# What is the Common Reference String (CRS) model

I came across the notion of Common Reference String (CRS) model while reading this paper on a protocol for UC Oblivious Transfer: https://eprint.iacr.org/2007/348.pdf

I did some research and it seems to me that the CRS model is just some way to model hash functions: What are alternatives to the random oracle model for modelling hash functions?

My questions are:

1. What is exactly the CRS model?

2. What are the main differences, comparing to the Random Oracle Model (ROM)?

3. What are the advantages and disadvantages of using the CRS model instead of using the ROM?

• As a special case, imagine a setup where the secret key is shared among parties as $sk=\sum_i sk_i$, the public-key is $pk=g^{sk}$ (in a discrete-logarithm secure group $G$). Finally $pk$ is published while $sk_i$ is given only to party $i$ ( I mean the setup returns $pk$ and $sk_i$ for party $i$). Is this a CRS setup? For me $pk$ is the string that is generated in a trusted way and everybody has access to it. But then what about $sk_i$ they are just for one party. Sep 24, 2020 at 13:23