Abstract This paper proposes JERIM-320 as an efficient 320-bit hash function for use in message integrity applications and explores its randomness property for proving the dual functioning in cryptographic applications. JERIM-320 operates on four parallel lines of message processing, resulting in higher degree of security than other hash functions like MD5 and SHA1 at comparable speed and memory requirement. The randomness property of JERIM-320 is analysed by means of statistical experiments. The focus of this work is to propound it for applications requiring message integrity as well as for pseudo-random number generations, which are of increasing importance in the fast growing internet world.