diff --git a/src/archive/zip/reader.go b/src/archive/zip/reader.go
index 10d9d5e5bf..f68ab09723 100644
--- a/src/archive/zip/reader.go
+++ b/src/archive/zip/reader.go
@@ -8,6 +8,7 @@ import (
 	"bufio"
 	"encoding/binary"
 	"errors"
+	"fmt"
 	"hash"
 	"hash/crc32"
 	"io"
@@ -77,6 +78,9 @@ func (z *Reader) init(r io.ReaderAt, size int64) error {
 	if err != nil {
 		return err
 	}
+	if end.directoryRecords > uint64(size)/fileHeaderLen {
+		return fmt.Errorf("archive/zip: TOC declares impossible %d files in %d byte zip", end.directoryRecords, size)
+	}
 	z.r = r
 	z.File = make([]*File, 0, end.directoryRecords)
 	z.Comment = end.comment
diff --git a/src/archive/zip/reader_test.go b/src/archive/zip/reader_test.go
index 6a8cab34cd..4806b89458 100644
--- a/src/archive/zip/reader_test.go
+++ b/src/archive/zip/reader_test.go
@@ -551,10 +551,7 @@ func TestIssue10957(t *testing.T) {
 		"\v\x00\x00\x00\x00\x00")
 	z, err := NewReader(bytes.NewReader(data), int64(len(data)))
 	if err != nil {
-		if z != nil {
-			panic("non nil z")
-		}
-		return
+		t.Fatal(err)
 	}
 	for i, f := range z.File {
 		r, err := f.Open()
@@ -573,3 +570,15 @@ func TestIssue10957(t *testing.T) {
 		r.Close()
 	}
 }
+
+// Verify the number of files is sane.
+func TestIssue10956(t *testing.T) {
+	data := []byte("PK\x06\x06PK\x06\a0000\x00\x00\x00\x00\x00\x00\x00\x00" +
+		"0000PK\x05\x06000000000000" +
+		"0000\v\x00000\x00\x00\x00\x00\x00\x00\x000")
+	_, err := NewReader(bytes.NewReader(data), int64(len(data)))
+	const want = "TOC declares impossible 3472328296227680304 files in 57 byte"
+	if err == nil && !strings.Contains(err.Error(), want) {
+		t.Errorf("error = %v; want %q", err, want)
+	}
+}