Non-interactive public sum of private values Suppose there is a large number of participants each with a secret value. The secret values are very large (e.g. 256-bit integers). Each participant has published a public commitment to their secret value.

Is it possible for them to determine what their values sum up to in a single round of communication but without revealing their private values?

This can also be thought of as a voting scheme: each participant holds a value with which they can vote. Knowing public commitments for the votes that have been cast, we'd like to figure out the total number of votes that was cast without the need for voters to collaborate with each other (beyond casting of the original vote).
If all the participants have a random secret key which sums to 0. They can each post the sum of their key with their number. Anyone can then some the values posted, the key will cancel out and we what will remain is the sum. 

This only works if everybody posts their value and we have an appropriate key distributed.