diff --git a/kernel/bpf/syscall.c b/kernel/bpf/syscall.c
index 2843bbb..4e6dee1 100644
--- a/kernel/bpf/syscall.c
+++ b/kernel/bpf/syscall.c
@@ -623,9 +623,20 @@ static int bpf_map_mmap(struct file *filp, struct vm_area_struct *vma)
 
 	mutex_lock(&map->freeze_mutex);
 
-	if ((vma->vm_flags & VM_WRITE) && map->frozen) {
-		err = -EPERM;
-		goto out;
+	if (vma->vm_flags & VM_WRITE) {
+		if (map->frozen) {
+			err = -EPERM;
+			goto out;
+		}
+		/* map is meant to be read-only, so do not allow mapping as
+		 * writable, because it's possible to leak a writable page
+		 * reference and allows user-space to still modify it after
+		 * freezing, while verifier will assume contents do not change
+		 */
+		if (map->map_flags & BPF_F_RDONLY_PROG) {
+			err = -EACCES;
+			goto out;
+		}
 	}
 
 	/* set default open/close callbacks */