The backup logic on the host is entirely contained within https://github.com/android/platform_system_core/blob/master/adb/commandline.c, in the function named backup. The function is very simple: it validates the command line options, sends the command mostly as-is to the adb daemon on the phone, and writes the phone's output to the file. There isn't even error-checking: if, for example, you refuse the backup on the phone, adb just writes out an empty file.
On the phone, the backup logic starts in service_to_fd() in https://github.com/android/platform_system_core/blob/master/adb/services.c. The function identifies that the command from the host is "backup", and passes the unparsed command to backup_service() in https://github.com/android/platform_system_core/blob/master/adb/backup_service.c. That, in turn, is a thin wrapper around /system/bin/bu, which is a trivial shell script to launch com.android.commands.bu.Backup as then main-class of a new Android app process. That calls ServiceManager.getService("backup") to get the backup service as an IBackupManager, and calls IBackupManager.fullBackup(), passing it the still-unused file descriptor (very indirectly) connected to the backup.ab file on the host.
Control passes to fullBackup() in com.android.server.BackupManagerService, which pops up the GUI asking the user to confirm/reject the backup. When the user do so, acknowledgeFullBackupOrRestore() (same file) is called. If the user approved the request, acknowledgeFullBackupOrRestore() figures out if the backup is encrypted, and passes a message to BackupHandler (same file.) BackupHandler then instantiates and kicks off a PerformFullBackupTask (same file, line 2228 as of time of writing)
We finally start generating output there, in PerformFullBackupTask.run(), between line 2367 and line 2453.
First, run() writes a header, which consists of either 4 or 9 ASCII lines:
"ANDROID BACKUP"
the backup format version: currently always "1"
either "0" if the backup is uncompressed or "1" if it is
the encryption method: currently either "none" or "AES-256"
(if encrypted), the "user password salt" encoded in hex, all caps
(if encrypted), the "master key checksum salt" encoded in hex, all caps
(if encrypted), the "number of PBKDF2 rounds used" as a decimal number
(if encrypted), the "IV of the user key" encoded in hex, all caps
(if encrypted), the "master IV + key blob, encrypted by the user key" encoded in hex, all caps
The actual backup data follows, either as (depending on compression and encryption) tar, deflate(tar), encrypt(tar), or encrypt(deflate(tar)).
TODO: write up the code path that generates the tar output -- you can simply use tar as long as entries are in the proper order (see below).
Tar archive format
App data is stored under the app/ directory, starting with a _manifest file, the APK (if requested) in a/, app files in f/, databases in db/ and shared preferences in sp/. If you requested external storage backup (using the -shared option), there will also be a shared/ directory in the archive containing external storage files.
$ tar tvf mybackup.tar
-rw------- 1000/1000 1019 2012-06-04 16:44 apps/org.myapp/_manifest
-rw-r--r-- 1000/1000 1412208 2012-06-02 23:53 apps/org.myapp/a/org.myapp-1.apk
-rw-rw---- 10091/10091 231 2012-06-02 23:41 apps/org.myapp/f/share_history.xml
-rw-rw---- 10091/10091 0 2012-06-02 23:41 apps/org.myapp/db/myapp.db-journal
-rw-rw---- 10091/10091 5120 2012-06-02 23:41 apps/org.myapp/db/myapp.db
-rw-rw---- 10091/10091 1110 2012-06-03 01:29 apps/org.myapp/sp/org.myapp_preferences.xml
Encryption details
An AES 256 key is derived from the backup encryption password using 10000 rounds of PBKDF2 with a randomly generated 512 bit salt.
An AES 256 master key is randomly generated
A master key 'checksum' is generated by running the master key through 10000 rounds of PBKDF2 with a new randomly generated 512 bit salt.
A random backup encryption IV is generated.
The IV, master key, and checksum are concatenated and encrypted with the key derived in 1. The resulting blob is saved in the header as a hex string.
The actual backup data is encrypted with the master key and appended to end of the file.
Sample pack/unpack code implementation (produces/uses) tar archives: https://github.com/nelenkov/android-backup-extractor
Some more details here: http://nelenkov.blogspot.com/2012/06/unpacking-android-backups.html
Perl scripts for packing/unpacking and fixing broken archives:
http://forum.xda-developers.com/showthread.php?p=27840175#post27840175