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.
2n-Bit Hash-Functions Using n-Bit Symmetric Block Cipher Algorithms
