feat(docs): technical overview

[kunxian-xia]

Summary

Goal: Add docs to explain our technical design in details.

This should remove the burden to understand Ceno for both developers or AI. These materials will also be helpful for design / review AI agents to have a thorough understanding of our technology.

Contents

topics that're covered:

1. architecture overview

   • multi-chip architecture (frontend): each instance of each chip can span multiple rows, therefore the witness polynomials are $f_i(r, i)$, we allow
     • same-row constraint/gate $0 = C(f_1(r,i), \ldots, f_w(r,i))$
     • cross-row constraint/gate $0 = C(f_1(r,i), \ldots, f_w(r,i), f_1(r', i), \ldots, f_w(r', i))$.
   • multi-shards workflow

2. optimizations

   • distributed sumcheck

3. appendix

   • gkr protocol for tower tree
   • gkr protocol for logup
   • local rotation piop
   • ecc grand sum piop

   PIOP	Purpose	Sumcheck instances	Opening points per committed MLE
   GKR for Grand Product	Grand product $\prod_i a_i$ of $N = 2^d$ inputs	$d - 1$	Input MLE $a$ at a single point $z \in B_d$
   Local Rotation PIOP	Round-to-round state transition for round-based computations (e.g. Keccak-f)	$1$	Each $f_j$ at three points $(\mathbf{s}_r, \mathbf{s}_i), (\mathbf{p}_0, \mathbf{s}_i), (\mathbf{p}_1, \mathbf{s}_i) \in B_m \times B_n$
   EC-Sum Quark PIOP	Sum $\sum_i P_i$ of EC points on a short-Weierstrass curve	$1$	$x, y$ at $(\mathbf{r}, 0), (\mathbf{r}, 1), (1, \mathbf{r}) \in B_{n+1}$; $s$ at $(1, \mathbf{r})$

[hero78119]

LGTM! 🔥 🔥 🔥