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I have a question about OT? we assume that sender has $m_0,m_1,m_2$, and $m_3$ and selects random $S_0, S_1, S_2, S_3, S_4, S_5$ and compute this statement than sends to receiver.
$C_0 = S_0 \oplus S_2 \oplus m_0$
$C_1 = S_0 \oplus S_3 \oplus m_1$
$C_2 = S_1 \oplus S_4 \oplus m_2$
$C_3 = S_1 \oplus S_5 \oplus m_3$
Can i change above statement into this?
$C_0 = S_0 \oplus S_2 \oplus m_0$
$C_1 = S_0 \oplus S_3 \oplus m_1$
$C_2 = S_1 \oplus S_2 \oplus m_2$
$C_3 = S_1 \oplus S_3 \oplus m_3$
No, your proposed alternative allows the attacker to deduce things beyond the value he selects.
For example, suppose that during his OT transfers, he decides to learn the values $s0$ and $s2$, allowing him to recover $m0 = c0 \oplus s0 \oplus s2$. That is intended to be allowed, and so is fine as far as it goes.
However, the receiver can also deduce the value $m1 \oplus m2 \oplus m3 = c1 \oplus c2 \oplus c3 \oplus s0 \oplus s2$. As the receiver is supposed to learn only the value he selected ($m0$ in this case), and nothing about the other messages, this is a violation of the OT properties.
