Bulletproof and random oracle model I am trying to deal with Bulletproof. I can not find confirmation or refutation of the following assumption:


  Bulletproof cannot work without the random oracle, which is a
  necessary part of the protocol.


Thanks in advance for your answers.
A core component of Bulletproof is a "range proof". Since Bulletproofs are designed to be used in the blockchain setting, it is important for the range proof to be non-interactive. The one used in Bulletproof is obtained by taking an interactive range proof and then compiling it into a non-interactive one using the Fiat-Shamir transform. The random oracle is used to establish the soundness of this transformed protocol. In practice one would instantiate this random oracle with a concrete hash function (say SHA-$3$). 

Now, to answer your question whether a random oracle is necessary, it is not clear and is an active line of research. It has been shown that in some cases it is possible to instantiate the Fiat-Shamir transform with concrete hash functions (e.g., the recent construction of NIZK from LWE relies on such an instantiation of the Fiat-Shamir transform [PS19]).

[PS19]: Peikert and Sheihan Non-Interactive Zero Knowledge for NP from (Plain) LWE.