A new design paradigm for provably secure keyless hash function with subsets and two variables polynomial function

Abstract

Abstract Provably secure keyless hash function uses Random Oracle (RO) or Sponge principles for the design and construction of security-centric hash algorithms. It capitalizes the aforesaid principles to produce outcomes like MD2, MD5, SHA-160, SHA-224/256, SHA-256, SHA-224/512, SHA-256/512, SHA-384/512, SHA-512, and SHA-3. These functions use bitwise AND, OR, XOR, and MOD operators to foresee randomness in their hash outputs. However, the partial breaking of SHA2 and SHA3 families and the breaking of MD5 and SHA-160 algorithms raise concerns on the use of bitwise operators at the block level. The proposed design tries to address this structural flaw through a polynomial function. A polynomial function of degree 128 demands arduous effort to be decoded in the opposing direction. The application of a polynomial on the blocks produces an unpredictable random response. It is a fact that the new design exhibits the merits of the polynomial function on subsets to achieve the avalanche response to a significant level. The output from experiments with more than 24 Million hash searches proves the proposed system is a provably secure hash function. The experiments on avalanche response and confusion and diffusion analysis prove it is an apt choice for security-centric cryptographic applications.