How does APE: Authenticated Permutation-Based Encryption work?

Question

I am trying to understand the encryption and decryption process of the APE: APE: Authenticated Permutation-Based Encryption for Lightweight Cryptography

Full paper

The Encryption

what is exactly the Vc and the Vr here? Example instead of the permutation p, what if I decide to replace it with a block cipher? Will the Vc be the key for the block cipher? What will the Vr then be which is xor'ed with the Plaintext?

A simple human-readble pseudo code will be helpful. I started trying to rewrite the pseudo code but there soo many unanswered questions.

[CipherText, Tag] function Encrypt(Key, A, Plaintext):
begin
  u = len(A)
  w = total number of blocks in the plaintext// eg. 1 block 64 bit block size
  V = [0,....K]
  if(A not zero) then
    A = {A[1] .... A[u]}
     for i = 1 to u do
         V = p(A[i] xor Vr, Vc) // can replace this with block cipher eg bcp(plaintext,key)
     end
  endif

  V = V xor [0,1] // What is (0,1)?
  M = {Plaintext[1],.......Plaintext[w]} // devide into blocks eg. 64 bits each.
  for i = 1 to w do
     V = p(M[i] xor Vr, Vc) // what is the Vr and Vc here?
     C[i] = Vr
  end

 CipherText = {C[1],.......C[w]} 
 Tag = Vc Xor Key // what is the Vc here from?
end