I am curious that how to deal with the message or randomness overflow in pedersen commitment? <br/>
For more details: <br/>
For ec pedersen commitment: The two generators are G and H <br/> two messages and randomness are $m_1$, $m_2$, $r_1$, $r_2$ <br/>
so the two Pedersen commitments are $Gm_1+Hr_1$ and $Gm_2+Hr_2$ <br/>
If adding these two, I got a new Pedersen commitment as $G(m_1+m_2)+H(r_1+r_2)$ with message $m_1+m_2$ and randomness $r_1+r_2$<br/>
But then what if the message $m_1+m_2$(or randomness $r_1+r_2$) overflows<br/>
For example messages are in field mod 2^64, than if message becomes some 2^64+1, it would becomes 1<br/>
As G*(2^64+1) should not equal to G*1, unless G has the order of 2^64
<br/> So I am curious about how it works <br/>
Any help would be truly appreciated