diff --git a/ecdsa.cpp b/ecdsa.cpp
index 1b8ab6905e..fa6f9a6d07 100644
--- a/ecdsa.cpp
+++ b/ecdsa.cpp
@@ -40,7 +40,28 @@ bool Signature::Parse(const unsigned char *sig, int size) {
     return true;
 }
 
-bool Signature::RecomputeR(Number &r2, const GroupElemJac &pubkey, const Number &message) {
+bool Signature::Serialize(unsigned char *sig, int *size) {
+    int lenR = (r.GetBits() + 7)/8;
+    if (lenR == 0 || r.CheckBit(lenR*8-1))
+        lenR++;
+    int lenS = (s.GetBits() + 7)/8;
+    if (lenS == 0 || s.CheckBit(lenS*8-1))
+        lenS++;
+    if (*size < 6+lenS+lenR)
+        return false;
+    *size = 6 + lenS + lenR;
+    sig[0] = 0x30;
+    sig[1] = 4 + lenS + lenR;
+    sig[2] = 0x02;
+    sig[3] = lenR;
+    r.GetBytes(sig+4, lenR);
+    sig[4+lenR] = 0x02;
+    sig[5+lenR] = lenS;
+    s.GetBytes(sig+6, lenS);
+    return true;
+}
+
+bool Signature::RecomputeR(Number &r2, const GroupElemJac &pubkey, const Number &message) const {
     const GroupConstants &c = GetGroupConst();
 
     if (r.IsNeg() || s.IsNeg())
@@ -63,13 +84,36 @@ bool Signature::RecomputeR(Number &r2, const GroupElemJac &pubkey, const Number
     return true;
 }
 
-bool Signature::Verify(const GroupElemJac &pubkey, const Number &message) {
+bool Signature::Verify(const GroupElemJac &pubkey, const Number &message) const {
     Number r2;
     if (!RecomputeR(r2, pubkey, message))
         return false;
     return r2.Compare(r) == 0;
 }
 
+bool Signature::Sign(const Number &seckey, const Number &message, const Number &nonce) {
+    const GroupConstants &c = GetGroupConst();
+
+    GroupElemJac rp;
+    ECMultBase(rp, nonce);
+    FieldElem rx;
+    rp.GetX(rx);
+    unsigned char b[32];
+    rx.GetBytes(b);
+    r.SetBytes(b, 32);
+    r.SetMod(r, c.order);
+    Number n;
+    n.SetModMul(r, seckey, c.order);
+    n.SetAdd(message, n);
+    s.SetModInverse(nonce, c.order);
+    s.SetModMul(s, n, c.order);
+    if (s.IsZero())
+        return false;
+    if (s.IsOdd())
+        s.SetSub(c.order, s);
+    return true;
+}
+
 void Signature::SetRS(const Number &rin, const Number &sin) {
     r = rin;
     s = sin;
diff --git a/ecdsa.h b/ecdsa.h
index 4763dc3194..bef35dbd0a 100644
--- a/ecdsa.h
+++ b/ecdsa.h
@@ -9,8 +9,10 @@ private:
 
 public:
     bool Parse(const unsigned char *sig, int size);
-    bool RecomputeR(Number &r2, const GroupElemJac &pubkey, const Number &message);
-    bool Verify(const GroupElemJac &pubkey, const Number &message);
+    bool Serialize(unsigned char *sig, int *size);
+    bool RecomputeR(Number &r2, const GroupElemJac &pubkey, const Number &message) const;
+    bool Verify(const GroupElemJac &pubkey, const Number &message) const;
+    bool Sign(const Number &seckey, const Number &message, const Number &nonce);
     void SetRS(const Number &rin, const Number &sin);
     std::string ToString() const;
 };
diff --git a/ecmult.cpp b/ecmult.cpp
index e48c09bac9..67d78547d4 100644
--- a/ecmult.cpp
+++ b/ecmult.cpp
@@ -112,6 +112,8 @@ class ECMultConsts {
 public:
     WNAFPrecomp<GroupElem,WINDOW_G> wpg;
     WNAFPrecomp<GroupElem,WINDOW_G> wpg128;
+    GroupElem prec[64][16]; // prec[j][i] = 16^j * (i+1) * G
+    GroupElem fin; // -(sum(prec[j][0], j=0..63))
 
     ECMultConsts() {
         const GroupElem &g = GetGroupConst().g;
@@ -121,6 +123,20 @@ public:
         GroupElem g128; g128.SetJac(g128j);
         wpg.Build(g);
         wpg128.Build(g128);
+        GroupElemJac gg(g);
+        GroupElem ad(g);
+        GroupElemJac fn;
+        for (int j=0; j<64; j++) {
+            prec[j][0].SetJac(gg);
+            fn.SetAdd(fn, gg);
+            for (int i=1; i<16; i++) {
+                gg.SetAdd(gg, ad);
+                prec[j][i].SetJac(gg);
+            }
+            ad = prec[j][15];
+        }
+        fn.SetNeg(fn);
+        fin.SetJac(fn);
     }
 };
 
@@ -129,6 +145,16 @@ const ECMultConsts &GetECMultConsts() {
     return ecmult_consts;
 }
 
+void ECMultBase(GroupElemJac &out, const Number &gn) {
+    Number n; n.SetNumber(gn);
+    const ECMultConsts &c = GetECMultConsts();
+    out.SetAffine(c.prec[0][n.ShiftLowBits(4)]);
+    for (int j=1; j<64; j++) {
+        out.SetAdd(out, c.prec[j][n.ShiftLowBits(4)]);
+    }
+    out.SetAdd(out, c.fin);
+}
+
 void ECMult(GroupElemJac &out, const GroupElemJac &a, const Number &an, const Number &gn) {
     Number an1, an2;
     Number gn1, gn2;
diff --git a/ecmult.h b/ecmult.h
index 0ad57e76a6..b779feaf62 100644
--- a/ecmult.h
+++ b/ecmult.h
@@ -6,6 +6,7 @@
 
 namespace secp256k1 {
 
+void ECMultBase(GroupElemJac &out, const Number &gn);
 void ECMult(GroupElemJac &out, const GroupElemJac &a, const Number &an, const Number &gn);
 
 }
diff --git a/group.cpp b/group.cpp
index af38b5d440..3a66174e20 100644
--- a/group.cpp
+++ b/group.cpp
@@ -47,10 +47,17 @@ GroupElemJac::GroupElemJac(const FieldElem &xin, const FieldElem &yin) : GroupEl
 
 GroupElemJac::GroupElemJac(const GroupElem &in) : GroupElem(in), z(1) {}
 
-void GroupElemJac::SetJac(GroupElemJac &jac) {
+void GroupElemJac::SetJac(const GroupElemJac &jac) {
     *this = jac;
 }
 
+void GroupElemJac::SetAffine(const GroupElem &aff) {
+    fInfinity = aff.fInfinity;
+    x = aff.x;
+    y = aff.y;
+    z = FieldElem(1);
+}
+
 bool GroupElemJac::IsValid() const {
     if (IsInfinity())
         return false;
diff --git a/group.h b/group.h
index d95e08cdbb..42a167797f 100644
--- a/group.h
+++ b/group.h
@@ -55,7 +55,9 @@ public:
 
     GroupElemJac(const GroupElem &in);
 
-    void SetJac(GroupElemJac &jac);
+    void SetJac(const GroupElemJac &jac);
+
+    void SetAffine(const GroupElem &aff);
 
     /** Checks whether this is a non-infinite point on the curve */
     bool IsValid() const;
diff --git a/num_gmp.cpp b/num_gmp.cpp
index 7945d60563..5f04c40cbc 100644
--- a/num_gmp.cpp
+++ b/num_gmp.cpp
@@ -58,6 +58,10 @@ void Number::SetBytes(const unsigned char *bin, unsigned int len) {
     mpz_import(bn, len, 1, 1, 1, 0, bin);
 }
 
+bool Number::CheckBit(int pos) const {
+    return mpz_tstbit(bn, pos);
+}
+
 void Number::GetBytes(unsigned char *bin, unsigned int len) {
     unsigned int size = (mpz_sizeinbase(bn,2)+7)/8;
     assert(size <= len);
diff --git a/num_gmp.h b/num_gmp.h
index ea330b446b..850328dee6 100644
--- a/num_gmp.h
+++ b/num_gmp.h
@@ -33,6 +33,7 @@ public:
     bool IsZero() const;
     bool IsOdd() const;
     bool IsNeg() const;
+    bool CheckBit(int pos) const;
     void Negate();
     void Shift1();
     void Inc();
diff --git a/num_openssl.cpp b/num_openssl.cpp
index c95a733d67..cd2673ea53 100644
--- a/num_openssl.cpp
+++ b/num_openssl.cpp
@@ -138,6 +138,10 @@ bool Number::IsOdd() const {
     return BN_is_odd((const BIGNUM*)*this);
 }
 
+bool Number::CheckBit(int pos) const {
+    return BN_is_bit_set((const BIGNUM*)*this, pos);
+}
+
 bool Number::IsNeg() const {
     return BN_is_negative((const BIGNUM*)*this);
 }
diff --git a/num_openssl.h b/num_openssl.h
index ddd73b9834..586d49f69b 100644
--- a/num_openssl.h
+++ b/num_openssl.h
@@ -35,6 +35,7 @@ public:
     bool IsZero() const;
     bool IsOdd() const;
     bool IsNeg() const;
+    bool CheckBit(int pos) const;
     void Negate();
     void Shift1();
     void Inc();
diff --git a/secp256k1.cpp b/secp256k1.cpp
index 0ea273ac2e..755f93cf3e 100644
--- a/secp256k1.cpp
+++ b/secp256k1.cpp
@@ -25,4 +25,5 @@ int VerifyECDSA(const unsigned char *msg, int msglen, const unsigned char *sig,
     return 1;
 }
 
+
 }
\ No newline at end of file
diff --git a/tests.cpp b/tests.cpp
index 2f342b6950..49ca712120 100644
--- a/tests.cpp
+++ b/tests.cpp
@@ -103,9 +103,31 @@ void test_run_wnaf() {
     }
 }
 
+void test_ecdsa_sign_verify() {
+    const GroupConstants &c = GetGroupConst();
+    Number msg; msg.SetPseudoRand(c.order);
+    Number key; key.SetPseudoRand(c.order);
+    Number nonce;
+    GroupElemJac pub; ECMultBase(pub, key);
+    Signature sig;
+    do {
+        nonce.SetPseudoRand(c.order);
+    } while(!sig.Sign(key, msg, nonce));
+    assert(sig.Verify(pub, msg));
+    msg.Inc();
+    assert(!sig.Verify(pub, msg));
+}
+
+void test_run_ecdsa_sign_verify() {
+    for (int i=0; i<1000; i++) {
+        test_ecdsa_sign_verify();
+    }
+}
+
 int main(void) {
     test_run_wnaf();
     test_run_point_times_order();
     test_run_ecmult_chain();
+    test_run_ecdsa_sign_verify();
     return 0;
 }