diff --git a/peer/internal/uprng/uprng.go b/peer/internal/uprng/uprng.go
index ead5a4c78..f858d32a1 100644
--- a/peer/internal/uprng/uprng.go
+++ b/peer/internal/uprng/uprng.go
@@ -6,7 +6,9 @@ package uprng
 
 import (
 	cryptorand "crypto/rand"
+	"encoding/binary"
 	"io"
+	"math/bits"
 	"sync"
 	"time"
 
@@ -27,20 +29,42 @@ const (
 	maxCipherDuration = 20 * time.Second
 )
 
-var (
-	key   = make([]byte, chacha20.KeySize)
-	nonce = make([]byte, chacha20.NonceSize)
-)
+// nonce implements a 12-byte little endian counter suitable for use as an
+// incrementing ChaCha20 nonce.
+type nonce struct {
+	limbs [3]uint32
+	bytes []byte
+}
+
+func newNonce() *nonce {
+	return &nonce{bytes: make([]byte, chacha20.NonceSize)}
+}
+
+func (n *nonce) inc() {
+	var carry uint32
+	n.limbs[0], carry = bits.Add32(n.limbs[0], 1, carry)
+	n.limbs[1], carry = bits.Add32(n.limbs[1], 0, carry)
+	n.limbs[2], carry = bits.Add32(n.limbs[2], 0, carry)
+	n.limbs[0], _ = bits.Add32(n.limbs[0], 0, carry)
+	binary.LittleEndian.PutUint32(n.bytes[0:4], n.limbs[0])
+	binary.LittleEndian.PutUint32(n.bytes[4:8], n.limbs[1])
+	binary.LittleEndian.PutUint32(n.bytes[8:12], n.limbs[2])
+}
 
 type prng struct {
 	cipher *chacha20.Cipher
 	read   int
 	t      time.Time
+	key    []byte
+	nonce  *nonce
 	mu     sync.Mutex
 }
 
 func newPRNG() *prng {
-	p := new(prng)
+	p := &prng{
+		nonce: newNonce(),
+		key:   make([]byte, chacha20.KeySize),
+	}
 	p.seed()
 	return p
 }
@@ -49,20 +73,17 @@ func newPRNG() *prng {
 // cipher has been originally seeded.
 // Panics only during initial seeding if a crypto/rand read errors.
 func (p *prng) seed() {
-	_, err := cryptorand.Read(key)
+	_, err := cryptorand.Read(p.key)
 	if err != nil && p.cipher == nil {
 		panic(err)
 	}
 	if p.cipher != nil {
-		p.cipher.XORKeyStream(key, key)
+		p.cipher.XORKeyStream(p.key, p.key)
 	}
 
 	// never errors with correct key and nonce sizes
-	cipher, _ := chacha20.NewUnauthenticatedCipher(key, nonce)
-
-	for i := range key {
-		key[i] = 0
-	}
+	cipher, _ := chacha20.NewUnauthenticatedCipher(p.key, p.nonce.bytes)
+	p.nonce.inc()
 
 	p.cipher = cipher
 	p.read = 0