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This is amazing work!
Are there any even draft implementations of this?
How long would you estimate that it would take to prove EVM execution (in seconds per gas)?
What would you expect are the least efficient (in seconds per gas) operations?
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We don’t have such an estimate as of now - we are just starting the implementation. We think however that the prover time will likely be dominated by commitment generation - of which there are very many. It also means that there will be a lot of parallelization. As for the second per gas efficiency, we believe that the least efficient operations would be those that involve modular arithmetics (MOD, ADDMOD, MULMOD), on 256 bits, as they involve a significant number of costly word comparison operations.

Are you sure that all the operations (including calls and returning from calls) actually do cost O(1) constraints (or at most O(log(n)) per operation?

That is an excellent question: while, for a given clock cycle, the total number of constraints to verify does not depend on the opcode being executed- for some opcodes (CALL/RETURN opcodes for instance), the execution spans multiple clock cycles, which increases the total size of the commitments to generate. For instance, for a CALL opcode, one has to prove/verify that the whole CALLDATA has been loaded correctly in the new execution environment - the number of clock cycles will scale linearly with the length of the CALLDATA. Besides, one has to initialize the new RAM (and in some cases the new Storage) of the contract being called - the number of clockcycles will scale linearly with the total maximum size of the RAM (in EVM words) at the end of execution of the called contract (for the storage it will scale linearly with the number of storage cells accessed). A similar reasoning applies to the RETURN opcode as the number of clockcycles needed to process the opcode depends on the total length of the data returned to the caller contract.

Thanks a lot for your feedback. Please don’t hesitate if you have any other comment on the specification, or if you would like us to clarify some points !