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To: Proxmox Backup Server development discussion <pbs-devel@lists.proxmox.com>,
 Lubomir Apostolov <Lubomir.Apostolov@directique.com>
References: <20201209152553.8752-1-d.csapak@proxmox.com>
 <718D0AF11703FA4C85B0535448A05610038195BAB5@SCOM4.directique.net>
From: Dominik Csapak <d.csapak@proxmox.com>
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Date: Thu, 10 Dec 2020 08:37:39 +0100
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Subject: Re: [pbs-devel] [PATCH proxmox-backup] docs: explain some technical
 details about datastores/chunks
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On 12/9/20 5:23 PM, Lubomir Apostolov wrote:
> Hi,

Hi,

thanks for your message, your questions mean i did not
write the documentation clear enough, i try to answer here,
but i'll also incorporate that info in a v2

> 
> After reading https://bugzilla.proxmox.com/show_bug.cgi?id=3138 and your mail, I'd like to discuss the following statement :
> "we have to read all files again in every backup" for both cases - file and image based backup.

just to clarify, that sentence only relates to 'file-based backups', 
since for block based backups, we do not care about files at all,
just about the 'block image' we try back up.

> 
> The image-backup seems simpler - fixed-size chunks.
> PBS should be able to link a snapshot with it's backup, and backup only differencies with parent snapshot as for example zfs send/recv works.
> Every backup knows the chunk order and chunk size, so it can map every chunk to the original image extents.
> The snapshot differences gives extents, which PBS can map to overlapped chunks, and send only those chunks, while referencing unchanged chunks from previous backup chunks list.

while something like that *could* work, it is not how we do it.
instead of relying on storage snapshots (which may
not be available, e.g. for '.raw' files)
we simply iterate over the content of the block level image,
and create the chunks hashes. this normally means that we have
to read the whole image, but in case of pve qemu vms,
we use (as written in my patch) dirty-bitmaps
which keeps track of the changed blocks
(only those have to be hashed and backed up)

> 
> The variable-size chunks based on files needs another mapping between chunks and filenames.
> The rolling hash over the data may be linked a list containing the filenames inside, and then the snapshot diff containing files can flag the chunks to be saved.
> 
> So where's the catch ?

again, we do not rely on storage snapshots, since those may
not be available (e.g. ext4)

so, first we iterate over the filesystem/directory, from there,
we create a consistent archive format (pxar). this is something
like 'tar' but can be created in a streaming fashion (which we
need).

only over that archive, we create the chunks. so the data that
the chunker gets, has no direct relation to any files

hope that explains it better

> 
> Best regards,
> Lubomir Apostolov
> 
> -----Message d'origine-----
> De : pbs-devel [mailto:pbs-devel-bounces@lists.proxmox.com] De la part de Dominik Csapak
> Envoyé : mercredi 9 décembre 2020 16:26
> À : pbs-devel@lists.proxmox.com
> Objet : [pbs-devel] [PATCH proxmox-backup] 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              |   1 +
>   docs/technical-overview.rst | 152 ++++++++++++++++++++++++++++++++++++
>   docs/terminology.rst        |   3 +
>   3 files changed, 156 insertions(+)
>   create mode 100644 docs/technical-overview.rst
> 
> diff --git a/docs/index.rst b/docs/index.rst
> index fffcb4fd..f3e6bf0c 100644
> --- a/docs/index.rst
> +++ b/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
> diff --git a/docs/technical-overview.rst b/docs/technical-overview.rst
> new file mode 100644
> index 00000000..20f937bd
> --- /dev/null
> +++ b/docs/technical-overview.rst
> @@ -0,0 +1,152 @@
> +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 indexes contained in a snapshot reference chunks on which the deduplication
> +of datastores is based.
> +
> +Chunks
> +------
> +
> +A chunk is some (sometimes encrypted) data with a CRC-32 checksum at
> +the end and a type marker at the beginning. It is identified by a
> +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 the 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 touched chunks of the disk have to be uploaded for a backup.
> +
> +Dynamically-sized Chunks
> +^^^^^^^^^^^^^^^^^^^^^^^^
> +
> +If does not want to backup block-based systems but 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 effect of deduplication.
> +
> +To improve this, `Proxmox Backup`_ Server uses dynamically-sized chunks
> +instead. Instead of splitting an image into fixed sizes, it generates
> +a consistent file archive and uses a rolling hash over the data
> +to calculate chunk boundaries. We use a variant of Buzhash which
> +is a cyclic polynomial algorithm.
> +
> +It works by continuously calculating a hashsum while iterating over the
> +data, and on certain conditions it triggers a hash boundary.
> +
> +Assuming that there is not a change in every file of the to system to
> +be backed up, eventually the algorithm triggers the boundary on the
> +same data as a previous backup, resulting in a chunk that can be reused.
> +
> +Encrypted Chunks
> +^^^^^^^^^^^^^^^^
> +
> +A special case are encrypted chunks. Both fixed- and dynamically-sized
> +chunks can be encrypted, and their handling is slightly different
> +from normal chunks.
> +
> +The hash 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 and chunks that exist
> +already in the previous backup, do not need to be encrypted and uploaded.
> +
> +Caveats and Limitations
> +-----------------------
> +
> +Notes on hash collisions
> +^^^^^^^^^^^^^^^^^^^^^^^^
> +Every hash has a chance to produce collisions, meaning two (or more) inputs
> +generating the same hashsum. 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 not feasible to
> +calculate with normal 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 sizes are, this is not
> +problem, since a potential attacker cannot arbitrarily add the content.
> +
> +
> +File-based Backup
> +^^^^^^^^^^^^^^^^^
> +
> +Since there is no relation between files and dynamically-sized chunks,
> +we have to read all files again in every backup. Otherwise it would not be
> +possible to generate a format 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.
> +
> +
> diff --git a/docs/terminology.rst b/docs/terminology.rst
> index 89ec7646..3eff9780 100644
> --- a/docs/terminology.rst
> +++ b/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
>   ---------------
>