fix: Poseidon2 verify_batch start_top_level is not constrained only at start

[jonathanpwang]

Finding Link: https://cantina.xyz/code/c486d600-bed0-4fc6-aed1-de759fd29fa2/findings/167

Description of Fix

While the variable was called start_top_level, we only constrained that the top level has start_top_level = 1 but never that it must be equal to 0 on non-top levels. We change the existing constraint so that it enforces start_top_level = 1 iff its the start of a top level (meaning previous row is end and current row is incorporate_row).

Closes INT-3567

[TlatoaniHJ]

Looks good to me. I should note that when the row is not top level at all we are not constraining start_top_level. We don't need to because the value of start_top_level is not relevant for those rows (setting it to 1 on those rows neither allows an exploit nor causes a constraint to fail), but this maybe should be documented (or we could just constrain it to be 0 on those rows).

[jonathanpwang]

Looks good to me. I should note that when the row is not top level at all we are not constraining start_top_level. We don't need to because the value of start_top_level is not relevant for those rows (setting it to 1 on those rows neither allows an exploit nor causes a constraint to fail), but this maybe should be documented (or we could just constrain it to be 0 on those rows).

I'll constrain it's zero just for clarity.

[zlangley]

Can't we just do

    builder.assert_eq(end.clone() * next.incorporate_row, next.start_top_level);

instead of

    builder
        .when(end.clone())
        .when(next.incorporate_row)
        .assert_one(next.start_top_level);

[jonathanpwang]

Can't we just do

    builder.assert_eq(end.clone() * next.incorporate_row, next.start_top_level);

instead of

    builder
        .when(end.clone())
        .when(next.incorporate_row)
        .assert_one(next.start_top_level);

I think so, will add it.

[github-actions]

group	app.proof_time_ms	app.cycles	app.cells_used	leaf.proof_time_ms	leaf.cycles	leaf.cells_used
verify_fibair	(+13 [+1.0%]) 1,381	147,009	8,194,532	-	-	-
fibonacci_program	(-24 [-0.5%]) 4,974	1,500,096	51,485,167	-	-	-
regex_program	(+112 [+0.8%]) 14,036	4,140,164	167,389,450	-	-	-
ecrecover_program	(-23 [-0.9%]) 2,516	295,181	15,586,346	-	-	-

Commit: 2c23fa1

Benchmark Workflow

[TlatoaniHJ]

Amazing