diff --git a/pypdf/_writer.py b/pypdf/_writer.py
index 00b9d498c..4a003856f 100644
--- a/pypdf/_writer.py
+++ b/pypdf/_writer.py
@@ -32,6 +32,7 @@
 import enum
 import hashlib
 import re
+import time
 import uuid
 from io import BytesIO, FileIO, IOBase
 from pathlib import Path
@@ -136,13 +137,6 @@ class ObjectDeletionFlag(enum.IntFlag):
     IMAGES = XOBJECT_IMAGES | INLINE_IMAGES | DRAWING_IMAGES
 
 
-def _rolling_checksum(stream: BytesIO, blocksize: int = 65536) -> str:
-    hash = hashlib.md5()
-    for block in iter(lambda: stream.read(blocksize), b""):
-        hash.update(block)
-    return hash.hexdigest()
-
-
 class PdfWriter(PdfDocCommon):
     """
     Write a PDF file out, given pages produced by another class or through
@@ -1152,10 +1146,14 @@ def clone_document_from_reader(
                 after_page_append(page.get_object())
 
     def _compute_document_identifier(self) -> ByteStringObject:
-        stream = BytesIO()
-        self._write_pdf_structure(stream)
-        stream.seek(0)
-        return ByteStringObject(_rolling_checksum(stream).encode("utf8"))
+        md5 = hashlib.md5()
+        md5.update(str(time.time()).encode("utf-8"))
+        md5.update(str(self.fileobj).encode("utf-8"))
+        md5.update(str(len(self._objects)).encode("utf-8"))
+        if hasattr(self, "_info"):
+            for k, v in cast(DictionaryObject, self._info.get_object()).items():
+                md5.update(f"{k}={v}".encode())
+        return ByteStringObject(md5.hexdigest().encode("utf-8"))
 
     def generate_file_identifiers(self) -> None:
         """
@@ -1174,7 +1172,7 @@ def generate_file_identifiers(self) -> None:
             id2 = self._compute_document_identifier()
         else:
             id1 = self._compute_document_identifier()
-            id2 = id1
+            id2 = ByteStringObject(id1.original_bytes)
         self._ID = ArrayObject((id1, id2))
 
     def encrypt(