Example of internal function for Sponge scheme built on the basis of the generalized AES design methodology

The purpose of this article is to construct an internal function underlying the “Sponge” scheme for constructing  cryptographic  hash  functions.  An  internal  function in  the  “Sponge”  scheme  is  a  fixed-length transformation  or  permutation  that  operates  on  a  fixed  number  of  bits  that  make  up  the  internal  state  of  the function. There are various constructive approaches to functiondesign. The most common approach is to use a permutation based on a symmetric block encryption algorithm with constants as the key. This article builds an internal  function  using  the  generalized  AES  design  methodology. This  methodology  makes  it  easy  to  design block  ciphers  to  encrypt  large  blocks  of  plaintext  with  small  components,  representing  the  processed  data as  multidimensional  arrays.  The  internal  function  is  a  block  cipher  that  processes  2048  bits,  represented as  a  9-dimensional  array  of  512  4-bit  elements  with  size  2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2.  Each  round of encryption  consists  of  three  transformations  (S-blocks,  linear  transformation,  and  permutation),  similar  to the three round transformations of AES SubBytes, MixColumns, and ShiftRows. The constructed function can be used as an internal function in the modified “Sponge” schemefor constructing cryptographic hash functions.

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