diff --git a/Lib/gzip.py b/Lib/gzip.py
index aa8386e..e82cc61 100644
--- a/Lib/gzip.py
+++ b/Lib/gzip.py
@@ -25,19 +25,16 @@
     return i
 
 def LOWU32(i):
-    """Return the low-order 32 bits of an int, as a non-negative int."""
+    """Return the low-order 32 bits, as a non-negative int"""
     return i & 0xFFFFFFFF
 
-def write32(output, value):
-    output.write(struct.pack("<l", value))
-
 def write32u(output, value):
     # The L format writes the bit pattern correctly whether signed
     # or unsigned.
     output.write(struct.pack("<L", value))
 
 def read32(input):
-    return struct.unpack("<l", input.read(4))[0]
+    return struct.unpack("<I", input.read(4))[0]
 
 def open(filename, mode="rb", compresslevel=9):
     """Shorthand for GzipFile(filename, mode, compresslevel).
@@ -141,7 +138,7 @@
 
     def _init_write(self, filename):
         self.name = filename
-        self.crc = zlib.crc32("")
+        self.crc = zlib.crc32("") & 0xffffffff
         self.size = 0
         self.writebuf = []
         self.bufsize = 0
@@ -168,7 +165,7 @@
             self.fileobj.write(fname + b'\000')
 
     def _init_read(self):
-        self.crc = zlib.crc32("")
+        self.crc = zlib.crc32("") & 0xffffffff
         self.size = 0
 
     def _read_gzip_header(self):
@@ -214,7 +211,7 @@
             raise ValueError("write() on closed GzipFile object")
         if len(data) > 0:
             self.size = self.size + len(data)
-            self.crc = zlib.crc32(data, self.crc)
+            self.crc = zlib.crc32(data, self.crc) & 0xffffffff
             self.fileobj.write( self.compress.compress(data) )
             self.offset += len(data)
 
@@ -306,7 +303,7 @@
             self._new_member = True
 
     def _add_read_data(self, data):
-        self.crc = zlib.crc32(data, self.crc)
+        self.crc = zlib.crc32(data, self.crc) & 0xffffffff
         self.extrabuf = self.extrabuf + data
         self.extrasize = self.extrasize + len(data)
         self.size = self.size + len(data)
@@ -319,25 +316,19 @@
         # stored is the true file size mod 2**32.
         self.fileobj.seek(-8, 1)
         crc32 = read32(self.fileobj)
-        isize = U32(read32(self.fileobj))   # may exceed 2GB
-        if U32(crc32) != U32(self.crc):
-            raise IOError("CRC check failed %s != %s" % (hex(U32(crc32)),
-                                                         hex(U32(self.crc))))
-        elif isize != LOWU32(self.size):
+        isize = read32(self.fileobj)  # may exceed 2GB
+        if crc32 != self.crc:
+            raise IOError("CRC check failed %s != %s" % (hex(crc32),
+                                                         hex(self.crc)))
+        elif isize != self.size:
             raise IOError("Incorrect length of data produced")
 
     def close(self):
         if self.mode == WRITE:
             self.fileobj.write(self.compress.flush())
-            # The native zlib crc is an unsigned 32-bit integer, but
-            # the Python wrapper implicitly casts that to a signed C
-            # long.  So, on a 32-bit box self.crc may "look negative",
-            # while the same crc on a 64-bit box may "look positive".
-            # To avoid irksome warnings from the `struct` module, force
-            # it to look positive on all boxes.
-            write32u(self.fileobj, LOWU32(self.crc))
+            write32u(self.fileobj, self.crc)
             # self.size may exceed 2GB, or even 4GB
-            write32u(self.fileobj, LOWU32(self.size))
+            write32u(self.fileobj, self.size)
             self.fileobj = None
         elif self.mode == READ:
             self.fileobj = None