Recover a overwritten encrypted luks device - encryption

Question

Yesterday I was very tired and I had a friend of
mine that was kind of annoying. I had to put an
Linux ISO on a usb drive.
I had stored all of my data temporarily on one
device, which is a 5 TB drive. This device was/is
encrypted using :
cryptsetup -luksFormat ...
I mounted this device to /a and did a dd of an
Linux ISO on the 5 TB drive. The second I hit
enter I realized this and then I did a control C
and removed the plug from my drive.
After this I had a complete mental breakdown and
i started hyperventilating.
Anyhow I have read that even if data is overwritten
there is till a chance of reading the data below the
overwritten part.
I assume this is far more complicated then simply
running testdisk ( maybe testdisk can do this, no clue ).
The entire process of yesterday can be seen below :
:/a/1master-targz/iso# ls
debian-8.1.0-amd64-xfce-CD-1.iso FreeBSD-11.0-RELEASE-amd64-disc1.iso
linuxmint-18.1-cinnamon-32bit.iso nonpaelubuntu.iso
:/a/1master-targz/iso# lsblk
NAME MAJ:MIN RM SIZE RO TYPE MOUNTPOINT
sda 8:0 0 4.6T 0 disk
└─sda 254:0 0 4.6T 0 crypt /a
sdb 8:16 1 28.7G 0 disk
├─sdb1 8:17 1 648M 0 part
└─sdb2 8:18 1 416K 0 part
:/a/1master-targz/iso# dd if=linuxmint-18.1-
linuxmint-18.1-cinnamon-32bit.iso linuxmint-18.1-mate-32bit.iso
linuxmint-18.1-mate-64bit.iso
:/a/1master-targz/iso# dd if=linuxmint-18.1-cinnamon-32bit.iso 5~^C
:/a/1master-targz/iso# lsblk
NAME MAJ:MIN RM SIZE RO TYPE MOUNTPOINT
sda 8:0 0 4.6T 0 disk
└─sda 254:0 0 4.6T 0 crypt /a
sdb 8:16 1 28.7G 0 disk
├─sdb1 8:17 1 648M 0 part
└─sdb2 8:18 1 416K 0 part
:/a/1master-targz/iso# dd if=linuxmint-18.1-cinnamon-32bit.iso of=/dev/sda bs=512k
10+1 records in
10+1 records out
5685920 bytes (5.7 MB, 5.4 MiB) copied, 0.81171 s, 7.0 MB/s
:/a/1master-targz/iso#
:/a/1master-targz/iso# ^C
:/a/1master-targz/iso# lsblk
NAME MAJ:MIN RM SIZE RO TYPE MOUNTPOINT
sdb 8:16 1 28.7G 0 disk
├─sdb1 8:17 1 648M 0 part
└─sdb2 8:18 1 416K 0 part
sdc 8:32 0 4.6T 0 disk
└─sdc1 8:33 0 1.6G 0 part
mmcblk0 179:0 0 29.8G 0 disk
├─mmcblk0p1 179:1 0 41.8M 0 part /boot
└─mmcblk0p2 179:2 0 29.8G 0 part /
:/a/1master-targz/iso#
#somewhere here I got a panic attack
TestDisk 7.0, Data Recovery Utility, April 2015
Christophe GRENIER <grenier#cgsecurity.org>
http://www.cgsecurity.org
Disk /dev/sdc - 5000 GB / 4657 GiB - CHS 4769307 64 32
Partition Start End Size in sectors
>P ext4 0 63 31 4769306 63 30 9767538688 [Ghost] # doubt this is right
fdisk -l /dev/sdb
Disk /dev/sdb: 4.6 TiB, 5000981077504 bytes, 9767541167 sectors
Units: sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 4096 bytes
I/O size (minimum/optimal): 4096 bytes / 4096 bytes
Disklabel type: dos
Disk identifier: 0x69e72c6a
Device Boot Start End Sectors Size Id Type
/dev/sdb1 * 0 3289087 3289088 1.6G 17 Hidden HPFS/NTFS
# head /dev/mapper/sda
head: error reading '/dev/mapper/sda': Input/output error
Summary
What do I have :
1 : Overwritten part of an encrypted luks device.
2 : I still have the mapper of when cryptsetup opened the device ( I have not
touched my computer since then )
My hope:
-There may be a way of tricking my OS of seeing my encrypted drive as /dev/sda
and connect the /dev/mapper/sda to this device, and then remount the device ignoring the part of the drive being destroyed ? ( I really have no clue ..)
-I know which image I used to overwrite the data, maybe this helps in possibly reading the data it destroyed.
-Any other idea's are very helpful

Answer 1

Clean up the question and remove the story.
"I have read that even if data is overwritten there is till a chance of reading the data below the overwritten part."
You will not be able to recover the over written data with your computer and drive as-is. In order to attempt to recover overwritten data it is necessary to be able to see the drive read head actual voltage so that the remnant of the over written value can be seen as a slight difference in the voltage. That means opening the HD and using specialized equipment. IOW: no.
You have learned the hard way to have continual backups, it seems the "hard way" is the only way that works and often takes multiple lessons, make this one count.