# What does “constant rate” mean in universal composable commitment scheme?

I'm wondering what does the "constant rate" mean in universal composable commitment scheme? I have known the rate of a commitment scheme is message length divided by the communication complexity of the scheme. What's the "constant" mean here? Must the constant be a number less than 1?

• Can you please post a reference to a paper or something where you encountered this term? – SEJPM Dec 18 '18 at 17:21

Constant rate in general means that the overhead from a non-secure method is constant. So, in a simple way, if I am committing to an $$\ell$$-bit message, then the size of the commitment is $$O(\ell)$$. In some cases, however, one also allows an additive factor that is independent of the message size. Thus, for example, it could be that to commit to a message of size $$\ell$$ the amount is $$O(\ell)+{\rm poly}(n)$$, where $$n$$ is the security parameter.
• Good or bad depends on your setting and what you want. In general, $O(n\cdot\ell)$ is of course much worse than $O(\ell)+poly(n)$, but if you want to commit to a little bit only, sometimes a simpler scheme is better. – Yehuda Lindell Jan 11 '19 at 1:23