Exponentiation circuit and EXP opcode

[roynalnaruto]

• Design Document: https://hackmd.io/@rohitnarurkar/BJhpYGiCc
• Circuits Implementation: Exponentiation circuit and EXP opcode zkevm-circuits#700

This PR implements the following:

• EXP Gadget
• Exponentiation Circuit
• Exponentiation Table (verified within Exponentiation Circuit)

The EXP opcode computes the exponentiation result of an integer base to an integer exponent:

base ^ exponent == exponentiation (mod 2^256)

The exponentiation circuit verifies the exponentiation trace, i.e. intermediate multiplication steps generated by the Exponentiation by Squaring algorithm.

The EXP opcode gadget does lookups (conditional based on the exponent value) to the exponentiation table.

[ChihChengLiang]

I reviewed the text description parts.
There are many unorganized questions. Feel free to pick just the ones you feel important to answer

[adria0]

@roynalnaruto really nice written spec, very easy to follow the py code from it!

I am not able to find anything, just curious about your answers, to approve the PR.

[adria0]

@roynalnaruto any blocker for finishing this PR?

[roynalnaruto]

@adria0 no blockers. I am updating the specs repo and also the design document. Should push an update this week

[adria0]

Thanks for the update, @roynalnaruto!

[roynalnaruto]

@ChihChengLiang @adria0 Apologies I was a little occupied with some other tasks. I will post updates to the design doc as well as the specs PR this week. Will also post answers to all your comments. Thanks for the review :)

[adria0]

LGTM

[roynalnaruto]

@ChihChengLiang I've answered all your questions and updated the documents/specs. Could you review again?

[ChihChengLiang]

rereviewing now. Thanks for waiting.

[ChihChengLiang]

LGTM. Epic PR! I added some nitpicks.

[roynalnaruto]

@ChihChengLiang updated the PR with all suggestions. Shall we merge it now?