diff --git a/internal/edwards25519/scalarMul.go b/internal/edwards25519/scalarMul.go
new file mode 100644
index 0000000..79a0179
--- /dev/null
+++ b/internal/edwards25519/scalarMul.go
@@ -0,0 +1,86 @@
+// Copyright (c) 2019 Henry de Valence.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package edwards25519
+
+import (
+	"github.com/gtank/ristretto255/internal/scalar"
+)
+
+// Set v to x*B, where B is the Ed25519 basepoint, and return v.
+//
+// The scalar multiplication is done in constant time.
+func (v *ProjP3) BasepointMul(x *scalar.Scalar) *ProjP3 {
+	panic("unimplemented")
+	return v
+}
+
+// Set v to x*Q, and return v.  v and q may alias.
+//
+// The scalar multiplication is done in constant time.
+func (v *ProjP3) ScalarMul(x *scalar.Scalar, q *ProjP3) *ProjP3 {
+	var table ProjLookupTable
+	table.FromP3(q)
+	// v and q could alias, but once the table is built we can clobber v.
+	v.Zero()
+
+	// Write x = sum(x_i * 16^i)
+	// so  x*Q = sum( Q*x_i*16^i )
+	//         = Q*x_0 + 16*(Q*x_1 + 16*( ... + Q*x_63) ... )
+	//           <------compute inside out---------
+	//
+	// We use the lookup table to get the x_i*Q values
+	// and do four doublings to compute 16*Q
+	digits := x.SignedRadix16()
+
+	// Unwrap first loop iteration to save computing 16*identity
+	multiple := &ProjCached{}
+	tmp1 := &ProjP1xP1{}
+	tmp2 := &ProjP2{}
+	table.SelectInto(multiple, digits[63])
+	tmp1.Add(v, multiple) // tmp1 = x_63*Q in P1xP1 coords
+	for i := 62; i >= 0; i-- {
+		tmp2.FromP1xP1(tmp1) // tmp2 =    (prev) in P2 coords
+		tmp1.Double(tmp2)    // tmp1 =  2*(prev) in P1xP1 coords
+		tmp2.FromP1xP1(tmp1) // tmp2 =  2*(prev) in P2 coords
+		tmp1.Double(tmp2)    // tmp1 =  4*(prev) in P1xP1 coords
+		tmp2.FromP1xP1(tmp1) // tmp2 =  4*(prev) in P2 coords
+		tmp1.Double(tmp2)    // tmp1 =  8*(prev) in P1xP1 coords
+		tmp2.FromP1xP1(tmp1) // tmp2 =  8*(prev) in P2 coords
+		tmp1.Double(tmp2)    // tmp1 = 16*(prev) in P1xP1 coords
+		v.FromP1xP1(tmp1)    //    v = 16*(prev) in P3 coords
+		table.SelectInto(multiple, digits[i])
+		tmp1.Add(v, multiple) // tmp1 = x_i*Q + 16*(prev) in P1xP1 coords
+	}
+	v.FromP1xP1(tmp1)
+	return v
+}
+
+// Set v to a*A + b*B, where B is the Ed25519 basepoint, and return v.
+//
+// The scalar multiplication is done in variable time.
+func (v *ProjP3) VartimeDoubleBaseMul(a, b *scalar.Scalar, A *ProjP3) *ProjP3 {
+	panic("unimplemented")
+	return v
+}
+
+// Set v to the result of a multiscalar multiplication and return v.
+//
+// The multiscalar multiplication is sum(scalars[i]*points[i]).
+//
+// The multiscalar multiplication is performed in constant time.
+func (v *ProjP3) MultiscalarMul(scalars []scalar.Scalar, points []*ProjP3) *ProjP3 {
+	panic("unimplemented")
+	return v
+}
+
+// Set v to the result of a multiscalar multiplication and return v.
+//
+// The multiscalar multiplication is sum(scalars[i]*points[i]).
+//
+// The multiscalar multiplication is performed in variable time.
+func (v *ProjP3) VartimeMultiscalarMul(scalars []scalar.Scalar, points []*ProjP3) *ProjP3 {
+	panic("unimplemented")
+	return v
+}
diff --git a/internal/edwards25519/scalarMul_test.go b/internal/edwards25519/scalarMul_test.go
new file mode 100644
index 0000000..b244d84
--- /dev/null
+++ b/internal/edwards25519/scalarMul_test.go
@@ -0,0 +1,70 @@
+package edwards25519
+
+import (
+	"github.com/gtank/ristretto255/internal/radix51"
+	"github.com/gtank/ristretto255/internal/scalar"
+	"testing"
+	"testing/quick"
+)
+
+// quickCheckConfig will make each quickcheck test run (1024 * -quickchecks)
+// times. The default value of -quickchecks is 100.
+var (
+	quickCheckConfig = &quick.Config{MaxCountScale: 1 << 10}
+)
+
+func TestScalarMulSmallScalars(t *testing.T) {
+	var z scalar.Scalar
+	var p, check ProjP3
+	p.ScalarMul(&z, &B)
+	check.Zero()
+	if check.Equal(&p) != 1 {
+		t.Error("0*B != 0")
+	}
+
+	z = scalar.Scalar([32]byte{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0})
+	p.ScalarMul(&z, &B)
+	check.Set(&B)
+	if check.Equal(&p) != 1 {
+		t.Error("1*B != 1")
+	}
+}
+
+func TestScalarMulVsDalek(t *testing.T) {
+	expected := ProjP3{
+		X: radix51.FieldElement([5]uint64{778774234987948, 1589187156384239, 1213330452914652, 186161118421127, 2186284806803213}),
+		Y: radix51.FieldElement([5]uint64{1241255309069369, 1115278942994853, 1016511918109334, 1303231926552315, 1801448517689873}),
+		Z: radix51.FieldElement([5]uint64{353337085654440, 1327844406437681, 2207296012811921, 707394926933424, 917408459573183}),
+		T: radix51.FieldElement([5]uint64{585487439439725, 1792815221887900, 946062846079052, 1954901232609667, 1418300670001780}),
+	}
+	z := scalar.Scalar([32]byte{219, 106, 114, 9, 174, 249, 155, 89, 69, 203, 201, 93, 92, 116, 234, 187, 78, 115, 103, 172, 182, 98, 62, 103, 187, 136, 13, 100, 248, 110, 12, 4})
+
+	var p ProjP3
+	p.ScalarMul(&z, &B)
+	if expected.Equal(&p) != 1 {
+		t.Error("Scalar mul does not match dalek")
+	}
+}
+
+func TestScalarMulDistributesOverAdd(t *testing.T) {
+	scalarMulDistributesOverAdd := func(x, y scalar.Scalar) bool {
+		// The quickcheck generation strategy chooses a random
+		// 32-byte array, but we require that the high bit is
+		// unset.  FIXME: make Scalar opaque.  Until then,
+		// mask the high bits:
+		x[31] &= 127
+		y[31] &= 127
+		var z scalar.Scalar
+		z.Add(&x, &y)
+		var p, q, r, check ProjP3
+		p.ScalarMul(&x, &B)
+		q.ScalarMul(&y, &B)
+		r.ScalarMul(&z, &B)
+		check.Add(&p, &q)
+		return check.Equal(&r) == 1
+	}
+
+	if err := quick.Check(scalarMulDistributesOverAdd, quickCheckConfig); err != nil {
+		t.Error(err)
+	}
+}