeParametersForTwoPrimesOfEqualSize(modulusSize);
    m_p.GenerateRandom(rng, CombinedNameValuePairs(primeParam, MakeParameters("EquivalentTo", 3)("Mod", 8)));
    m_q.GenerateRandom(rng, CombinedNameValuePairs(primeParam, MakeParameters("EquivalentTo", 7)("Mod", 8)));

    m_n = m_p * m_q;
    m_u = m_q.InverseMod(m_p);

    Precompute();
}

void InvertibleRWFunction::Initialize(const Integer &n, const Integer &p, const Integer &q, const Integer &u)
{
    m_n = n; m_p = p; m_q = q; m_u = u;

    Precompute();
}

void InvertibleRWFunction::PrecomputeTweakedRoots() const
{
    ModularArithmetic modp(m_p), modq(m_q);

    #pragma omp parallel sections if(CRYPTOPP_RW_USE_OMP)
    {
        #pragma omp section
            m_pre_2_9p = modp.Exponentiate(2, (9 * m_p - 11)/8);
        #pragma omp section
            m_pre_2_3q = modq.Exponentiate(2, (3 * m_q - 5)/8);
        #pragma omp section
            m_pre_q_p = modp.Exponentiate(m_q, m_p - 2);
    }

    m_precompute = true;
}

void InvertibleRWFunction::LoadPrecomputation(BufferedTransformation &bt)
{
    BERSequenceDecoder seq(bt);
    m_pre_2_9p.BERDecode(seq);
    m_pre_2_3q.BERDecode(seq);
    m_pre_q_p.BERDecode(seq);
    seq.MessageEnd();

    m_precompute = true;
}

void InvertibleRWFunction::SavePrecomputation(BufferedTransformation &bt) const
{
    if(!m_precompute)
        Precompute();

    DERSequenceEncoder seq(bt);
    m_pre_2_9p.DEREncode(seq);
    m_pre_2_3q.DEREncode(seq);
    m_pre_q_p.DEREncode(seq);
    seq.MessageEnd();
}

void InvertibleRWFunction::BERDecode(BufferedTransformation &bt)
{
    BERSequenceDecoder seq(bt);
    m_n.BERDecode(seq);
    m_p.BERDecode(seq);
    m_q.BERDecode(seq);
    m_u.BERDecode(seq);
    seq.MessageEnd();

    m_precompute = false;
}

void InvertibleRWFunction::DEREncode(BufferedTransformation &bt) const
{
    DERSequenceEncoder seq(bt);
    m_n.DEREncode(seq);
    m_p.DEREncode(seq);
    m_q.DEREncode(seq);
    m_u.DEREncode(seq);
    seq.MessageEnd();
}

// DJB's "RSA signatures and Rabin-Williams signatures..." (http://cr.yp.to/sigs/rwsota-20080131.pdf).
Integer InvertibleRWFunction::CalculateInverse(RandomNumberGenerator &rng, const Integer &x) const
{
    DoQuickSanityCheck();

    if(!m_precompute)
        Precompute();

    ModularArithmetic modn(m_n), modp(m_p), modq(m_q);
    Integer r, rInv;

    do
    {
        // Do this in a loop for people using small numbers for testing
        r.Randomize(rng, Integer::One(), m_n - Integer::One());
        // Fix for CVE-2015-2141. Thanks to Evgeny Sidorov for reporting.
        // Squaring to satisfy Jacobi requirements suggested by Jean-Pierre Munch.
        r = modn.Square(r);
        rInv = modn.MultiplicativeInverse(r);
    } while (rInv.IsZero());

    Integer re = modn.Square(r);
    re = modn.Multiply(re, x);    // blind

    const Integer &h = re, &p = m_p, &q = m_q;
    Integer e, f;

    const Integer U = modq.Exponentiate(h, (q+1)/8);
    if(((modq.Exponentiate(U, 4) - h) % q).IsZero())
        e = Integer::One();
    else
        e = -1;

    const Integer eh = e*h, V = modp.Exponentiate(eh, (p-3)/8);
    if(((modp.Multiply(modp.Exponentiate(V, 4), modp.Exponentiate(eh, 2)) - eh) % p).IsZero())
        f = Integer::One();
    else
        f = 2;

    Integer W, X;
    #pragma omp parallel sections if(CRYPTOPP_RW_USE_OMP)
    {
        #pragma omp section
        {
            W = (f.IsUnit() ? U : modq.Multiply(m_pre_2_3q, U));
        }
        #pragma omp section
        {
            const Integer t = modp.Multiply(modp.Exponentiate(V, 3), eh);
            X = (f.IsUnit() ? t : modp.Multiply(m_pre_2_9p, t));
        }
    }
    const Integer Y = W + q * modp.Multiply(m_pre_q_p, (X - W));

    // Signature
    Integer s = modn.Multiply(modn.Square(Y), rInv);
    CRYPTOPP_ASSERT((e * f * s.Squared()) % m_n == x);

    // IEEE P1363, Section 8.2.8 IFSP-RW, p.44
    s = STDMIN(s, m_n - s);
    if (ApplyFunction(s) != x)                      // check
        throw Exception(Exception::OTHER_ERROR, "InvertibleRWFunction: computational error during private key operation");

    return s;
}

bool InvertibleRWFunction::Validate(RandomNumberGenerator &rng, unsigned int level) const
{
    bool pass = RWFunction::Validate(rng, level);
    CRYPTOPP_ASSERT(pass);
    pass = pass && m_p > Integer::One() && m_p%8 == 3 && m_p < m_n;
    CRYPTOPP_ASSERT(pass);
    pass = pass && m_q > Integer::One() && m_q%8 == 7 && 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);
    }
    if (level >= 2)
    {
        pass = pass && VerifyPrime(rng, m_p, level-2) && VerifyPrime(rng, m_q, level-2);
        CRYPTOPP_ASSERT(pass);
    }
    return pass;
}

bool InvertibleRWFunction::GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
{
    return GetValueHelper<RWFunction>(this, name, valueType, pValue).Assignable()
        CRYPTOPP_GET_FUNCTION_ENTRY(Prime1)
        CRYPTOPP_GET_FUNCTION_ENTRY(Prime2)
        CRYPTOPP_GET_FUNCTION_ENTRY(MultiplicativeInverseOfPrime2ModPrime1)
        ;
}

void InvertibleRWFunction::AssignFrom(const NameValuePairs &source)
{
    AssignFromHelper<RWFunction>(this, source)
        CRYPTOPP_SET_FUNCTION_ENTRY(Prime1)
        CRYPTOPP_SET_FUNCTION_ENTRY(Prime2)
        CRYPTOPP_SET_FUNCTION_ENTRY(MultiplicativeInverseOfPrime2ModPrime1)
        ;

    m_precompute = false;
}

NAMESPACE_END

#endif