With DES, is ECB encryption mode equivalent to CBC with null IV for short data blocks? I got to this by experimentation, but can someone maybe provide an explanation for this?
The CBC mode processed as $c_i = E_k(p_i \oplus c_{i-1})$ with $c_0 = IV$
The ECB mode processed as $c_i = E_k(p_i)$


If you set the first block with $$c_o = IV = 0$$ in the CBC mode, than it is calculated as $$c_1 = E_k(p_1).$$ This is exactly as ECB mode.

The next blocks, however, will not be equal;


in ECB mode $$c_i = E_k(p_i)$$ 
whereas in CBC mode $$c_i = E_k(p_i \oplus c_{i-1}) \neq E_k(p_i) \text{ for } 1 &lt; i \leq m$$ where $m$ is the number of blocks.


Therefore the equality is only valid for the first block.