Creating a private cryptocurrency without trusted setup
The cryptocurrency you're describing does currently exist and implements, among other features, using unique Spend/View Keys in Monero (XMR). It capitalizes on a number of clever cryptographic techniques to implement a hardened total anonymization of source/destination (Ring Signatures/Stealth Addresses) and quantity (Ring Confidential Transactions/Bulletproofs).
It has also focused on maintaining a robust decentralized network via the (previously CryptoNote, GPU-optimized) RandomX PoW algorithm (CPU-optimized) that is highly ASIC-resistant, maintaining an optimal network dissemination by preventing any mining dominance by any centralized entity.
The original PoW and subsequent whitepapers can all be found at the webpage for the Monero Research Lab: https://web.getmonero.org/resources/research-lab/