[Keccak] Thinest and longest

[ChihChengLiang]

highlight:

• Moved all greeks to the component.rs as functions.
• 3 advice columns from the generic gate
• 18 fixed columns from (lookup 1 selector + 3 table columns) * 4 + 1 constant fixed column + 1 selector from generic gate.
• added the convert back to base 2 part, which was missing in the current implementation.

Num advice columns: 3
Num fixed columns: 18
Num instance columns: 0
Num lookups: 4
Num gates: 1
Max advice rows 64794 - add advice
num polys: 1
max_gate_degree_poly: 3 - 

Circuit layout: Click to expand!

[CPerezz]

So far looks nice.

I's always a nice and grateful job if you can chop off 1000+ lines of code!!
I've added a comment and some remarks about performance and layout structure.

Just need you to fix the comment, the other stuff is just informative :)

[CPerezz]

This is where I think we can optimize this a way more by not increasing the offset each time we add and input and instead increase the amount of columns used and not repeat it.

[CPerezz]

If we pass the config with the columns already assigned instead of creating new ones, we are directly increasing the height of the entire thing.

Not saying to address it now, but these are the things that are causing us to have really tall layouts.

[CPerezz]

Results of the benchmarks:

running 1 test
Start:   Setup generation with degree = 19
End:     Setup generation with degree = 19 .........................................4.534s
Start:   Keccak Proof generation with 19 degree
End:     Keccak Proof generation with 19 degree ....................................2.298s
Start:   Keccak Proof verification
End:     Keccak Proof verification .................................................3.668ms
test keccak_permutation::tests::bench_keccak_round ... ok

test result: ok. 1 passed; 0 failed; 0 ignored; 0 measured; 3 filtered out; finished in 23.94s

Maximum CPU Usage at 17.8%
Maximum Mem Usage at 4.4Gb

The results are really really nice!
We would just need to bring down the height of the layout of the circuit and make it a bit more wide so that the permutations don't blow up the degree required by the SRS.

[han0110]

LGTM!

To compare with #634, this implementation can process ²¹⁹/₆₄₇₉₄ = 8.09 keccak_f per 2.298 seconds (≈ 3.52 ^keccak_f/_s).

One low hanging fruit to improve is to stack all tables into one as 4-columns table, with an extra fixed tag column to select the table, it should be helpful to reduce both prove and verify.

[CPerezz]

LGTM!

To compare with #634, this implementation can process 219/64794 = 8.09 keccak_f per 2.298 seconds (≈ 3.52 keccak_f/s).

One low hanging fruit to improve is to stack all tables into one as 4-columns table, with an extra fixed tag column to select the table, it should be helpful to reduce both prove and verify.

I think the most significant thing to address if we want to bring this impl to the competition is to fix the height of the base conversion.
On that way, we would be able to stack a way more permutations/DEGREE

[CPerezz]

LGTM!

Nice job @ChihChengLiang 🎉