Security of a cipher with some imperfection in round function I got specific problem with round function in my symmetric cipher. It works on $128$-bit blocks. Every round got two $128$-bit keys. Block is xored with $k_{1}$ on the beggining of the round. Then it goes into round function (which is using the same $k_{1}$ and $k_{2}$ keys, both $128$-bit long). And then it is xored with $k_{2}$ in the end.
Problem is with round function. Let's asssume that it transom every $128$-bit block into $128$-bit block indistinguishable from random, if you don't have $k_{1}$ and $k_{2}$. But there is one exception. All zeros block is always encrypted into all zeros block (with every key). So only xoring makes it different from all zeros block before it goes into round function.
If we will consider let's say $10$ rounds - is it secure cipher? Is it possible to broke it because of that problem with all zeros block?
EDIT:
I clarified my question, specifically when xoring is performed:
$INPUT \oplus k_{1}$ $\to$ $F_{roundfunction}$ $\to$ $OUTPUT \oplus k_{2}$
If an all-zeroes block creates all-zeroes for every key that's definitely an issue. It's not necessarily likely to be serious, but could leak data about the plaintext and does not qualify as a secure block cipher.
However, the solution is fairly simple... simply XOR one of k1 or k2 with a constant value to turn your all-zero block into something that'll produce a better result. Personally I'd XOR with the current round number in each round because that'll prevent your algorithm from accidentally ending up with another input that produces the same issue.