Since May 2023, Bitcoin Cash contracts have been able to implement: zk-SNARKs, STARKs, BLS signatures, Lamport signatures & hash-based signature schemes, post-quantum cryptography, verifiable delay functions, bulletproofs, ring signatures, confidential transactions (within covenants), homomorphic encryption, multi-party computation, and any other cryptosystem being implemented on or in any other cryptocurrency.
(Note these were also possible on Bitcoin Cash in 2009, but they were broken by the 2010 emergency anti-DoS patches.)
Bitcoin Cash's May 2023 upgrade allowed computations to be split across inputs and/or transactions, so even without further upgrades, it is already possible to perform any kind of computation within Bitcoin Cash contracts. In practice though, important use cases require KBs or MBs of transactions to incrementally complete a computation, presenting a practical barrier to development and deployment.
After the 2025 BCH upgrade, many constructions that would have ballooned transaction sizes by KBs or MBs will now require only a few bytes: larger stack items and bigint arithmetic bring down these transaction sizes by 10-100x. Technically only a quantitative improvement, but significant enough to feel qualitative.
So for the record, BCH has been computationally universal since May 2023, the 2025 upgrade just makes things more efficient: smaller transactions, lower fees, and simplified development/security audits.
For comparison, I'll note again that these constructions have also been possible on ETH since it's inception (but with higher fees), and BTC since the Taproot Schnorr hack (but with KBs or MBs of waste in transaction sizes vs BCH).
This is not part of the 2025 Bitcoin Cash upgrade, but over the next few years I expect to see Bitcoin Cash covenants that allow users to deposit BCH and CashTokens and receive "privacy-wrapped" BCH and CashTokens.
Within these privacy covenants, users can indefinitely transact with strong privacy, and transactions/withdrawals will not be possible to link to a previous transaction. With layer 1 transparency, you'll always be able to see the covenant's total BCH and CashToken(s) balances, but individual holdings and transaction info won't be leaked.
These systems are possible on any cryptocurrency with sufficiently advanced math capabilities in the contract layer. It's actually been possible (but hard) on BCH for a while, various teams claim to have partial support on BTC, and of course multiple such systems have existed on ETH for years.
I think this application-layer privacy approach – full transparency on layer 1 a good calculator – has better tradeoffs than systems that bet their layer 1 network on monolithic privacy solutions.
Full layer 1 transparency increases the addressable market (and ultimately – anonymity set size), eliminates supply auditing concerns, and minimizes existential cryptography risks.
With a well designed virtual machine (the "calculator"), transaction sizes and validation costs can be practically equivalent, while only the application-layer privacy approach can fully isolate privacy systems, maximizing user choice to 1) individually opt in, 2) switch and diversify across systems, and 3) deprecate/ignore outdated or vulnerable systems.