docs: explain some technical details about datastores/chunks

adds explanations for:
* what datastores are
* their relation with snapshots/chunks
* basic information about chunk directory structures
* fixed-/dynamically-sized chunks
* special handling of encrypted chunks
* hash collision probability
* limitation of file-based backups

Signed-off-by: Dominik Csapak <d.csapak@proxmox.com>

docs/index.rst

@@ -33,6 +33,7 @@ in the section entitled "GNU Free Documentation License".
    pve-integration.rst
    pxar-tool.rst
    sysadmin.rst
+   technical-overview.rst
    faq.rst
 
 .. raw:: latex

docs/technical-overview.rst

@@ -0,0 +1,166 @@
+Technical Overview
+==================
+
+.. _technical_overview:
+
+Datastores
+----------
+
+A Datastore is the logical place where :ref:`Backup Snapshots <backup_snapshot>`
+and their chunks are stored. Snapshots consist of a manifest, blobs,
+dynamic- and fixed-indexes (see :ref:`terminology`), and are stored in the
+following directory structure:
+
+ <datastore-root>/<type>/<id>/<time>/
+
+The deduplication of datastores is based on reusing chunks, which are
+referenced by the indexes in a backup snapshot. This means that multiple
+indexes can reference the same chunks, reducing the amount of space
+needed to contain the data (even across backup snapshots).
+
+Chunks
+------
+
+A chunk is some (possibly encrypted) data with a CRC-32 checksum at
+the end and a type marker at the beginning. It is identified by the
+SHA-256 checksum of its content.
+
+To generate such chunks, backup data is split either into fixed-size or
+dynamically sized chunks. The same content will be hashed to the same
+checksum.
+
+The chunks of a datastore are found in
+
+ <datastore-root>/.chunks/
+
+This chunk directory is further subdivided by the first four byte of the
+chunks checksum, so the chunk with the checksum
+
+ a342e8151cbf439ce65f3df696b54c67a114982cc0aa751f2852c2f7acc19a8b
+
+lives in
+
+ <datastore-root>/.chunks/a342/
+
+This is done to reduce the number of files per directory, as having
+many files per directory can be bad for file system performance.
+
+These chunk directories ('0000'-'ffff') will be preallocated when a datastore is
+created.
+
+Fixed-sized Chunks
+^^^^^^^^^^^^^^^^^^
+
+For block based backups (like VMs), fixed-sized chunks are used. The content
+(disk image), is split into chunks of the same length (typically 4 MiB).
+
+This works very well for VM images, since the file system on the guest
+most often tries to allocate files in contiguous pieces, so new files get
+new blocks, and changing existing files changes only their own blocks.
+
+As an optimization, VMs in `Proxmox VE`_ can make use of 'dirty bitmaps',
+which can track the changed blocks of an image. Since these bitmap
+are also a representation of the image split into chunks, we have
+a direct relation between dirty blocks of the image and chunks we have
+to upload, so only modified chunks of the disk have to be uploaded for a backup.
+
+Since we always split the image into chunks of the same size, unchanged
+blocks will result in identical checksums for those chunks, so such chunks do not
+need to be backed up again. This way storage snapshots are not needed to find
+the changed blocks.
+
+For consistency, `Proxmox VE`_ uses a QEMU internal snapshot mechanism, that
+does not rely on storage snapshots either.
+
+Dynamically sized Chunks
+^^^^^^^^^^^^^^^^^^^^^^^^
+
+If one does not want to backup block-based systems but rather file-based systems,
+using fixed-sized chunks is not a good idea, since every time a file
+would change in size, the remaining data gets shifted around and this
+would result in many chunks changing, reducing the amount of deduplication.
+
+To improve this, `Proxmox Backup`_ Server uses dynamically sized chunks
+instead. Instead of splitting an image into fixed sizes, it first generates
+a consistent file archive (:ref:`pxar <pxar-format>`) and uses a rolling hash
+over this on-the-fly generated archive to calculate chunk boundaries.
+
+We use a variant of Buzhash which is a cyclic polynomial algorithm.
+It works by continuously calculating a checksum while iterating over the
+data, and on certain conditions it triggers a hash boundary.
+
+Assuming that most files of the system that is to be backed up have not changed,
+eventually the algorithm triggers the boundary on the same data as a previous
+backup, resulting in chunks that can be reused.
+
+Encrypted Chunks
+^^^^^^^^^^^^^^^^
+
+Encrypted chunks are a special case. Both fixed- and dynamically sized
+chunks can be encrypted, and they are handled in a slightly different manner
+than normal chunks.
+
+The hashes of encrypted chunks are calculated not with the actual (encrypted)
+chunk content, but with the plaintext content concatenated with
+the encryption key. This way, two chunks of the same data encrypted with
+different keys generate two different checksums and no collisions occur for
+multiple encryption keys.
+
+This is done to speed up the client part of the backup, since it only needs
+to encrypt chunks that are actually getting uploaded. Chunks that exist
+already in the previous backup, do not need to be encrypted and uploaded.
+
+Caveats and Limitations
+-----------------------
+
+Notes on hash collisions
+^^^^^^^^^^^^^^^^^^^^^^^^
+
+Every hashing algorithm has a chance to produce collisions, meaning two (or more)
+inputs generate the same checksum. For SHA-256, this chance is negligible.
+To calculate such a collision, one can use the ideas of the 'birthday problem'
+from probability theory. For big numbers, this is actually infeasible to
+calculate with regular computers, but there is a good approximation:
+
+.. math::
+
+ p(n, d) = 1 - e^{-n^2/(2d)}
+
+Where `n` is the number of tries, and `d` is the number of possibilities.
+So for example, if we assume a large datastore of 1 PiB, and an average chunk
+size of 4 MiB, we have :math:`n = 268435456` tries, and :math:`d = 2^{256}`
+possibilities.  Using the above formula we get that the probability of a
+collision in that scenario is:
+
+.. math::
+
+ 3.1115 * 10^{-61}
+
+For context, in a lottery game of 6 of 45, the chance to correctly guess all
+6 numbers is only :math:`1.2277 * 10^{-7}`.
+
+So it is extremely unlikely that such a collision would occur by accident
+in a normal datastore.
+
+Additionally, SHA-256 is prone to length extension attacks, but since
+there is an upper limit for how big the chunk are, this is not a
+problem, since a potential attacker cannot arbitrarily add content to
+the data beyond that limit.
+
+File-based Backup
+^^^^^^^^^^^^^^^^^
+
+Since dynamically sized chunks (for file-based backups) are created on a custom
+archive format (pxar) and not over the files directly, there is no relation
+between files and the chunks. This means we have to read all files again
+for every backup, otherwise it would not be possible to generate a consistent
+pxar archive where the original chunks can be reused.
+
+Verification of encrypted chunks
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+For encrypted chunks, only the checksum of the original (plaintext) data
+is available, making it impossible for the server (without the encryption key),
+to verify its content against it. Instead only the CRC-32 checksum gets checked.
+
+

docs/terminology.rst

@@ -1,3 +1,5 @@
+.. _terminology:
+
 Terminology
 ===========
 
@@ -99,6 +101,7 @@ Backup Group
 The tuple ``<type>/<ID>`` is called a backup group. Such a group
 may contain one or more backup snapshots.
 
+.. _backup_snapshot:
 
 Backup Snapshot
 ---------------