LogUp

[HiddenAndBound]

Summary

Implements the LogUp* indexed lookup argument (#1368) to prove indexed lookup evaluations.

Key code

• Prover: crates/prover/src/protocols/logup/ (mod.rs, pushforward.rs, log_sum.rs, prover.rs, helper.rs)
• Verifier: crates/verifier/src/protocols/logup.rs

Supporting additions:

• Batched/shareable frac-add prover: crates/prover/src/protocols/fracaddcheck.rs
• Batched frac-add verifier: crates/verifier/src/protocols/fracaddcheck.rs
• Batched quadratic sumcheck prover: crates/prover/src/protocols/sumcheck/batch_quadratic.rs
• Shared last-layer frac-add MLE prover: crates/prover/src/protocols/sumcheck/frac_add_last_layer_mle.rs

Tests / Bench

• Test: crates/prover/src/protocols/logup/tests.rs
• Bench: crates/prover/benches/logup.rs (registered in crates/prover/Cargo.toml)

Commands:

• cargo test -p binius-prover -p binius-verifier
• cargo bench -p binius-prover --bench logup

Notes

• prove_pushforward currently assumes equal table sizes (crates/prover/src/protocols/logup/pushforward.rs).
• API currently takes concrete usize index arrays; integration with committed bitwise index MLEs is a follow-up (helper.rs Index).