SHA algorithim with different hash value I am new in hash cryptography. I am trying to build the sha256 hardware accelerator. I am thinking about using the different hash value to optimize the performance. I am trying to fetch custom hash initial value which already computed sometime ago. Does this approach valid and what problem i would get.

Thanks
I'll assume that you are thinking this way:

I am hashing a series of values that share the same prefix $X$ (which is a multiple of 64 bytes in length), that is, you are computing:

\begin{gather*}
\operatorname{SHA256}(X \mathbin\Vert A) \\
\operatorname{SHA256}(X \mathbin\Vert B) \\
\vdots \\
\operatorname{SHA256}(X \mathbin\Vert B)
\end{gather*}

and you are wondering "can I just compute the internal SHA256 state immediately after X, and then just use that as the "initial SHA256 state" when I process the strings $A, B, \dots, Z$?

Answer: yes, absolutely.  In fact, this is fairly common practice when these sorts of hashes are needed (which happens more than you'd expect; for example, when computing HMAC's).


  What problem I would get?


One thing you need to be careful is in the length field in the SHA-256 padding at the end; it needs to include the length of the entire message (including $X$), not just the message you just processed.