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);
 
        // GCC warning bug, https://stackoverflow.com/q/12842306/608639
#ifdef _OPENMP
        #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);
        }
#else
        m_pre_2_9p = modp.Exponentiate(2, (9 * m_p - 11)/8);
        m_pre_2_3q = modq.Exponentiate(2, (3 * m_q - 5)/8);
        m_pre_q_p = modp.Exponentiate(m_q, m_p - 2);
#endif
 
        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;
 
#ifdef _OPENMP
        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));
                }
        }
#else
        const Integer W = (f.IsUnit() ? U : modq.Multiply(m_pre_2_3q, U));
        const Integer t = modp.Multiply(modp.Exponentiate(V, 3), eh);
        const Integer X = (f.IsUnit() ? t : modp.Multiply(m_pre_2_9p, t));
#endif
 
        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