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Given a collision-resistant hash function $H(x)$, and I device another hash function by $H'(x)=\sum^{m}_{1}H(x||i) \mod p$. The summation is defined on finite field of prime order $p$.

Is the new hash function $H'(x)$ still collision resistant? How hard is it to find a collision? Any advice would be greatly appreciated!

Given a collision-resistant hash function $H(x)$, say SHA256, and I devise another hash function by $H'(x)=\sum^{m}_{1}H(x||i) \mod p$. The summation is defined on finite field of prime order $p$.

Is the new hash function $H'(x)$ still collision resistant? How hard is it to find a collision? Any advice would be greatly appreciated!

Given a collision-resistant hash function $H(x)$, and I device another hash function by $H'(x)=\sum^{m}_{1}H(x||i) mod p$. The summation is defined on finite field of prime order $p$. Is the new hash function $H'(x)$ still collision resistant? How hard is it to find a collision? Any advice would be greatly appreciated!

Given a collision-resistant hash function $H(x)$, and I device another hash function by $H'(x)=\sum^{m}_{1}H(x||i) \mod p$. The summation is defined on finite field of prime order $p$. 

Is the new hash function $H'(x)$ still collision resistant? How hard is it to find a collision? Any advice would be greatly appreciated!

Given a collision-resistant hash function $H(x)$, and I device another hash function by $H'(x)=\sum^{m}_{1}H(x||i)$. Is the new hash function $H'(x)$ still collision resistant? How hard is it to find a collision? Any advice would be greatly appreciated!

Given a collision-resistant hash function $H(x)$, and I device another hash function by $H'(x)=\sum^{m}_{1}H(x||i) mod p$. The summation is defined on finite field of prime order $p$. Is the new hash function $H'(x)$ still collision resistant? How hard is it to find a collision? Any advice would be greatly appreciated!