diff --git a/internal/poly1305/bits_compat.go b/internal/poly1305/bits_compat.go
deleted file mode 100644
index d33c889..0000000
--- a/internal/poly1305/bits_compat.go
+++ /dev/null
@@ -1,39 +0,0 @@
-// Copyright 2019 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-//go:build !go1.13
-
-package poly1305
-
-// Generic fallbacks for the math/bits intrinsics, copied from
-// src/math/bits/bits.go. They were added in Go 1.12, but Add64 and Sum64 had
-// variable time fallbacks until Go 1.13.
-
-func bitsAdd64(x, y, carry uint64) (sum, carryOut uint64) {
-	sum = x + y + carry
-	carryOut = ((x & y) | ((x | y) &^ sum)) >> 63
-	return
-}
-
-func bitsSub64(x, y, borrow uint64) (diff, borrowOut uint64) {
-	diff = x - y - borrow
-	borrowOut = ((^x & y) | (^(x ^ y) & diff)) >> 63
-	return
-}
-
-func bitsMul64(x, y uint64) (hi, lo uint64) {
-	const mask32 = 1<<32 - 1
-	x0 := x & mask32
-	x1 := x >> 32
-	y0 := y & mask32
-	y1 := y >> 32
-	w0 := x0 * y0
-	t := x1*y0 + w0>>32
-	w1 := t & mask32
-	w2 := t >> 32
-	w1 += x0 * y1
-	hi = x1*y1 + w2 + w1>>32
-	lo = x * y
-	return
-}
diff --git a/internal/poly1305/bits_go1.13.go b/internal/poly1305/bits_go1.13.go
deleted file mode 100644
index 495c1fa..0000000
--- a/internal/poly1305/bits_go1.13.go
+++ /dev/null
@@ -1,21 +0,0 @@
-// Copyright 2019 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-//go:build go1.13
-
-package poly1305
-
-import "math/bits"
-
-func bitsAdd64(x, y, carry uint64) (sum, carryOut uint64) {
-	return bits.Add64(x, y, carry)
-}
-
-func bitsSub64(x, y, borrow uint64) (diff, borrowOut uint64) {
-	return bits.Sub64(x, y, borrow)
-}
-
-func bitsMul64(x, y uint64) (hi, lo uint64) {
-	return bits.Mul64(x, y)
-}
diff --git a/internal/poly1305/sum_generic.go b/internal/poly1305/sum_generic.go
index e041da5..ec2202b 100644
--- a/internal/poly1305/sum_generic.go
+++ b/internal/poly1305/sum_generic.go
@@ -7,7 +7,10 @@
 
 package poly1305
 
-import "encoding/binary"
+import (
+	"encoding/binary"
+	"math/bits"
+)
 
 // Poly1305 [RFC 7539] is a relatively simple algorithm: the authentication tag
 // for a 64 bytes message is approximately
@@ -114,13 +117,13 @@
 }
 
 func mul64(a, b uint64) uint128 {
-	hi, lo := bitsMul64(a, b)
+	hi, lo := bits.Mul64(a, b)
 	return uint128{lo, hi}
 }
 
 func add128(a, b uint128) uint128 {
-	lo, c := bitsAdd64(a.lo, b.lo, 0)
-	hi, c := bitsAdd64(a.hi, b.hi, c)
+	lo, c := bits.Add64(a.lo, b.lo, 0)
+	hi, c := bits.Add64(a.hi, b.hi, c)
 	if c != 0 {
 		panic("poly1305: unexpected overflow")
 	}
@@ -155,8 +158,8 @@
 		// hide leading zeroes. For full chunks, that's 1 << 128, so we can just
 		// add 1 to the most significant (2¹²⁸) limb, h2.
 		if len(msg) >= TagSize {
-			h0, c = bitsAdd64(h0, binary.LittleEndian.Uint64(msg[0:8]), 0)
-			h1, c = bitsAdd64(h1, binary.LittleEndian.Uint64(msg[8:16]), c)
+			h0, c = bits.Add64(h0, binary.LittleEndian.Uint64(msg[0:8]), 0)
+			h1, c = bits.Add64(h1, binary.LittleEndian.Uint64(msg[8:16]), c)
 			h2 += c + 1
 
 			msg = msg[TagSize:]
@@ -165,8 +168,8 @@
 			copy(buf[:], msg)
 			buf[len(msg)] = 1
 
-			h0, c = bitsAdd64(h0, binary.LittleEndian.Uint64(buf[0:8]), 0)
-			h1, c = bitsAdd64(h1, binary.LittleEndian.Uint64(buf[8:16]), c)
+			h0, c = bits.Add64(h0, binary.LittleEndian.Uint64(buf[0:8]), 0)
+			h1, c = bits.Add64(h1, binary.LittleEndian.Uint64(buf[8:16]), c)
 			h2 += c
 
 			msg = nil
@@ -219,9 +222,9 @@
 		m3 := h2r1
 
 		t0 := m0.lo
-		t1, c := bitsAdd64(m1.lo, m0.hi, 0)
-		t2, c := bitsAdd64(m2.lo, m1.hi, c)
-		t3, _ := bitsAdd64(m3.lo, m2.hi, c)
+		t1, c := bits.Add64(m1.lo, m0.hi, 0)
+		t2, c := bits.Add64(m2.lo, m1.hi, c)
+		t3, _ := bits.Add64(m3.lo, m2.hi, c)
 
 		// Now we have the result as 4 64-bit limbs, and we need to reduce it
 		// modulo 2¹³⁰ - 5. The special shape of this Crandall prime lets us do
@@ -243,14 +246,14 @@
 
 		// To add c * 5 to h, we first add cc = c * 4, and then add (cc >> 2) = c.
 
-		h0, c = bitsAdd64(h0, cc.lo, 0)
-		h1, c = bitsAdd64(h1, cc.hi, c)
+		h0, c = bits.Add64(h0, cc.lo, 0)
+		h1, c = bits.Add64(h1, cc.hi, c)
 		h2 += c
 
 		cc = shiftRightBy2(cc)
 
-		h0, c = bitsAdd64(h0, cc.lo, 0)
-		h1, c = bitsAdd64(h1, cc.hi, c)
+		h0, c = bits.Add64(h0, cc.lo, 0)
+		h1, c = bits.Add64(h1, cc.hi, c)
 		h2 += c
 
 		// h2 is at most 3 + 1 + 1 = 5, making the whole of h at most
@@ -287,9 +290,9 @@
 	// in constant time, we compute t = h - (2¹³⁰ - 5), and select h as the
 	// result if the subtraction underflows, and t otherwise.
 
-	hMinusP0, b := bitsSub64(h0, p0, 0)
-	hMinusP1, b := bitsSub64(h1, p1, b)
-	_, b = bitsSub64(h2, p2, b)
+	hMinusP0, b := bits.Sub64(h0, p0, 0)
+	hMinusP1, b := bits.Sub64(h1, p1, b)
+	_, b = bits.Sub64(h2, p2, b)
 
 	// h = h if h < p else h - p
 	h0 = select64(b, h0, hMinusP0)
@@ -301,8 +304,8 @@
 	//
 	// by just doing a wide addition with the 128 low bits of h and discarding
 	// the overflow.
-	h0, c := bitsAdd64(h0, s[0], 0)
-	h1, _ = bitsAdd64(h1, s[1], c)
+	h0, c := bits.Add64(h0, s[0], 0)
+	h1, _ = bits.Add64(h1, s[1], c)
 
 	binary.LittleEndian.PutUint64(out[0:8], h0)
 	binary.LittleEndian.PutUint64(out[8:16], h1)