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Move "doc" to root dir
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Alexander Neumann
@@ -1,489 +0,0 @@
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This document gives a high-level overview of the design and repository layout
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of the restic backup program.
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Terminology
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===========
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This section introduces terminology used in this document.
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*Repository*: All data produced during a backup is sent to and stored in a
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repository in a structured form, for example in a file system hierarchy with
|
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several subdirectories. A repository implementation must be able to fulfill a
|
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number of operations, e.g. list the contents.
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*Blob*: A Blob combines a number of data bytes with identifying information
|
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like the SHA-256 hash of the data and its length.
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*Pack*: A Pack combines one or more Blobs, e.g. in a single file.
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|
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*Snapshot*: A Snapshot stands for the state of a file or directory that has
|
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been backed up at some point in time. The state here means the content and meta
|
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data like the name and modification time for the file or the directory and its
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contents.
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*Storage ID*: A storage ID is the SHA-256 hash of the content stored in the
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repository. This ID is required in order to load the file from the repository.
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Repository Format
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=================
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All data is stored in a restic repository. A repository is able to store data
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of several different types, which can later be requested based on an ID. This
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so-called "storage ID" is the SHA-256 hash of the content of a file. All files
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in a repository are only written once and never modified afterwards. This
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allows accessing and even writing to the repository with multiple clients in
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parallel. Only the delete operation removes data from the repository.
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At the time of writing, the only implemented repository type is based on
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directories and files. Such repositories can be accessed locally on the same
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system or via the integrated SFTP client (or any other storage back end).
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The directory layout is the same for both access methods.
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This repository type is described in the following section.
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Repositories consist of several directories and a file called `config`. For
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all other files stored in the repository, the name for the file is the lower
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case hexadecimal representation of the storage ID, which is the SHA-256 hash of
|
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the file's contents. This allows for easy verification of files for accidental
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modifications, like disk read errors, by simply running the program `sha256sum`
|
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and comparing its output to the file name. If the prefix of a filename is
|
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unique amongst all the other files in the same directory, the prefix may be
|
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used instead of the complete filename.
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|
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Apart from the files stored within the `keys` directory, all files are encrypted
|
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with AES-256 in counter mode (CTR). The integrity of the encrypted data is
|
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secured by a Poly1305-AES message authentication code (sometimes also referred
|
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to as a "signature").
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In the first 16 bytes of each encrypted file the initialisation vector (IV) is
|
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stored. It is followed by the encrypted data and completed by the 16 byte
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MAC. The format is: `IV || CIPHERTEXT || MAC`. The complete encryption
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overhead is 32 bytes. For each file, a new random IV is selected.
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The file `config` is encrypted this way and contains a JSON document like the
|
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following:
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{
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"version": 1,
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"id": "5956a3f67a6230d4a92cefb29529f10196c7d92582ec305fd71ff6d331d6271b",
|
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"chunker_polynomial": "25b468838dcb75"
|
||||
}
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After decryption, restic first checks that the version field contains a version
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number that it understands, otherwise it aborts. At the moment, the version is
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expected to be 1. The field `id` holds a unique ID which consists of 32
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random bytes, encoded in hexadecimal. This uniquely identifies the repository,
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regardless if it is accessed via SFTP or locally. The field
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`chunker_polynomial` contains a parameter that is used for splitting large
|
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files into smaller chunks (see below).
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The basic layout of a sample restic repository is shown here:
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/tmp/restic-repo
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├── config
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├── data
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│ ├── 21
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│ │ └── 2159dd48f8a24f33c307b750592773f8b71ff8d11452132a7b2e2a6a01611be1
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||||
│ ├── 32
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│ │ └── 32ea976bc30771cebad8285cd99120ac8786f9ffd42141d452458089985043a5
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│ ├── 59
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│ │ └── 59fe4bcde59bd6222eba87795e35a90d82cd2f138a27b6835032b7b58173a426
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||||
│ ├── 73
|
||||
│ │ └── 73d04e6125cf3c28a299cc2f3cca3b78ceac396e4fcf9575e34536b26782413c
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||||
│ [...]
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├── index
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||||
│ ├── c38f5fb68307c6a3e3aa945d556e325dc38f5fb68307c6a3e3aa945d556e325d
|
||||
│ └── ca171b1b7394d90d330b265d90f506f9984043b342525f019788f97e745c71fd
|
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├── keys
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│ └── b02de829beeb3c01a63e6b25cbd421a98fef144f03b9a02e46eff9e2ca3f0bd7
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├── locks
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├── snapshots
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│ └── 22a5af1bdc6e616f8a29579458c49627e01b32210d09adb288d1ecda7c5711ec
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└── tmp
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A repository can be initialized with the `restic init` command, e.g.:
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$ restic -r /tmp/restic-repo init
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Pack Format
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-----------
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All files in the repository except Key and Pack files just contain raw data,
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stored as `IV || Ciphertext || MAC`. Pack files may contain one or more Blobs
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of data.
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|
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A Pack's structure is as follows:
|
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|
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EncryptedBlob1 || ... || EncryptedBlobN || EncryptedHeader || Header_Length
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|
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At the end of the Pack file is a header, which describes the content. The
|
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header is encrypted and authenticated. `Header_Length` is the length of the
|
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encrypted header encoded as a four byte integer in little-endian encoding.
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Placing the header at the end of a file allows writing the blobs in a
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continuous stream as soon as they are read during the backup phase. This
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reduces code complexity and avoids having to re-write a file once the pack is
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complete and the content and length of the header is known.
|
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All the blobs (`EncryptedBlob1`, `EncryptedBlobN` etc.) are authenticated and
|
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encrypted independently. This enables repository reorganisation without having
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to touch the encrypted Blobs. In addition it also allows efficient indexing,
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for only the header needs to be read in order to find out which Blobs are
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contained in the Pack. Since the header is authenticated, authenticity of the
|
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header can be checked without having to read the complete Pack.
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|
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After decryption, a Pack's header consists of the following elements:
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Type_Blob1 || Length(EncryptedBlob1) || Hash(Plaintext_Blob1) ||
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[...]
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Type_BlobN || Length(EncryptedBlobN) || Hash(Plaintext_Blobn) ||
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|
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This is enough to calculate the offsets for all the Blobs in the Pack. Length
|
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is the length of a Blob as a four byte integer in little-endian format. The
|
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type field is a one byte field and labels the content of a blob according to
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||||
the following table:
|
||||
|
||||
Type | Meaning
|
||||
-----|---------
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||||
0 | data
|
||||
1 | tree
|
||||
|
||||
All other types are invalid, more types may be added in the future.
|
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|
||||
For reconstructing the index or parsing a pack without an index, first the last
|
||||
four bytes must be read in order to find the length of the header. Afterwards,
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the header can be read and parsed, which yields all plaintext hashes, types,
|
||||
offsets and lengths of all included blobs.
|
||||
|
||||
Indexing
|
||||
--------
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|
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Index files contain information about Data and Tree Blobs and the Packs they
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are contained in and store this information in the repository. When the local
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cached index is not accessible any more, the index files can be downloaded and
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used to reconstruct the index. The files are encrypted and authenticated like
|
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Data and Tree Blobs, so the outer structure is `IV || Ciphertext || MAC` again.
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The plaintext consists of a JSON document like the following:
|
||||
|
||||
{
|
||||
"supersedes": [
|
||||
"ed54ae36197f4745ebc4b54d10e0f623eaaaedd03013eb7ae90df881b7781452"
|
||||
],
|
||||
"packs": [
|
||||
{
|
||||
"id": "73d04e6125cf3c28a299cc2f3cca3b78ceac396e4fcf9575e34536b26782413c",
|
||||
"blobs": [
|
||||
{
|
||||
"id": "3ec79977ef0cf5de7b08cd12b874cd0f62bbaf7f07f3497a5b1bbcc8cb39b1ce",
|
||||
"type": "data",
|
||||
"offset": 0,
|
||||
"length": 25
|
||||
},{
|
||||
"id": "9ccb846e60d90d4eb915848add7aa7ea1e4bbabfc60e573db9f7bfb2789afbae",
|
||||
"type": "tree",
|
||||
"offset": 38,
|
||||
"length": 100
|
||||
},
|
||||
{
|
||||
"id": "d3dc577b4ffd38cc4b32122cabf8655a0223ed22edfd93b353dc0c3f2b0fdf66",
|
||||
"type": "data",
|
||||
"offset": 150,
|
||||
"length": 123
|
||||
}
|
||||
]
|
||||
}, [...]
|
||||
]
|
||||
}
|
||||
|
||||
This JSON document lists Packs and the blobs contained therein. In this
|
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example, the Pack `73d04e61` contains two data Blobs and one Tree blob, the
|
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plaintext hashes are listed afterwards.
|
||||
|
||||
The field `supersedes` lists the storage IDs of index files that have been
|
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replaced with the current index file. This happens when index files are
|
||||
repacked, for example when old snapshots are removed and Packs are recombined.
|
||||
|
||||
There may be an arbitrary number of index files, containing information on
|
||||
non-disjoint sets of Packs. The number of packs described in a single file is
|
||||
chosen so that the file size is kept below 8 MiB.
|
||||
|
||||
Keys, Encryption and MAC
|
||||
------------------------
|
||||
|
||||
All data stored by restic in the repository is encrypted with AES-256 in
|
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counter mode and authenticated using Poly1305-AES. For encrypting new data first
|
||||
16 bytes are read from a cryptographically secure pseudorandom number generator
|
||||
as a random nonce. This is used both as the IV for counter mode and the nonce
|
||||
for Poly1305. This operation needs three keys: A 32 byte for AES-256 for
|
||||
encryption, a 16 byte AES key and a 16 byte key for Poly1305. For details see
|
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the original paper [The Poly1305-AES message-authentication
|
||||
code](http://cr.yp.to/mac/poly1305-20050329.pdf) by Dan Bernstein.
|
||||
The data is then encrypted with AES-256 and afterwards a message authentication
|
||||
code (MAC) is computed over the ciphertext, everything is then stored as
|
||||
IV || CIPHERTEXT || MAC.
|
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|
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The directory `keys` contains key files. These are simple JSON documents which
|
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contain all data that is needed to derive the repository's master encryption and
|
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message authentication keys from a user's password. The JSON document from the
|
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repository can be pretty-printed for example by using the Python module `json`
|
||||
(shortened to increase readability):
|
||||
|
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$ python -mjson.tool /tmp/restic-repo/keys/b02de82*
|
||||
{
|
||||
"hostname": "kasimir",
|
||||
"username": "fd0"
|
||||
"kdf": "scrypt",
|
||||
"N": 65536,
|
||||
"r": 8,
|
||||
"p": 1,
|
||||
"created": "2015-01-02T18:10:13.48307196+01:00",
|
||||
"data": "tGwYeKoM0C4j4/9DFrVEmMGAldvEn/+iKC3te/QE/6ox/V4qz58FUOgMa0Bb1cIJ6asrypCx/Ti/pRXCPHLDkIJbNYd2ybC+fLhFIJVLCvkMS+trdywsUkglUbTbi+7+Ldsul5jpAj9vTZ25ajDc+4FKtWEcCWL5ICAOoTAxnPgT+Lh8ByGQBH6KbdWabqamLzTRWxePFoYuxa7yXgmj9A==",
|
||||
"salt": "uW4fEI1+IOzj7ED9mVor+yTSJFd68DGlGOeLgJELYsTU5ikhG/83/+jGd4KKAaQdSrsfzrdOhAMftTSih5Ux6w==",
|
||||
}
|
||||
|
||||
When the repository is opened by restic, the user is prompted for the
|
||||
repository password. This is then used with `scrypt`, a key derivation function
|
||||
(KDF), and the supplied parameters (`N`, `r`, `p` and `salt`) to derive 64 key
|
||||
bytes. The first 32 bytes are used as the encryption key (for AES-256) and the
|
||||
last 32 bytes are used as the message authentication key (for Poly1305-AES).
|
||||
These last 32 bytes are divided into a 16 byte AES key `k` followed by 16 bytes
|
||||
of secret key `r`. The key `r` is then masked for use with Poly1305 (see the
|
||||
paper for details).
|
||||
|
||||
Those message authentication keys (`k` and `r`) are used to compute a MAC over
|
||||
the bytes contained in the JSON field `data` (after removing the Base64
|
||||
encoding and not including the last 32 byte). If the password is incorrect or
|
||||
the key file has been tampered with, the computed MAC will not match the last
|
||||
16 bytes of the data, and restic exits with an error. Otherwise, the data is
|
||||
decrypted with the encryption key derived from `scrypt`. This yields a JSON
|
||||
document which contains the master encryption and message authentication keys
|
||||
for this repository (encoded in Base64). The command `restic cat masterkey` can
|
||||
be used as follows to decrypt and pretty-print the master key:
|
||||
|
||||
$ restic -r /tmp/restic-repo cat masterkey
|
||||
{
|
||||
"mac": {
|
||||
"k": "evFWd9wWlndL9jc501268g==",
|
||||
"r": "E9eEDnSJZgqwTOkDtOp+Dw=="
|
||||
},
|
||||
"encrypt": "UQCqa0lKZ94PygPxMRqkePTZnHRYh1k1pX2k2lM2v3Q=",
|
||||
}
|
||||
|
||||
All data in the repository is encrypted and authenticated with these master keys.
|
||||
For encryption, the AES-256 algorithm in Counter mode is used. For message
|
||||
authentication, Poly1305-AES is used as described above.
|
||||
|
||||
A repository can have several different passwords, with a key file for each.
|
||||
This way, the password can be changed without having to re-encrypt all data.
|
||||
|
||||
Snapshots
|
||||
---------
|
||||
|
||||
A snapshots represents a directory with all files and sub-directories at a
|
||||
given point in time. For each backup that is made, a new snapshot is created. A
|
||||
snapshot is a JSON document that is stored in an encrypted file below the
|
||||
directory `snapshots` in the repository. The filename is the storage ID. This
|
||||
string is unique and used within restic to uniquely identify a snapshot.
|
||||
|
||||
The command `restic cat snapshot` can be used as follows to decrypt and
|
||||
pretty-print the contents of a snapshot file:
|
||||
|
||||
$ restic -r /tmp/restic-repo cat snapshot 22a5af1b
|
||||
enter password for repository:
|
||||
{
|
||||
"time": "2015-01-02T18:10:50.895208559+01:00",
|
||||
"tree": "2da81727b6585232894cfbb8f8bdab8d1eccd3d8f7c92bc934d62e62e618ffdf",
|
||||
"dir": "/tmp/testdata",
|
||||
"hostname": "kasimir",
|
||||
"username": "fd0",
|
||||
"uid": 1000,
|
||||
"gid": 100
|
||||
}
|
||||
|
||||
Here it can be seen that this snapshot represents the contents of the directory
|
||||
`/tmp/testdata`. The most important field is `tree`.
|
||||
|
||||
All content within a restic repository is referenced according to its SHA-256
|
||||
hash. Before saving, each file is split into variable sized Blobs of data. The
|
||||
SHA-256 hashes of all Blobs are saved in an ordered list which then represents
|
||||
the content of the file.
|
||||
|
||||
In order to relate these plaintext hashes to the actual location within a Pack
|
||||
file , an index is used. If the index is not available, the header of all data
|
||||
Blobs can be read.
|
||||
|
||||
Trees and Data
|
||||
--------------
|
||||
|
||||
A snapshot references a tree by the SHA-256 hash of the JSON string
|
||||
representation of its contents. Trees and data are saved in pack files in a
|
||||
subdirectory of the directory `data`.
|
||||
|
||||
The command `restic cat tree` can be used to inspect the tree referenced above:
|
||||
|
||||
$ restic -r /tmp/restic-repo cat tree b8138ab08a4722596ac89c917827358da4672eac68e3c03a8115b88dbf4bfb59
|
||||
enter password for repository:
|
||||
{
|
||||
"nodes": [
|
||||
{
|
||||
"name": "testdata",
|
||||
"type": "dir",
|
||||
"mode": 493,
|
||||
"mtime": "2014-12-22T14:47:59.912418701+01:00",
|
||||
"atime": "2014-12-06T17:49:21.748468803+01:00",
|
||||
"ctime": "2014-12-22T14:47:59.912418701+01:00",
|
||||
"uid": 1000,
|
||||
"gid": 100,
|
||||
"user": "fd0",
|
||||
"inode": 409704562,
|
||||
"content": null,
|
||||
"subtree": "b26e315b0988ddcd1cee64c351d13a100fedbc9fdbb144a67d1b765ab280b4dc"
|
||||
}
|
||||
]
|
||||
}
|
||||
|
||||
A tree contains a list of entries (in the field `nodes`) which contain meta
|
||||
data like a name and timestamps. When the entry references a directory, the
|
||||
field `subtree` contains the plain text ID of another tree object.
|
||||
|
||||
When the command `restic cat tree` is used, the storage hash is needed to print
|
||||
a tree. The tree referenced above can be dumped as follows:
|
||||
|
||||
$ restic -r /tmp/restic-repo cat tree 8b238c8811cc362693e91a857460c78d3acf7d9edb2f111048691976803cf16e
|
||||
enter password for repository:
|
||||
{
|
||||
"nodes": [
|
||||
{
|
||||
"name": "testfile",
|
||||
"type": "file",
|
||||
"mode": 420,
|
||||
"mtime": "2014-12-06T17:50:23.34513538+01:00",
|
||||
"atime": "2014-12-06T17:50:23.338468713+01:00",
|
||||
"ctime": "2014-12-06T17:50:23.34513538+01:00",
|
||||
"uid": 1000,
|
||||
"gid": 100,
|
||||
"user": "fd0",
|
||||
"inode": 416863351,
|
||||
"size": 1234,
|
||||
"links": 1,
|
||||
"content": [
|
||||
"50f77b3b4291e8411a027b9f9b9e64658181cc676ce6ba9958b95f268cb1109d"
|
||||
]
|
||||
},
|
||||
[...]
|
||||
]
|
||||
}
|
||||
|
||||
This tree contains a file entry. This time, the `subtree` field is not present
|
||||
and the `content` field contains a list with one plain text SHA-256 hash.
|
||||
|
||||
The command `restic cat data` can be used to extract and decrypt data given a
|
||||
plaintext ID, e.g. for the data mentioned above:
|
||||
|
||||
$ restic -r /tmp/restic-repo cat blob 50f77b3b4291e8411a027b9f9b9e64658181cc676ce6ba9958b95f268cb1109d | sha256sum
|
||||
enter password for repository:
|
||||
50f77b3b4291e8411a027b9f9b9e64658181cc676ce6ba9958b95f268cb1109d -
|
||||
|
||||
As can be seen from the output of the program `sha256sum`, the hash matches the
|
||||
plaintext hash from the map included in the tree above, so the correct data has
|
||||
been returned.
|
||||
|
||||
Locks
|
||||
-----
|
||||
|
||||
The restic repository structure is designed in a way that allows parallel
|
||||
access of multiple instance of restic and even parallel writes. However, there
|
||||
are some functions that work more efficient or even require exclusive access of
|
||||
the repository. In order to implement these functions, restic processes are
|
||||
required to create a lock on the repository before doing anything.
|
||||
|
||||
Locks come in two types: Exclusive and non-exclusive locks. At most one
|
||||
process can have an exclusive lock on the repository, and during that time
|
||||
there must not be any other locks (exclusive and non-exclusive). There may be
|
||||
multiple non-exclusive locks in parallel.
|
||||
|
||||
A lock is a file in the subdir `locks` whose filename is the storage ID of
|
||||
the contents. It is encrypted and authenticated the same way as other files
|
||||
in the repository and contains the following JSON structure:
|
||||
|
||||
{
|
||||
"time": "2015-06-27T12:18:51.759239612+02:00",
|
||||
"exclusive": false,
|
||||
"hostname": "kasimir",
|
||||
"username": "fd0",
|
||||
"pid": 13607,
|
||||
"uid": 1000,
|
||||
"gid": 100
|
||||
}
|
||||
|
||||
The field `exclusive` defines the type of lock. When a new lock is to be
|
||||
created, restic checks all locks in the repository. When a lock is found, it
|
||||
is tested if the lock is stale, which is the case for locks with timestamps
|
||||
older than 30 minutes. If the lock was created on the same machine, even for
|
||||
younger locks it is tested whether the process is still alive by sending a
|
||||
signal to it. If that fails, restic assumes that the process is dead and
|
||||
considers the lock to be stale.
|
||||
|
||||
When a new lock is to be created and no other conflicting locks are
|
||||
detected, restic creates a new lock, waits, and checks if other locks
|
||||
appeared in the repository. Depending on the type of the other locks and the
|
||||
lock to be created, restic either continues or fails.
|
||||
|
||||
Backups and Deduplication
|
||||
=========================
|
||||
|
||||
For creating a backup, restic scans the source directory for all files,
|
||||
sub-directories and other entries. The data from each file is split into
|
||||
variable length Blobs cut at offsets defined by a sliding window of 64 byte.
|
||||
The implementation uses Rabin Fingerprints for implementing this Content
|
||||
Defined Chunking (CDC). An irreducible polynomial is selected at random and
|
||||
saved in the file `config` when a repository is initialized, so that watermark
|
||||
attacks are much harder.
|
||||
|
||||
Files smaller than 512 KiB are not split, Blobs are of 512 KiB to 8 MiB in
|
||||
size. The implementation aims for 1 MiB Blob size on average.
|
||||
|
||||
For modified files, only modified Blobs have to be saved in a subsequent
|
||||
backup. This even works if bytes are inserted or removed at arbitrary positions
|
||||
within the file.
|
||||
|
||||
Threat Model
|
||||
============
|
||||
|
||||
The design goals for restic include being able to securely store backups in a
|
||||
location that is not completely trusted, e.g. a shared system where others can
|
||||
potentially access the files or (in the case of the system administrator) even
|
||||
modify or delete them.
|
||||
|
||||
General assumptions:
|
||||
|
||||
* The host system a backup is created on is trusted. This is the most basic
|
||||
requirement, and essential for creating trustworthy backups.
|
||||
|
||||
The restic backup program guarantees the following:
|
||||
|
||||
* Accessing the unencrypted content of stored files and metadata should not
|
||||
be possible without a password for the repository. Everything except the
|
||||
metadata included for informational purposes in the key files is encrypted and
|
||||
authenticated.
|
||||
|
||||
* Modifications (intentional or unintentional) can be detected automatically
|
||||
on several layers:
|
||||
|
||||
1. For all accesses of data stored in the repository it is checked whether
|
||||
the cryptographic hash of the contents matches the storage ID (the
|
||||
file's name). This way, modifications (bad RAM, broken harddisk) can be
|
||||
detected easily.
|
||||
|
||||
2. Before decrypting any data, the MAC on the encrypted data is
|
||||
checked. If there has been a modification, the MAC check will
|
||||
fail. This step happens even before the data is decrypted, so data that
|
||||
has been tampered with is not decrypted at all.
|
||||
|
||||
However, the restic backup program is not designed to protect against attackers
|
||||
deleting files at the storage location. There is nothing that can be done about
|
||||
this. If this needs to be guaranteed, get a secure location without any access
|
||||
from third parties. If you assume that attackers have write access to your
|
||||
files at the storage location, attackers are able to figure out (e.g. based on
|
||||
the timestamps of the stored files) which files belong to what snapshot. When
|
||||
only these files are deleted, the particular snapshot vanished and all
|
||||
snapshots depending on data that has been added in the snapshot cannot be
|
||||
restored completely. Restic is not designed to detect this attack.
|
||||
@@ -1,38 +0,0 @@
|
||||
# Maintainer: Florian Daniel <fd@noxa.de>
|
||||
# Contributor: Eldar Tsraev <elts@culab.org>
|
||||
# Contributor: Andreas Guth <andreas.guth@rwth-aachen.de>
|
||||
# Contributor: Alexander Neumann <alexander@bumpern.de>
|
||||
options=(!strip)
|
||||
pkgname=restic-git
|
||||
pkgver=v0.1.0.r172.g1f1b8e1
|
||||
pkgrel=1
|
||||
pkgdesc="restic is a program that does backups right."
|
||||
arch=('i686' 'x86_64')
|
||||
url="https://github.com/restic/restic"
|
||||
license=('BSD')
|
||||
depends=('glibc')
|
||||
makedepends=('git' 'go>=1.3')
|
||||
provides=('restic')
|
||||
conflicts=('restic')
|
||||
source=("${pkgname}::git+https://github.com/restic/restic")
|
||||
md5sums=('SKIP')
|
||||
|
||||
importpath='github.com/restic/restic'
|
||||
|
||||
pkgver() {
|
||||
cd "$pkgname"
|
||||
git describe --long | sed 's/\([^-]*-g\)/r\1/;s/-/./g'
|
||||
}
|
||||
|
||||
build() {
|
||||
cd "$pkgname"
|
||||
go run build.go
|
||||
}
|
||||
|
||||
package() {
|
||||
install -Dm755 "$pkgname/restic" "$pkgdir/usr/bin/restic"
|
||||
install -Dm644 "$pkgname/LICENSE" "$pkgdir/usr/share/licenses/$pkgname/LICENSE"
|
||||
install -Dm644 "$pkgname/README.md" "$pkgdir/usr/share/doc/$pkgname/README"
|
||||
}
|
||||
|
||||
# vim:set ts=2 sw=2 et:
|
||||
Binary file not shown.
@@ -1,93 +0,0 @@
|
||||
Copyright (c) 2011, Eduardo Tunni (http://www.tipo.net.ar),
|
||||
with Reserved Font Name "Lemon"
|
||||
This Font Software is licensed under the SIL Open Font License, Version 1.1.
|
||||
This license is copied below, and is also available with a FAQ at:
|
||||
http://scripts.sil.org/OFL
|
||||
|
||||
|
||||
-----------------------------------------------------------
|
||||
SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007
|
||||
-----------------------------------------------------------
|
||||
|
||||
PREAMBLE
|
||||
The goals of the Open Font License (OFL) are to stimulate worldwide
|
||||
development of collaborative font projects, to support the font creation
|
||||
efforts of academic and linguistic communities, and to provide a free and
|
||||
open framework in which fonts may be shared and improved in partnership
|
||||
with others.
|
||||
|
||||
The OFL allows the licensed fonts to be used, studied, modified and
|
||||
redistributed freely as long as they are not sold by themselves. The
|
||||
fonts, including any derivative works, can be bundled, embedded,
|
||||
redistributed and/or sold with any software provided that any reserved
|
||||
names are not used by derivative works. The fonts and derivatives,
|
||||
however, cannot be released under any other type of license. The
|
||||
requirement for fonts to remain under this license does not apply
|
||||
to any document created using the fonts or their derivatives.
|
||||
|
||||
DEFINITIONS
|
||||
"Font Software" refers to the set of files released by the Copyright
|
||||
Holder(s) under this license and clearly marked as such. This may
|
||||
include source files, build scripts and documentation.
|
||||
|
||||
"Reserved Font Name" refers to any names specified as such after the
|
||||
copyright statement(s).
|
||||
|
||||
"Original Version" refers to the collection of Font Software components as
|
||||
distributed by the Copyright Holder(s).
|
||||
|
||||
"Modified Version" refers to any derivative made by adding to, deleting,
|
||||
or substituting -- in part or in whole -- any of the components of the
|
||||
Original Version, by changing formats or by porting the Font Software to a
|
||||
new environment.
|
||||
|
||||
"Author" refers to any designer, engineer, programmer, technical
|
||||
writer or other person who contributed to the Font Software.
|
||||
|
||||
PERMISSION & CONDITIONS
|
||||
Permission is hereby granted, free of charge, to any person obtaining
|
||||
a copy of the Font Software, to use, study, copy, merge, embed, modify,
|
||||
redistribute, and sell modified and unmodified copies of the Font
|
||||
Software, subject to the following conditions:
|
||||
|
||||
1) Neither the Font Software nor any of its individual components,
|
||||
in Original or Modified Versions, may be sold by itself.
|
||||
|
||||
2) Original or Modified Versions of the Font Software may be bundled,
|
||||
redistributed and/or sold with any software, provided that each copy
|
||||
contains the above copyright notice and this license. These can be
|
||||
included either as stand-alone text files, human-readable headers or
|
||||
in the appropriate machine-readable metadata fields within text or
|
||||
binary files as long as those fields can be easily viewed by the user.
|
||||
|
||||
3) No Modified Version of the Font Software may use the Reserved Font
|
||||
Name(s) unless explicit written permission is granted by the corresponding
|
||||
Copyright Holder. This restriction only applies to the primary font name as
|
||||
presented to the users.
|
||||
|
||||
4) The name(s) of the Copyright Holder(s) or the Author(s) of the Font
|
||||
Software shall not be used to promote, endorse or advertise any
|
||||
Modified Version, except to acknowledge the contribution(s) of the
|
||||
Copyright Holder(s) and the Author(s) or with their explicit written
|
||||
permission.
|
||||
|
||||
5) The Font Software, modified or unmodified, in part or in whole,
|
||||
must be distributed entirely under this license, and must not be
|
||||
distributed under any other license. The requirement for fonts to
|
||||
remain under this license does not apply to any document created
|
||||
using the Font Software.
|
||||
|
||||
TERMINATION
|
||||
This license becomes null and void if any of the above conditions are
|
||||
not met.
|
||||
|
||||
DISCLAIMER
|
||||
THE FONT SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF
|
||||
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT
|
||||
OF COPYRIGHT, PATENT, TRADEMARK, OR OTHER RIGHT. IN NO EVENT SHALL THE
|
||||
COPYRIGHT HOLDER BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
||||
INCLUDING ANY GENERAL, SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL
|
||||
DAMAGES, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
FROM, OUT OF THE USE OR INABILITY TO USE THE FONT SOFTWARE OR FROM
|
||||
OTHER DEALINGS IN THE FONT SOFTWARE.
|
||||
Binary file not shown.
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Before Width: | Height: | Size: 36 KiB |
@@ -1,25 +0,0 @@
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# This file is a script for GAP and tests a list of polynomials in hexadecimal
|
||||
# for irreducibility over F_2
|
||||
|
||||
# create x over F_2 = GF(2)
|
||||
x := Indeterminate(GF(2), "x");
|
||||
|
||||
# test if polynomial is irreducible, i.e. the number of factors is one
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IrredPoly := function (poly)
|
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return (Length(Factors(poly)) = 1);
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end;;
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# create a polynomial in x from the hexadecimal representation of the
|
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# coefficients
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Hex2Poly := function (s)
|
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return ValuePol(CoefficientsQadic(IntHexString(s), 2), x);
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end;;
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# list of candidates, in hex
|
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candidates := [ "3DA3358B4DC173" ];
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# create real polynomials
|
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L := List(candidates, Hex2Poly);
|
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|
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# filter and display the list of irreducible polynomials contained in L
|
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Display(Filtered(L, x -> (IrredPoly(x))));
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Reference in New Issue
Block a user