path: root/src/bls.cpp

/**
    @file
    @author MITSUNARI Shigeo(@herumi)
    @license modified new BSD license
    http://opensource.org/licenses/BSD-3-Clause
*/
#include <bls.hpp>
#include <mcl/bn.hpp>
#include <cybozu/crypto.hpp>
#include <cybozu/random_generator.hpp>
#include <vector>
#include <string>

typedef mcl::FpT<mcl::FpTag, 256> Fp;
typedef mcl::bn::BNT<Fp> BN;
typedef BN::Fp2 Fp2;
typedef BN::Fp6 Fp6;
typedef BN::Fp12 Fp12;
typedef BN::G1 G1;
typedef BN::G2 G2;
typedef std::vector<int> IntVec;

struct FrTag;
typedef mcl::FpT<FrTag, 256> Fr;
typedef std::vector<Fr> FrVec;


#define PUT(x) std::cout << #x << "=" << x << std::endl;

static cybozu::RandomGenerator& getRG()
{
    static cybozu::RandomGenerator rg;
    return rg;
}

namespace bls {

void init()
{
    BN::init(mcl::bn::CurveFp254BNb);
    G1::setCompressedExpression();
//  G2::setCompressedExpression();
    Fr::init(BN::param.r);
}

static const G2& getQ()
{
    static const G2 Q(
        Fp2("12723517038133731887338407189719511622662176727675373276651903807414909099441", "4168783608814932154536427934509895782246573715297911553964171371032945126671"),
        Fp2("13891744915211034074451795021214165905772212241412891944830863846330766296736", "7937318970632701341203597196594272556916396164729705624521405069090520231616")
    );
    return Q;
}

static void mapToG1(G1& P, const Fp& t)
{
    static mcl::bn::MapTo<Fp> mapTo;
    mapTo.calcG1(P, t);
}
static void HashAndMapToG1(G1& P, const std::string& m)
{
    std::string digest = cybozu::crypto::Hash::digest(cybozu::crypto::Hash::N_SHA256, m);
    Fp t;
    t.setArrayMask(digest.c_str(), digest.size());
    mapToG1(P, t);
}

template<class T, class G>
void evalPoly(G& y, const T& x, const std::vector<G>& c)
{
    if (c.size() < 2) throw cybozu::Exception("bls:evalPoly:bad size") << c.size();
    y = c[c.size() - 1];
    for (int i = (int)c.size() - 2; i >= 0; i--) {
        G::mul(y, y, x);
        G::add(y, y, c[i]);
    }
}

struct Polynomial {
    FrVec c; // f[x] = sum_{i=0}^{k-1} c[i] x^i
    void init(const Fr& s, int k)
    {
        if (k < 2) throw cybozu::Exception("bls:Polynomial:init:bad k") << k;
        c.resize(k);
        c[0] = s;
        for (size_t i = 1; i < c.size(); i++) {
            c[i].setRand(getRG());
        }
    }
    // y = f(id)
    void eval(Fr& y, int id) const
    {
        if (id == 0) throw cybozu::Exception("bls:Polynomial:eval:id is zero");
        evalPoly(y, Fr(id), c);
    }
};

/*
    delta_{i,S}(0) = prod_{j != i} S[j] / (S[j] - S[i]) = a / b
    where a = prod S[j], b = S[i] * prod_{j != i} (S[j] - S[i])
*/
static void calcDelta(FrVec& delta, const IntVec& S)
{
    const size_t k = S.size();
    if (k < 2) throw cybozu::Exception("bls:calcDelta:bad size") << k;
    delta.resize(k);
    Fr a = S[0];
    for (size_t i = 1; i < k; i++) {
        a *= S[i];
    }
    for (size_t i = 0; i < k; i++) {
        Fr b = S[i];
        for (size_t j = 0; j < k; j++) {
            if (j != i) {
                int v = S[j] - S[i];
                if (v == 0) throw cybozu::Exception("bls:calcDelta:S has same id") << i << j;
                b *= v;
            }
        }
        delta[i] = a / b;
    }
}

template<class G, class T>
void LagrangeInterpolation(G& r, const T& vec)
{
    IntVec S(vec.size());
    for (size_t i = 0; i < vec.size(); i++) {
        S[i] = vec[i].getId();
    }
    FrVec delta;
    calcDelta(delta, S);

    r.clear();
    G t;
    for (size_t i = 0; i < delta.size(); i++) {
        G::mul(t, vec[i].self_->get(), delta[i]);
        r += t;
    }
}

namespace impl {

struct Sign {
    G1 sHm; // s Hash(m)
    const G1& get() const { return sHm; }
};

struct PublicKey {
    G2 sQ;
    void init(const Fr& s)
    {
        G2::mul(sQ, getQ(), s);
    }
    bool verify(const Sign& sign, const std::string& m) const
    {
        G1 Hm;
        HashAndMapToG1(Hm, m); // Hm = Hash(m)
        Fp12 e1, e2;
        BN::pairing(e1, getQ(), sign.sHm); // e(Q, s Hm)
        BN::pairing(e2, sQ, Hm); // e(sQ, Hm)
        return e1 == e2;
    }
    const G2& get() const { return sQ; }
};

struct MasterPublicKey {
    std::vector<G2> vecR;
};

struct PrivateKey {
    Fr s;
    const Fr& get() const { return s; }
    void init()
    {
        s.setRand(getRG());
    }
    void getPublicKey(PublicKey& pub) const
    {
        pub.init(s);
    }
    void sign(Sign& sign, const std::string& m) const
    {
        G1 Hm;
        HashAndMapToG1(Hm, m);
        G1::mul(sign.sHm, Hm, s);
    }
};

} // mcl::bls::impl

Sign::Sign()
    : self_(new impl::Sign())
    , id_(0)
{
}

Sign::~Sign()
{
    delete self_;
}

Sign::Sign(const Sign& rhs)
    : self_(new impl::Sign(*rhs.self_))
    , id_(rhs.id_)
{
}

Sign& Sign::operator=(const Sign& rhs)
{
    *self_ = *rhs.self_;
    id_ = rhs.id_;
    return *this;
}

bool Sign::operator==(const Sign& rhs) const
{
    return id_ == rhs.id_ && self_->sHm == rhs.self_->sHm;
}

std::ostream& operator<<(std::ostream& os, const Sign& s)
{
    return os << s.id_ << ' ' << s.self_->sHm;
}

std::istream& operator>>(std::istream& os, Sign& s)
{
    return os >> s.id_ >> s.self_->sHm;
}

void Sign::recover(const std::vector<Sign>& signVec)
{
    G1 sHm;
    LagrangeInterpolation(sHm, signVec);
    self_->sHm = sHm;
    id_ = 0;
}

void Sign::add(const Sign& rhs)
{
    if (id_ != 0 || rhs.id_ != 0) throw cybozu::Exception("bls:Sign:add:bad id") << id_ << rhs.id_;
    self_->sHm += rhs.self_->sHm;
}

MasterPublicKey::MasterPublicKey()
    : self_(new impl::MasterPublicKey())
{
}

MasterPublicKey::~MasterPublicKey()
{
    delete self_;
}

MasterPublicKey::MasterPublicKey(const MasterPublicKey& rhs)
    : self_(new impl::MasterPublicKey(*rhs.self_))
{
}

MasterPublicKey& MasterPublicKey::operator=(const MasterPublicKey& rhs)
{
    *self_ = *rhs.self_;
    return *this;
}

bool MasterPublicKey::operator==(const MasterPublicKey& rhs) const
{
    return self_->vecR == rhs.self_->vecR;
}

std::ostream& operator<<(std::ostream& os, const MasterPublicKey& mpk)
{
    const size_t n = mpk.self_->vecR.size();
    os << n;
    for (size_t i = 0; i < n; i++) {
        os << '\n' << mpk.self_->vecR[i];
    }
    return os;
}

std::istream& operator>>(std::istream& is, MasterPublicKey& mpk)
{
    size_t n;
    is >> n;
    mpk.self_->vecR.resize(n);
    for (size_t i = 0; i < n; i++) {
        is >> mpk.self_->vecR[i];
    }
    return is;
}

PublicKey::PublicKey()
    : self_(new impl::PublicKey())
    , id_(0)
{
}

PublicKey::~PublicKey()
{
    delete self_;
}

PublicKey::PublicKey(const PublicKey& rhs)
    : self_(new impl::PublicKey(*rhs.self_))
    , id_(rhs.id_)
{
}

PublicKey& PublicKey::operator=(const PublicKey& rhs)
{
    *self_ = *rhs.self_;
    id_ = rhs.id_;
    return *this;
}

bool PublicKey::operator==(const PublicKey& rhs) const
{
    return id_ == rhs.id_ && self_->sQ == rhs.self_->sQ;
}

std::ostream& operator<<(std::ostream& os, const PublicKey& pub)
{
    return os << pub.id_ << ' ' << pub.self_->sQ;
}

std::istream& operator>>(std::istream& is, PublicKey& pub)
{
    return is >> pub.id_ >> pub.self_->sQ;
}

bool PublicKey::verify(const Sign& sign, const std::string& m) const
{
    return self_->verify(*sign.self_, m);
}

void PublicKey::recover(const std::vector<PublicKey>& pubVec)
{
    G2 sQ;
    LagrangeInterpolation(sQ, pubVec);
    self_->sQ = sQ;
    id_ = 0;
}

bool PublicKey::isValid(const MasterPublicKey& mpk) const
{
    G2 v;
    evalPoly(v, Fr(id_), mpk.self_->vecR);
    return v == self_->sQ;
}

void PublicKey::add(const PublicKey& rhs)
{
    if (id_ != 0 || rhs.id_ != 0) throw cybozu::Exception("bls:PublicKey:add:bad id") << id_ << rhs.id_;
    self_->sQ += rhs.self_->sQ;
}

PrivateKey::PrivateKey()
    : self_(new impl::PrivateKey())
    , id_(0)
{
}

PrivateKey::~PrivateKey()
{
    delete self_;
}

PrivateKey::PrivateKey(const PrivateKey& rhs)
    : self_(new impl::PrivateKey(*rhs.self_))
    , id_(rhs.id_)
{
}

PrivateKey& PrivateKey::operator=(const PrivateKey& rhs)
{
    *self_ = *rhs.self_;
    id_ = rhs.id_;
    return *this;
}

bool PrivateKey::operator==(const PrivateKey& rhs) const
{
    return id_ == rhs.id_ && self_->s == rhs.self_->s;
}

void PrivateKey::init()
{
    self_->init();
}

void PrivateKey::getPublicKey(PublicKey& pub) const
{
    self_->getPublicKey(*pub.self_);
    pub.id_ = id_;
}

std::ostream& operator<<(std::ostream& os, const PrivateKey& prv)
{
    return os << prv.id_ << ' ' << prv.self_->s;
}

std::istream& operator>>(std::istream& is, PrivateKey& prv)
{
    return is >> prv.id_ >> prv.self_->s;
}

void PrivateKey::sign(Sign& sign, const std::string& m) const
{
    self_->sign(*sign.self_, m);
    sign.id_ = id_;
}

void PrivateKey::share(std::vector<PrivateKey>& prvVec, int n, int k, MasterPublicKey *mpk)
{
    if (id_ != 0) throw cybozu::Exception("bls:PrivateKey:share:already shared") << id_;
    if (n <= 0 || k <= 0 || k > n) throw cybozu::Exception("bls:PrivateKey:share:bad n, k") << n << k;
    Polynomial poly;
    poly.init(self_->s, k);
    prvVec.resize(n);
    for (int i = 0; i < n; i++) {
        int id = i + 1;
        poly.eval(prvVec[i].self_->s, id);
        prvVec[i].id_ = id;
    }
    if (mpk == 0) return;
    std::vector<G2>& vecR = mpk->self_->vecR;
    vecR.resize(k);
    for (size_t i = 0; i < vecR.size(); i++) {
        G2::mul(vecR[i], getQ(), poly.c[i]);
    }
}

void PrivateKey::recover(const std::vector<PrivateKey>& prvVec)
{
    Fr s;
    LagrangeInterpolation(s, prvVec);
    self_->s = s;
    id_ = 0;
}

void PrivateKey::add(const PrivateKey& rhs)
{
    if (id_ != 0 || rhs.id_ != 0) throw cybozu::Exception("bls:PrivateKey:add:bad id") << id_ << rhs.id_;
    self_->s += rhs.self_->s;
}

} // bls