# security of a sponge construction

I don't get why the size of C (the capacity) of a sponge construction influences the security of the sponge construction. And what is the influence of the size of R?

The rate refers to the bits that are directly input/output into the permutation. A larger rate provides higher performance: Consider the extreme where the rate is only 1 bit - it would require $n$ invocations of the permutation to digest $n$ bits of data, which would be quite slow.