With the drastic growth in the addition of smart objects into the Internet, it has led to many challenges like standardizing the infrastructure, ensuring communication security and keeping user credential private. As these devices are having less resources it is necessity to have a lighter encryption and authentication schemes to ensure data integrity and user privacy. This work concentrates on evaluating the faster hashing function used for elliptic curve digital signature algorithm (ECDSA) that enables user authentication. Traditionally, SHA hash functions are used in various public key cryptography and applications. But SHA has 80 different iterations that consumes smart device's energy. Thus a lighter hash function called BLAKE2 based hashing is used to compare the time efficiency of ECDSA. BLAKE2 uses 8 rounds of permutations and combinations to produce the message digest of 256/512bits. This reduction in computation has attracted researchers to use BLAKE2 hashing functions for various applications. Thence this study concentrates on comparison of the time efficiency under ECDSA based digital signature for different message sizes and hashing functions. Through various experiments conducted on different operating systems, BLAKE2 has shown better computational efficiency than SHA family of hashing functions for ECDSA based scheme on different operating system.