Cryptographic hash functions are used in many applications of modern cryptography, such as authentication, integrity checking of data messages, digital signatures... This paper proposes a symmetry-key block crypto system 256 bits input /output. The encryption scheme is unbalanced four branches Feistel network; the encryption function and subkeys for the encryption loops are based on cyclic geometric progressions over even polynomial ring Z2[x]/x^n+1 with n=2^k. In the next part of the paper, the article recommended applies this crypto system to a hash function with 512 bits output length. Finally, some diffusion calculations of the proposed crypto system and hash function are also presented.
