If we look at a sample Luks header ( The tables taken from here )
- Luks Partition Header (PHDR) consists of the necessary information to decrypt/encrypt the luks device as followings,
-------------------------------+-----------------------------
| Partition Header Contents | Output by luksDump |
-------------------------------+-----------------------------
| Magic Byte | LUKS |
-------------------------------+-----------------------------
| Luks version | 1 |
-------------------------------+-----------------------------
| Cipher Name | serpent |
-------------------------------+-----------------------------
| Cipher Mode | xts-plain64 |
-------------------------------+-----------------------------
| Hash Type | whirpool |
-------------------------------+-----------------------------
| Payload offset | 4096 |
-------------------------------+-----------------------------
| Master Key Bits | 512 |
-------------------------------+-----------------------------
| Master Key Digest | 8a 90 77 7e ... |
-------------------------------+-----------------------------
| Master Key Salt | ca f3 40 fc ... |
-------------------------------+-----------------------------
| Master Key Digest Iteration | 23250 |
-------------------------------+-----------------------------
| Partition UUID | 46927c7d-7f17-4312-... |
-------------------------------+-----------------------------
Table - 1
2. 2nd portion of partition header (PHDR) consists of 8 key-slot descriptors i.e information about key-slot as following,
------------------------------+------------------------------
| Key Descriptors | Output by luksDump |
+-----------------------------+------------------------------
| Activation status | Enabled |
+-----------------------------+------------------------------
| Iteration | 146285 |
+-----------------------------+------------------------------
| Salt | 1e c1 94 24 36 4c 98.. |
+-----------------------------+------------------------------
| Key Material Offset | 8 |
+-----------------------------+------------------------------
| AF Stripes | 4000 |
------------------------------+------------------------------
Table - 2
will this make the bruteforce crack much more difficult?
One will see that an attacker will lose a lot of information about the header like cipher name, cipher mode, iteration, hash, key slots, etc.
The easy attack on the LUKS is brute-forcing the password (hashcat can do this) if the password is weak. When the LUKS header is lost, the attacker cannot test the password anymore; the user passwords decrypt the related key slot to release the Master Key (MK). If there is no data to decrypt, it is a random process that is not better than brute0force.
The rest is brute-forcing the MK. For 128-bit encryption algorithms, except for a foreseeable Cryptographic Quantum Computer (CQC), it is infeasible. When one uses a cipher with a 256-bit key it is safe from all targets including CQC.
Can softwares tell which type of the partition is?
No!
And, make sure that you removed the header without leaving a trace, i.e. secure erase.