R-Hash: Hash Function Using Random Quadratic Polynomials over GF(2)

In this paper we describe an improved version of HF-hash [7] viz. R-hash: Hash Function Using Random Quadratic Polynomials Over GF(2). The compression function of HF-hash consists of 32 polynomials with 64 variables over GF(2), which were taken from the first 32 polynomials of HFE challenge-1 by forcing last 16 variables as 0. The mode operation used in computing HF-hash was Merkle-Damgard. We have randomly selected 32 quadratic non-homogeneous polynomials having 64 variables over GF(2) in case of R-hash to improve the security of the compression function used in HF-hash. In designing R-hash, we have also changed the mode operation used in HF-hash, because of the theoretical weakness found in the Merkle-Damgard construction.

In this paper we will prove that R-hash is more secure than HF-hash and SHA-256 as well as we will show that it is also faster than HF-hash.