Hashing or Message Digest

Hashing is method to achieve Integrity

What is Hashing? Transforming String into FIXED-LENGTH string Value. From Hash Message cannot be retrieved back. Hash function should not generate same value for different input strings.
MD5 started producing that and hence considered broken. 

      Kumar >  | Hash Function |  > random_string
Why to use Hash
For security, password Hash is stored. Whenever someone enters password hashes are compared.
How GPU can crack a Hash?
GPUs are particularly effective at performing parallel computations.
They contain numerous cores that can execute instructions simultaneously, making them well-suited for tasks like hashing, which involve performing the same operation on multiple inputs simultaneously.
GPUs can test a large number of password guesses(Brute force) in parallel, making them much faster at trying different combinations.
But Argon2 hash is GPU resistant.

Hashing Algorithms

Algo SHA1
SHA0(broken)		 SHA256
(not broken)		 SHA3_512
Keccak		 MD4,MD5(broken)
Published 1995 2012 2015 2015
Input 2128 bit 2128 bit 264 bit infinite
Output Hash(bits) 160 256 512 128

MD5


      1. Take four 32-bit words, initialized to fixed constants.

      C1(01 23 45 67), C2:(89 ab cd ef), C3(fe dc ba 98), C4(76 54 32 10)

      2. Take 4 Functions
      
          f(x,y,z) = (x & y) | ((~x) & z)
          g(x,y,z) = (x & z)| (y & (~z))
          h(x,y,z) = x ^ y ^ z
          i(x,y,z) = y ^ (x | (~z))

      3. Break input into 32-bit words
      
                      Input(512 bits)  ->  |Break into 16 pieces| ->     m1 .. m16
      if input is not 512 bit pad it

      4. Perform 4 or 16 round Operations.
      
      //AM: Addition Modulo
        Round-1:    F(K2,K3,K4) ->  AM ->  AM -> |Rotate left bit by s places| ->  AM -> K2
                                    /\     /\                                      /\
                                    C1     m1                                      C2
        Round-2: For m2 and so on..

Argon2

How Argon2 is GPU resistant?
1. Memory Hardness:
Argon2 is a memory-hard hashing algorithm, meaning that it requires a lot of memory to be computed.
Since GPU typically have less memory available compared to CPUs. As a result, even though GPUs can perform computations quickly, they may struggle with the memory requirements of Argon2.
2. Parallelism resistance:
While GPUs excel at parallel computations, Argon2 is designed to require significant serial computation as well.
This means that even though GPUs can try many password guesses in parallel, they may still be limited by the sequential nature of certain parts of the Argon2 algorithm.
3. Configuration parameters
Argon2 allows for the adjustment of parameters(such as the memory cost, time cost, and parallelism degree)
By appropriately configuring these parameters, it's possible to tune Argon2 to be less susceptible to GPU-based attacks

Argon2, Argon2i, Argon2id

Usage/Feature Resistant to
argon2 preferred for password hashing and key derivation because it's resistant to side-channel attacks
argon2d more resistant to GPU attacks
argon2id hybrid of Argon2i and Argon2d

MAC

Examples: CMAC, SHA1-HMAC, MD5-HMAC, UMAC 

    (Message + Pvt Key) > |Hash function| > MAC

HMAC(Hashed MAC)

More complex way of calculating MAC

      secret Key ->(XOR) <- Inner Pad     Secret Key-> (XOR) <- Outer Pad
                    \/                                 \/
                    M1                                 M2
            |M-1| Message | M2 |