internal/bigmod: add more //go:norace annotations and refactoring

internal/bigmod/nat.go

@@ -18,6 +18,15 @@ const (
 	_S = _W / 8
 )
 
+// Note: These functions make many loops over all the words in a Nat.
+// These loops used to be in assembly, invisible to -race, -asan, and -msan,
+// but now they are in Go and incur significant overhead in those modes.
+// To bring the old performance back, we mark all functions that loop
+// over Nat words with //go:norace. Because //go:norace does not
+// propagate across inlining, we must also mark functions that inline
+// //go:norace functions - specifically, those that inline add, addMulVVW,
+// assign, cmpGeq, rshift1, and sub.
+
 // choice represents a constant-time boolean. The value of choice is always
 // either 1 or 0. We use an int instead of bool in order to make decisions in
 // constant time by turning it into a mask.
@@ -40,14 +49,6 @@ func ctEq(x, y uint) choice {
 	return not(choice(c1 | c2))
 }
 
-// ctGeq returns 1 if x >= y, and 0 otherwise. The execution time of this
-// function does not depend on its inputs.
-func ctGeq(x, y uint) choice {
-	// If x < y, then x - y generates a carry.
-	_, carry := bits.Sub(x, y, 0)
-	return not(choice(carry))
-}
-
 // Nat represents an arbitrary natural number
 //
 // Each Nat has an announced length, which is the number of limbs it has stored.
@@ -84,6 +85,7 @@ func (x *Nat) expand(n int) *Nat {
 		return x
 	}
 	extraLimbs := x.limbs[len(x.limbs):n]
+	// clear(extraLimbs)
 	for i := range extraLimbs {
 		extraLimbs[i] = 0
 	}
@@ -97,6 +99,7 @@ func (x *Nat) reset(n int) *Nat {
 		x.limbs = make([]uint, n)
 		return x
 	}
+	// clear(x.limbs)
 	for i := range x.limbs {
 		x.limbs[i] = 0
 	}
@@ -131,7 +134,7 @@ func (x *Nat) trim() *Nat {
 }
 
 // set assigns x = y, optionally resizing x to the appropriate size.
-func (x *Nat) Set(y *Nat) *Nat {
+func (x *Nat) set(y *Nat) *Nat {
 	x.reset(len(y.limbs))
 	copy(x.limbs, y.limbs)
 	return x
@@ -164,12 +167,14 @@ func (x *Nat) Bytes(m *Modulus) []byte {
 // SetBytes returns an error if b >= m.
 //
 // The output will be resized to the size of m and overwritten.
+//
+//go:norace
 func (x *Nat) SetBytes(b []byte, m *Modulus) (*Nat, error) {
 	x.resetFor(m)
 	if err := x.setBytes(b); err != nil {
 		return nil, err
 	}
-	if x.CmpGeq(m.nat) == yes {
+	if x.cmpGeq(m.nat) == yes {
 		return nil, errors.New("input overflows the modulus")
 	}
 	return x, nil
@@ -195,20 +200,6 @@ func (x *Nat) SetOverflowingBytes(b []byte, m *Modulus) (*Nat, error) {
 	return x, nil
 }
 
-// SetOverflowedBytes assigns x = (b mode (m-1)) + 1, where b is a slice of big-endian bytes.
-//
-// The output will be resized to the size of m and overwritten.
-func (x *Nat) SetOverflowedBytes(b []byte, m *Modulus) *Nat {
-	mMinusOne := NewNat().Set(m.nat)
-	mMinusOne.limbs[0]-- // due to m is odd, so we can safely subtract 1
-	one := NewNat().resetFor(m)
-	one.limbs[0] = 1
-	x.resetToBytes(b)
-	x = NewNat().modNat(x, mMinusOne) // x = x mod (m-1)
-	x.add(one)                        // we can safely add 1, no need to check overflow
-	return x
-}
-
 // bigEndianUint returns the contents of buf interpreted as a
 // big-endian encoded uint value.
 func bigEndianUint(buf []byte) uint {
@@ -309,8 +300,6 @@ func (x *Nat) IsMinusOne(m *Modulus) choice {
 }
 
 // IsOdd returns 1 if x is odd, and 0 otherwise.
-//
-//go:norace
 func (x *Nat) IsOdd() choice {
 	if len(x.limbs) == 0 {
 		return no
@@ -333,12 +322,12 @@ func (x *Nat) TrailingZeroBitsVarTime() uint {
 	return t
 }
 
-// CmpGeq returns 1 if x >= y, and 0 otherwise.
+// cmpGeq returns 1 if x >= y, and 0 otherwise.
 //
 // Both operands must have the same announced length.
 //
 //go:norace
-func (x *Nat) CmpGeq(y *Nat) choice {
+func (x *Nat) cmpGeq(y *Nat) choice {
 	// Eliminate bounds checks in the loop.
 	size := len(x.limbs)
 	xLimbs := x.limbs[:size]
@@ -564,6 +553,8 @@ func NewModulus(b []byte) (*Modulus, error) {
 
 // NewModulusProduct creates a new Modulus from the product of two numbers
 // represented as big-endian byte slices. The result must be greater than one.
+//
+//go:norace
 func NewModulusProduct(a, b []byte) (*Modulus, error) {
 	x := NewNat().resetToBytes(a)
 	y := NewNat().resetToBytes(b)
@@ -602,30 +593,23 @@ func (m *Modulus) Nat() *Nat {
 	// Make a copy so that the caller can't modify m.nat or alias it with
 	// another Nat in a modulus operation.
 	n := NewNat()
-	n.Set(m.nat)
+	n.set(m.nat)
 	return n
 }
 
-// shiftIn calculates x = x << _W + y mod m.
-//
-// This assumes that x is already reduced mod m, and that y < 2^_W.
-func (x *Nat) shiftIn(y uint, m *Modulus) *Nat {
-	return x.shiftInNat(y, m.nat)
-}
-
 // shiftIn calculates x = x << _W + y mod m.
 //
 // This assumes that x is already reduced mod m, and that y < 2^_W.
 //
 //go:norace
-func (x *Nat) shiftInNat(y uint, m *Nat) *Nat {
+func (x *Nat) shiftIn(y uint, m *Modulus) *Nat {
-	d := NewNat().reset(len(m.limbs))
+	d := NewNat().resetFor(m)
 
 	// Eliminate bounds checks in the loop.
-	size := len(m.limbs)
+	size := len(m.nat.limbs)
 	xLimbs := x.limbs[:size]
 	dLimbs := d.limbs[:size]
-	mLimbs := m.limbs[:size]
+	mLimbs := m.nat.limbs[:size]
 
 	// Each iteration of this loop computes x = 2x + b mod m, where b is a bit
 	// from y. Effectively, it left-shifts x and adds y one bit at a time,
@@ -657,17 +641,10 @@ func (x *Nat) shiftInNat(y uint, m *Nat) *Nat {
 // This works regardless how large the value of x is.
 //
 // The output will be resized to the size of m and overwritten.
+//
+//go:norace
 func (out *Nat) Mod(x *Nat, m *Modulus) *Nat {
-	return out.modNat(x, m.nat)
+	out.resetFor(m)
-}
-
-// Mod calculates out = x mod m.
-//
-// This works regardless how large the value of x is.
-//
-// The output will be resized to the size of m and overwritten.
-func (out *Nat) modNat(x *Nat, m *Nat) *Nat {
-	out.reset(len(m.limbs))
 	// Working our way from the most significant to the least significant limb,
 	// we can insert each limb at the least significant position, shifting all
 	// previous limbs left by _W. This way each limb will get shifted by the
@@ -676,7 +653,7 @@ func (out *Nat) modNat(x *Nat, m *Nat) *Nat {
 	i := len(x.limbs) - 1
 	// For the first N - 1 limbs we can skip the actual shifting and position
 	// them at the shifted position, which starts at min(N - 2, i).
-	start := len(m.limbs) - 2
+	start := len(m.nat.limbs) - 2
 	if i < start {
 		start = i
 	}
@@ -686,7 +663,7 @@ func (out *Nat) modNat(x *Nat, m *Nat) *Nat {
 	}
 	// We shift in the remaining limbs, reducing modulo m each time.
 	for i >= 0 {
-		out.shiftInNat(x.limbs[i], m)
+		out.shiftIn(x.limbs[i], m)
 		i--
 	}
 	return out
@@ -715,8 +692,10 @@ func (out *Nat) resetFor(m *Modulus) *Nat {
 // overflowed its size, meaning abstractly x > 2^_W*n > m even if x < m.
 //
 // x and m operands must have the same announced length.
+//
+//go:norace
 func (x *Nat) maybeSubtractModulus(always choice, m *Modulus) {
-	t := NewNat().Set(x)
+	t := NewNat().set(x)
 	underflow := t.sub(m.nat)
 	// We keep the result if x - m didn't underflow (meaning x >= m)
 	// or if always was set.
@@ -728,10 +707,12 @@ func (x *Nat) maybeSubtractModulus(always choice, m *Modulus) {
 //
 // The length of both operands must be the same as the modulus. Both operands
 // must already be reduced modulo m.
+//
+//go:norace
 func (x *Nat) Sub(y *Nat, m *Modulus) *Nat {
 	underflow := x.sub(y)
 	// If the subtraction underflowed, add m.
-	t := NewNat().Set(x)
+	t := NewNat().set(x)
 	t.add(m.nat)
 	x.assign(choice(underflow), t)
 	return x
@@ -752,6 +733,8 @@ func (x *Nat) SubOne(m *Modulus) *Nat {
 //
 // The length of both operands must be the same as the modulus. Both operands
 // must already be reduced modulo m.
+//
+//go:norace
 func (x *Nat) Add(y *Nat, m *Modulus) *Nat {
 	overflow := x.add(y)
 	x.maybeSubtractModulus(choice(overflow), m)
@@ -789,6 +772,8 @@ func (x *Nat) montgomeryReduction(m *Modulus) *Nat {
 //
 // All inputs should be the same length and already reduced modulo m.
 // x will be resized to the size of m and overwritten.
+//
+//go:norace
 func (x *Nat) montgomeryMul(a *Nat, b *Nat, m *Modulus) *Nat {
 	n := len(m.nat.limbs)
 	mLimbs := m.nat.limbs[:n]
@@ -946,11 +931,13 @@ func addMulVVW(z, x []uint, y uint) (carry uint) {
 //
 // The length of both operands must be the same as the modulus. Both operands
 // must already be reduced modulo m.
+//
+//go:norace
 func (x *Nat) Mul(y *Nat, m *Modulus) *Nat {
 	if m.odd {
 		// A Montgomery multiplication by a value out of the Montgomery domain
 		// takes the result out of Montgomery representation.
-		xR := NewNat().Set(x).montgomeryRepresentation(m) // xR = x * R mod m
+		xR := NewNat().set(x).montgomeryRepresentation(m) // xR = x * R mod m
 		return x.montgomeryMul(xR, y, m)                  // x = xR * y / R mod m
 	}
 	n := len(m.nat.limbs)
@@ -1009,6 +996,8 @@ func (x *Nat) Mul(y *Nat, m *Modulus) *Nat {
 // to the size of m and overwritten. x must already be reduced modulo m.
 //
 // m must be odd, or Exp will panic.
+//
+//go:norace
 func (out *Nat) Exp(x *Nat, e []byte, m *Modulus) *Nat {
 	if !m.odd {
 		panic("bigmod: modulus for Exp must be odd")
@@ -1025,7 +1014,7 @@ func (out *Nat) Exp(x *Nat, e []byte, m *Modulus) *Nat {
 		NewNat(), NewNat(), NewNat(), NewNat(), NewNat(),
 		NewNat(), NewNat(), NewNat(), NewNat(), NewNat(),
 	}
-	table[0].Set(x).montgomeryRepresentation(m)
+	table[0].set(x).montgomeryRepresentation(m)
 	for i := 1; i < len(table); i++ {
 		table[i].montgomeryMul(table[i-1], table[0], m)
 	}
@@ -1071,8 +1060,8 @@ func (out *Nat) ExpShortVarTime(x *Nat, e uint, m *Modulus) *Nat {
 	// For short exponents, precomputing a table and using a window like in Exp
 	// doesn't pay off. Instead, we do a simple conditional square-and-multiply
 	// chain, skipping the initial run of zeroes.
-	xR := NewNat().Set(x).montgomeryRepresentation(m)
+	xR := NewNat().set(x).montgomeryRepresentation(m)
-	out.Set(xR)
+	out.set(xR)
 	for i := bits.UintSize - bits.Len(e) + 1; i < bits.UintSize; i++ {
 		out.montgomeryMul(out, out, m)
 		if k := (e >> (bits.UintSize - i - 1)) & 1; k != 0 {
@@ -1088,6 +1077,8 @@ func (out *Nat) ExpShortVarTime(x *Nat, e uint, m *Modulus) *Nat {
 //
 // a must be reduced modulo m, but doesn't need to have the same size. The
 // output will be resized to the size of m and overwritten.
+//
+//go:norace
 func (x *Nat) InverseVarTime(a *Nat, m *Modulus) (*Nat, bool) {
 	// This is the extended binary GCD algorithm described in the Handbook of
 	// Applied Cryptography, Algorithm 14.61, adapted by BoringSSL to bound
@@ -1121,7 +1112,7 @@ func (x *Nat) InverseVarTime(a *Nat, m *Modulus) (*Nat, bool) {
 		return x, false
 	}
 
-	u := NewNat().Set(a).ExpandFor(m)
+	u := NewNat().set(a).ExpandFor(m)
 	v := m.Nat()
 
 	A := NewNat().reset(len(m.nat.limbs))
@@ -1148,7 +1139,7 @@ func (x *Nat) InverseVarTime(a *Nat, m *Modulus) (*Nat, bool) {
 		// If both u and v are odd, subtract the smaller from the larger.
 		// If u = v, we need to subtract from v to hit the modified exit condition.
 		if u.IsOdd() == yes && v.IsOdd() == yes {
-			if v.CmpGeq(u) == no {
+			if v.cmpGeq(u) == no {
 				u.sub(v)
 				A.Add(C, m)
 				B.Add(D, &Modulus{nat: a})
@@ -1189,7 +1180,7 @@ func (x *Nat) InverseVarTime(a *Nat, m *Modulus) (*Nat, bool) {
 			if u.IsOne() == no {
 				return x, false
 			}
-			return x.Set(A), true
+			return x.set(A), true
 		}
 	}
 }

internal/bigmod/nat_extension.go

@@ -0,0 +1,31 @@
+package bigmod
+
+func (x *Nat) Set(y *Nat) *Nat {
+	return x.set(y)
+}
+
+// SetOverflowedBytes assigns x = (b mode (m-1)) + 1, where b is a slice of big-endian bytes.
+//
+// The output will be resized to the size of m and overwritten.
+//
+//go:norace
+func (x *Nat) SetOverflowedBytes(b []byte, m *Modulus) *Nat {
+	mMinusOne := NewNat().set(m.nat)
+	mMinusOne.limbs[0]-- // due to m is odd, so we can safely subtract 1
+	mMinusOneM, _ := NewModulus(mMinusOne.Bytes(m))
+	one := NewNat().resetFor(m)
+	one.limbs[0] = 1
+	x.resetToBytes(b)
+	x = NewNat().Mod(x, mMinusOneM) // x = x mod (m-1)
+	x.add(one)                      // we can safely add 1, no need to check overflow
+	return x
+}
+
+// CmpGeq returns 1 if x >= y, and 0 otherwise.
+//
+// Both operands must have the same announced length.
+//
+//go:norace
+func (x *Nat) CmpGeq(y *Nat) choice {
+	return x.cmpGeq(y)
+}

internal/bigmod/nat_test.go

@@ -61,9 +61,9 @@ func (*Nat) Generate(r *rand.Rand, size int) reflect.Value {
 
 func testModAddCommutative(a *Nat, b *Nat) bool {
 	m := maxModulus(uint(len(a.limbs)))
-	aPlusB := new(Nat).Set(a)
+	aPlusB := new(Nat).set(a)
 	aPlusB.Add(b, m)
-	bPlusA := new(Nat).Set(b)
+	bPlusA := new(Nat).set(b)
 	bPlusA.Add(a, m)
 	return aPlusB.Equal(bPlusA) == 1
 }
@@ -77,7 +77,7 @@ func TestModAddCommutative(t *testing.T) {
 
 func testModSubThenAddIdentity(a *Nat, b *Nat) bool {
 	m := maxModulus(uint(len(a.limbs)))
-	original := new(Nat).Set(a)
+	original := new(Nat).set(a)
 	a.Sub(b, m)
 	a.Add(b, m)
 	return a.Equal(original) == 1
@@ -97,9 +97,9 @@ func TestMontgomeryRoundtrip(t *testing.T) {
 		aPlusOne := new(big.Int).SetBytes(natBytes(a))
 		aPlusOne.Add(aPlusOne, big.NewInt(1))
 		m, _ := NewModulus(aPlusOne.Bytes())
-		monty := new(Nat).Set(a)
+		monty := new(Nat).set(a)
 		monty.montgomeryRepresentation(m)
-		aAgain := new(Nat).Set(monty)
+		aAgain := new(Nat).set(monty)
 		aAgain.montgomeryMul(monty, one, m)
 		if a.Equal(aAgain) != 1 {
 			t.Errorf("%v != %v", a, aAgain)