From 7856bdece45b32251596a640a0ff733f2a34dcef Mon Sep 17 00:00:00 2001 From: adust09 Date: Sun, 23 Nov 2025 14:28:30 +0900 Subject: [PATCH 01/21] Refine preliminaries section and expand on QuickSilver protocol in VOLEitH research paper - Streamlined the preliminaries section for clarity, removing redundant phrasing. - Introduced a new subsection on QuickSilver, detailing its use of VOLE MAC homomorphism for verifying multiplication constraints in a zero-knowledge protocol. - Enhanced the description of the VOLE-in-the-Head (VOLEitH) framework, emphasizing its integration with QuickSilver for public verification. - Improved overall coherence and structure of the document to better articulate the mathematical foundations of the discussed protocols. --- paper/preliminaries.tex | 27 ++++++++++++++------------- 1 file changed, 14 insertions(+), 13 deletions(-) diff --git a/paper/preliminaries.tex b/paper/preliminaries.tex index 94f5aff..1428e19 100644 --- a/paper/preliminaries.tex +++ b/paper/preliminaries.tex @@ -1,5 +1,5 @@ \section{前提知識と関連研究} -本章では、後続のベンチマークと考察を理解するために必要な暗号学的前提を、簡潔に整理する。 +本章では、後続のベンチマークと考察を理解するために必要な暗号学的前提を簡潔に整理する。 \subsection{Vector Oblivious Linear Evaluation (VOLE)} VOLEは、二者間で線形関係を隠したままMAC相関を生成するプリミティブである。 @@ -16,6 +16,17 @@ \subsection{Vector Oblivious Linear Evaluation (VOLE)} FAESTなどでは、入力 $\mathbf{u}$ を $\mathbb{F}_2$ に制限しつつ、$\mathbf{v}, \mathbf{q}, \mathbf{\Delta}$ を拡大体 $\mathbb{F}_{2^\lambda}$ 上に置くサブフィールドVOLEが用いられる。 これはビット演算を保ちつつ、MACは大きな体で保持することで効率と安全性を両立するためである。 + +\subsection{QuickSilver} +QuickSilverは、VOLE MACの準同型性を用いて乗算制約を検査するゼロ知識プロトコルであり、VOLE相関を前提に軽量な検証を実現する。 +QuickSilverはLine-Point Zero-Knowledgeパラダイムを用い、VOLE MACの加法準同型性で乗算制約 $w_\alpha \cdot w_\beta = w_\gamma$ を検査する。 +証明者は応答を $\tilde{a}_0,\tilde{a}_1,\tilde{b}$ にマスクし、検証者は VOLE 関係 +\begin{equation} + \tilde{b} = \tilde{a}_0 + \tilde{a}_1 \cdot \Delta +\end{equation} +が成立することを確認するだけで健全性を得る。 +VOLEitHは、このQuickSilver型の検査をGGMベースのVCと組み合わせ、公開検証を実現している。 + \subsection{MPC-in-the-Head (MPCitH)} MPCitHは、NPリレーションの知識証明を「頭の中で」実行するMPCに還元し、ビュー開示で健全性を担保するZKフレームワークである。 NPリレーション $R(x, w)$ に対し、証明者 $P$ は証人 $w$ を $N$ 份のシェア $w_i$ に分割し(加法秘密分散等)、$f(x, w_1,\dots,w_N)=R(x,\bigoplus_i w_i)$ を計算する半正直MPC $\Pi_f$ を頭の中でエミュレートする。 @@ -29,20 +40,10 @@ \subsection{MPC-in-the-Head (MPCitH)} $\Pi_f$ が $(N-1)$-privacy を満たすとき、開示されなかった $V_{i^*}$ を偽造しない限り不正な $P$ は受理されないため、健全性が得られる。 通信量は回路サイズ $s$ に線形($O(s) + \mathrm{poly}(k,\log s)$)で、汎用性が高い。 -\subsection{QuickSilver} -QuickSilverは、VOLE MACの準同型性を用いて乗算制約を検査するLine-Point系ゼロ知識プロトコルであり、VOLE相関を前提に軽量な検証を実現する。 -QuickSilverはLine-Point Zero-Knowledgeパラダイムを用い、VOLE MACの加法準同型性で乗算制約 $w_\alpha \cdot w_\beta = w_\gamma$ を検査する。 -証明者は応答を $\tilde{a}_0,\tilde{a}_1,\tilde{b}$ にマスクし、検証者は VOLE 関係 -\begin{equation} - \tilde{b} = \tilde{a}_0 + \tilde{a}_1 \cdot \Delta -\end{equation} -が成立することを確認するだけで健全性を得る。 -VOLEitHは、このQuickSilver型の検査をGGMベースのVCと組み合わせ、公開検証を実現している。 - \subsection{VOLE-in-the-Head} VOLEitHは、MPC-in-the-Headの開示構造にQuickSilver型のVOLE検査を組み込み、指定検証者型VOLEを公開検証可能に拡張した手法である。 VOLEitHは、MPCitHの「開示しない1パーティ」を、VOLEのグローバル鍵 $\mathbf{\Delta}$ に対応付けることで、指定検証者型のVOLE系プロトコルを公開検証可能にする。 -鍵となるのが、長さ倍増PRGから構成するGGM木に基づく All-but-One ベクトルコミットメント (VC) である。 +鍵となるのが、長さ倍増PRGから構成するGGM treeに基づく All-but-One Vector Commitmentである。 \begin{itemize} \item 高さ $h=\log N$ のGGM木の根シードから $N$ 個の葉シード $sd_i$ を生成し、各葉にVOLE用の乱数列 $r_i$ を割り当てる。 \item 開示しないインデックス $j^*$ を除き、$P$ は各葉への経路で必要な兄弟ノードのシードを開示するだけで $N-1$ 個の $r_i$ を再現させられる(通信量は $O(\log N)$)。 @@ -55,7 +56,7 @@ \subsection{SNARKとオンチェーン検証の概観} ガスは主にペアリング(1回あたり\(\sim\)34k gas、合計15--20万gas規模)と公開入力数に比例するMSMで支配され、calldata課金は16 gas/非ゼロバイトで証明サイズ1055バイトなら約1.7万gasとなる。 コードサイズは24KB上限のため検証鍵の配置も設計上の制約となる。 -\subsection{設計指針(本稿で用いる前提)} +\subsection{設計指針} \begin{itemize} \item \textbf{証明サイズの固定性}: Groth16の証明サイズは一定(本稿では1055バイト)で、回路規模が増えてもcalldata課金は増えない。 \item \textbf{公開入力の削減}: MSMコストは公開入力数に線形。ハッシュ圧縮等で項目数を抑える。 From 497ba6db8c71a58d345309f8fcc8229d0ea14a25 Mon Sep 17 00:00:00 2001 From: adust09 Date: Sun, 23 Nov 2025 15:18:52 +0900 Subject: [PATCH 02/21] Revise abstract, introduction, and preliminaries sections in VOLEitH research paper - Updated the abstract to clarify the application of VOLE-in-the-Head (VOLEitH) in reducing proof generation costs and its implications for on-chain verification in Ethereum. - Enhanced the introduction by refining the explanation of VOLE-based zero-knowledge proofs and their advantages over traditional SNARKs, emphasizing the significance of VOLEitH. - Streamlined the preliminaries section to focus on essential concepts, including Groth16 and on-chain verification, while removing redundant content for improved clarity. - Improved overall coherence and structure of the document to better articulate the mathematical foundations and practical implications of the discussed protocols. --- paper/abstract.tex | 2 +- paper/intro.tex | 3 +- paper/out/main.pdf | Bin 314020 -> 296626 bytes paper/preliminaries.tex | 80 ++++++++++++++++++++++------------------ 4 files changed, 47 insertions(+), 38 deletions(-) diff --git a/paper/abstract.tex b/paper/abstract.tex index 31c28fd..691211e 100644 --- a/paper/abstract.tex +++ b/paper/abstract.tex @@ -1,5 +1,5 @@ \begin{abstract} -Vector Oblivious Linear Evaluation (VOLE) を用いたMPC-in-the-Head型ゼロ知識証明 VOLE-in-the-Head (VOLE-itH) は、線形演算をVOLEプリプロセスに置き換えることで証明生成コストを大幅に削減する。 +Vector Oblivious Linear Evaluation (VOLE) を用いたゼロ知識証明 VOLE-in-the-Head (VOLE-itH) は、線形演算をVOLEプリプロセスに置き換えることで証明生成コストを大幅に削減する。 一方、Ethereum での公開検証ではオンチェーン検証コストが実用性のボトルネックとなる。本研究は、VOLE-itH のオンチェーン適用に向けた実装ベースの評価として、(1) 証明生成・検証の計算量と証明サイズを測定し、(2) SNARK (Groth16) で圧縮した上で Ethereum verifier を実装し、そのガスコストを評価した。 SHA-256/Keccak-F/基本論理回路でベンチマークした結果、VOLE-itH の証明生成は Circom 実装より最大 15.5× 高速だが証明サイズは 6000× 増大した。SNARK で圧縮すると証明サイズを 1,055 バイトに固定でき、オンチェーン検証は実測で xxx gas で完了した。 これらの結果から、VOLE-itH をブロックチェーン応用に適用する際のコスト・圧縮トレードオフと実用条件を明らかにする。 diff --git a/paper/intro.tex b/paper/intro.tex index e667663..bd36bb6 100644 --- a/paper/intro.tex +++ b/paper/intro.tex @@ -7,7 +7,8 @@ \subsection{ゼロ知識証明の進化とオンチェーン検証の課題} \subsection{VOLEベースZKPとVOLE-in-the-Head} この課題に対し、証明者の計算効率を大幅に向上させる新しいZKPの系統として、VOLE(Vector Oblivious Linear Evaluation)ベースのプロトコルが登場した。 -これらのプロトコルは、従来のSNARKs(Succinct Non-Interactive Argument of Knowledge)で主流であったR1CS(Rank-1 Constraint System)とは異なるアプローチを取り、特に証明者の計算負荷を軽減することに成功している。SNARKsは証明サイズが小さく検証が高速なためオンチェーン検証で広く利用されており、Groth16\cite{groth16}やPLONK\cite{plonk}のような多くの証明システムが提案されている。 +これらのプロトコルは、従来のSNARKs(Succinct Non-Interactive Argument of Knowledge)で主流であったR1CS(Rank-1 Constraint System)とは異なるアプローチを取り、特に証明者の計算負荷を軽減することに成功している。 +SNARKsは証明サイズが小さく検証が高速なためオンチェーン検証で広く利用されており、Groth16\cite{groth16}やPLONK\cite{plonk}のような多くの証明システムが提案されている。 その中でもVOLE-in-the-Head (VOLE itH) は、VOLEベースの対話型プロトコルにFiat-Shamir変換を適用することで、誰でも検証可能な公開証明(publicly verifiable proof)を生成可能にした画期的な手法である\cite{voleith}。 これにより、証明者側の高い計算効率という利点を維持しつつ、オンチェーン検証への道が拓かれた。 diff --git a/paper/out/main.pdf b/paper/out/main.pdf index 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$\mathbb{F}_{2^\lambda}$ 上に置くサブフィールドVOLEが用いられる。 +一般的に、入力 $\mathbf{u}$ を $\mathbb{F}_2$ に制限しつつ、$\mathbf{v}, \mathbf{q}, \mathbf{\Delta}$ を拡大体 $\mathbb{F}_{2^\lambda}$ 上に置くサブフィールドVOLEが用いられる。 これはビット演算を保ちつつ、MACは大きな体で保持することで効率と安全性を両立するためである。 - -\subsection{QuickSilver} -QuickSilverは、VOLE MACの準同型性を用いて乗算制約を検査するゼロ知識プロトコルであり、VOLE相関を前提に軽量な検証を実現する。 -QuickSilverはLine-Point Zero-Knowledgeパラダイムを用い、VOLE MACの加法準同型性で乗算制約 $w_\alpha \cdot w_\beta = w_\gamma$ を検査する。 -証明者は応答を $\tilde{a}_0,\tilde{a}_1,\tilde{b}$ にマスクし、検証者は VOLE 関係 -\begin{equation} - \tilde{b} = \tilde{a}_0 + \tilde{a}_1 \cdot \Delta -\end{equation} -が成立することを確認するだけで健全性を得る。 -VOLEitHは、このQuickSilver型の検査をGGMベースのVCと組み合わせ、公開検証を実現している。 - -\subsection{MPC-in-the-Head (MPCitH)} -MPCitHは、NPリレーションの知識証明を「頭の中で」実行するMPCに還元し、ビュー開示で健全性を担保するZKフレームワークである。 -NPリレーション $R(x, w)$ に対し、証明者 $P$ は証人 $w$ を $N$ 份のシェア $w_i$ に分割し(加法秘密分散等)、$f(x, w_1,\dots,w_N)=R(x,\bigoplus_i w_i)$ を計算する半正直MPC $\Pi_f$ を頭の中でエミュレートする。 -識別プロトコルは次の4段階で構成される。 -\begin{enumerate} - \item \textbf{ビュー生成とコミット}: $\Pi_f$ の各仮想パーティのビュー $V_1,\dots,V_N$ にコミットする。 - \item \textbf{チャレンジ}: 検証者 $V$ はインデックス $i^* \in \{1,\dots,N\}$ をランダムに選ぶ。 - \item \textbf{開示}: $P$ は $i^*$ を除く $N-1$ 個のビューを開示する。 - \item \textbf{検証}: $V$ は開示ビューの整合性と、$\Pi_f$ の実行規則への準拠を検査する。 -\end{enumerate} -$\Pi_f$ が $(N-1)$-privacy を満たすとき、開示されなかった $V_{i^*}$ を偽造しない限り不正な $P$ は受理されないため、健全性が得られる。 -通信量は回路サイズ $s$ に線形($O(s) + \mathrm{poly}(k,\log s)$)で、汎用性が高い。 +\subsection{VOLE-based ZK} +todo \subsection{VOLE-in-the-Head} VOLEitHは、MPC-in-the-Headの開示構造にQuickSilver型のVOLE検査を組み込み、指定検証者型VOLEを公開検証可能に拡張した手法である。 @@ -51,15 +29,45 @@ \subsection{VOLE-in-the-Head} \end{itemize} この構成により、OTを用いずに非対話でVOLE相関を生成し、MACのbinding性を保ったままFiat--Shamir変換を適用できる。 -\subsection{SNARKとオンチェーン検証の概観} -Groth16を例に、オンチェーン検証は (i) 証明と公開入力をcalldataで受領、(ii) 回路固有の検証鍵をコントラクトに格納、(iii) 公開入力とICベクトルのMSMで\(\mathrm{vk\_x}\)を計算、(iv) ペアリングprecompileで等式を判定、の4段階からなる。 -ガスは主にペアリング(1回あたり\(\sim\)34k gas、合計15--20万gas規模)と公開入力数に比例するMSMで支配され、calldata課金は16 gas/非ゼロバイトで証明サイズ1055バイトなら約1.7万gasとなる。 -コードサイズは24KB上限のため検証鍵の配置も設計上の制約となる。 +\subsection{Groth16} +Groth16は、現在最も広く利用されているzk-SNARKsの一つであり、特にその証明サイズの小ささと検証の速さで知られている。 +ブロックチェーンのように検証コストが重視される環境において、特に強力な選択肢となる。 -\subsection{設計指針} -\begin{itemize} - \item \textbf{証明サイズの固定性}: Groth16の証明サイズは一定(本稿では1055バイト)で、回路規模が増えてもcalldata課金は増えない。 - \item \textbf{公開入力の削減}: MSMコストは公開入力数に線形。ハッシュ圧縮等で項目数を抑える。 - \item \textbf{検証鍵の配置}: コントラクトサイズ上限を考慮し、検証鍵を分離・共有する設計をとる。 - \item \textbf{フィールド整合性}: 証明生成・検証ともBN254を用いる。別曲線を選ぶ場合は専用プリコンパイルやロールアップを前提とする。 -\end{itemize} +Groth16プロトコルは主に3つのアルゴリズムから構成される: +\begin{description} + \item[Setup] 回路(通常はR1CS形式)から、証明鍵(Proving Key, pk)と検証鍵(Verification Key, vk)を生成する。 + このプロセスは回路ごとに一度だけ実行する必要があり、信頼できる第三者または複数当事者によるセレモニー(Trusted Setup)を必要とする。 + このセットアップで用いられた乱数("toxic waste")が漏洩すると、不正な証明が生成可能になるという課題がある。 + \item[Prove] 証明者は、証明鍵、公開入力(witness)、および秘密入力を用いて、証明(proof, $\pi$)を生成する。 + \item[Verify] 検証者は、検証鍵、公開入力、および証明$\pi$を受け取り、その正当性を検証する。 +\end{description} + +Groth16の証明は、特定の楕円曲線(例: BN254)上の3つの群要素($\mathbb{G}_1$の元2つ、$\mathbb{G}_2$の元1つ)で構成され、回路の規模に関わらず常に一定のサイズである。 +検証は、数回のペアリング演算によって行われ、極めて高速に完了する。 +この効率性の代償として、回路ごとに異なるTrusted Setupが必要であり、汎用性(universality)に欠けるというトレードオフが存在する。 + + +\subsection{オンチェーン検証} +オンチェーン検証とは、ブロックチェーン上で暗号学的証明の正当性を検証するプロセスを指す。本稿では特に、Ethereum仮想マシン(EVM)上でzk-SNARKの証明を検証するケースを扱う。 + +Ethereumは、\textbf{スマートコントラクト}と呼ばれるプログラムを実行できる分散型プラットフォームである。 +スマートコントラクトは一度デプロイされると、そのロジックは誰でも呼び出すことができ、実行結果はブロックチェーンに記録され、改ざんが困難となる。 +しかし、スマートコントラクトの実行には\textbf{ガス}と呼ばれる手数料が必要であり、計算が複雑であるほど高額になる。 +このため、オンチェーンでの利用には、検証コストが極めて低い証明システムが不可欠となる。 + +この文脈でGroth16が広く採用されるのは、その\textbf{証明サイズが小さい}(回路の規模に関わらず一定かつBN254曲線で約1KBと非常に小さい)点と、\textbf{検証が高速}である点にある。 +ブロックチェーンに送信するデータ(calldata)や計算はガス代に直結するため、これらの特性はオンチェーン検証の経済性を大きく左右する。 + +Ethereum上でGroth16の証明を検証するには、Solidityで記述された検証コントラクトが用いられる。 +この検証ロジックは、Ethereumに予め組み込まれた\textbf{プリコンパイル済みコントラクト}を利用することで、効率的に実行される。 +具体的には、アドレス`0x08`に配置された`ecPairing`というプリコンパイル済みコントラクトが、BN254曲線におけるペアリング演算をネイティブ実装に近い速度で提供する。 + +検証のプロセスは以下の通りである。 +まず、開発者は証明対象の回路に対応する検証鍵(Verification Key, vk)を含むスマートコントラクト(例: Verifier.sol)をEthereumにデプロイする。 +次に、証明を検証したいユーザーは、証明(proof, $\pi$)と公開入力(public inputs)をトランザクションとして検証コントラクトに送信する。 +検証コントラクトは、受け取った証明と公開入力、そしてコントラクト内に保管された検証鍵を用いてGroth16の検証方程式を評価する。 +この際、高コストなペアリング演算は`ecPairing`プリコンパイル済みコントラクトを呼び出して実行し、方程式が成立すれば証明は正当であると判定される。 +この結果に基づき、コントラクトは後続の処理(状態の更新や別のコントラクト呼び出しなど)を行う。 + +このようなオンチェーンZKアプリケーション開発において、\textbf{Circom}は算術回路を記述するためのドメイン固有言語(DSL)であり、そのツールチェーン(`snarkjs`を含む)は、回路記述の容易さに加え、コンパイルされた回路からGroth16の検証鍵を抽出し、それに基づいた\textbf{Solidity製の検証コントラクト(`Verifier.sol`)を自動生成する機能}を持つ。 +これにより、開発者は複雑なペアリング演算のロジックを自ら実装することなく、効率的にオンチェーン検証用のスマートコントラクトを準備することが可能となる。 From c59b914c22840d8376e418c0d51c5a3ec743e2ee Mon Sep 17 00:00:00 2001 From: adust09 Date: Sun, 23 Nov 2025 15:24:01 +0900 Subject: [PATCH 03/21] Add detailed explanation of VOLE-in-the-Head (VOLEitH) in new document - Introduced a comprehensive document on VOLE-in-the-Head (VOLEitH), outlining its theoretical foundations and applications in zero-knowledge proofs. - Explained the concepts of Vector Oblivious Linear Evaluation (VOLE) and its significance in cryptographic protocols. - Discussed the challenges of traditional VOLE-based zero-knowledge proofs and how VOLEitH addresses public verifiability. - Highlighted the mechanism of VOLEitH, including commitment processes and the role of delayed challenges for maintaining security. - Emphasized the practical applications of VOLEitH, particularly in post-quantum signature schemes like FAEST, showcasing its efficiency and verification capabilities. --- paper/preliminaries.tex | 46 ++++++++++++++++------------- vole.md | 65 +++++++++++++++++++++++++++++++++++++++++ 2 files changed, 91 insertions(+), 20 deletions(-) create mode 100644 vole.md diff --git a/paper/preliminaries.tex b/paper/preliminaries.tex index d39df4c..2bd45b3 100644 --- a/paper/preliminaries.tex +++ b/paper/preliminaries.tex @@ -2,32 +2,38 @@ \section{前提知識と関連研究} 本章では、後続のベンチマークと考察を理解するために必要な暗号学的前提を簡潔に整理する。 \subsection{Vector Oblivious Linear Evaluation (VOLE)} -VOLEは、二者間で線形関係を隠したままMAC相関を生成するプリミティブである。 -有限体 $F$ 上で、送信者はベクトル $\mathbf{u}, \mathbf{v} \in F^m$ を、受信者はグローバル鍵 $\mathbf{\Delta} \in F^m$ を入力とする。 -プロトコル終了後、受信者は +Vector Oblivious Linear Evaluation(VOLE)は、二者間で線形関係を秘匿したまま、ある種の相関を生成するための暗号学的プリミティブである。 +$k$をセキュリティパラメータ、$\mathbb{F}_{2^k}$を要素数$2^k$の有限体とする。 +証明者(Prover)はベクトル$\mathbf{u} \in \mathbb{F}_2^\ell$と$\mathbf{v} \in \mathbb{F}_{2^k}^\ell$を、検証者(Verifier)はグローバルキー$\Delta \in \mathbb{F}_{2^k}$を入力とする。 +プロトコル終了後、検証者は$\mathbf{q} \in \mathbb{F}_{2^k}^\ell$を得て、証明者は$(\mathbf{u}, \mathbf{v})$を、検証者は$(\Delta, \mathbf{q})$を保持する。これらの値は以下のVOLE相関式を満たす。 \begin{equation} - \mathbf{q} = \mathbf{u} \circ \mathbf{\Delta} - \mathbf{v} \in F^m + q_i = u_i \cdot \Delta + v_i \quad (i=0, \dots, \ell-1) \end{equation} -を満たすペア $(\mathbf{u}, \mathbf{q})$ を得る($\circ$ は要素積)。 -$\mathbf{q}$ は $\mathbf{u}$ に対する情報理論的MACとなり、$\mathbf{\Delta}$ を知らずに $\mathbf{q}$ を固定したまま $\mathbf{u}$ を改ざんすることはできない(binding)。 -この性質が後述の健全性担保に直接利用される。 - -一般的に、入力 $\mathbf{u}$ を $\mathbb{F}_2$ に制限しつつ、$\mathbf{v}, \mathbf{q}, \mathbf{\Delta}$ を拡大体 $\mathbb{F}_{2^\lambda}$ 上に置くサブフィールドVOLEが用いられる。 -これはビット演算を保ちつつ、MACは大きな体で保持することで効率と安全性を両立するためである。 +この相関は、$u_i$に対する線形準同型コミットメントとして機能する。 +\begin{description} + \item[秘匿性 (Hiding)] 検証者は$q_i$から$u_i$の情報を得られない。これは、証明者が知るランダムな値$v_i$が$u_i$をマスクするためである。 + \item[拘束性 (Binding)] 証明者は、コミットした$u_i$とは異なる値$u'_i$を開示することができない。これを行うには$\Delta$を推測する必要があるが、その成功確率は$2^{-k}$であり、計算論的に無視できる。 +\end{description} \subsection{VOLE-based ZK} -todo +VOLEの持つ線形性(加法準同型性)を利用することで、効率的なゼロ知識証明プロトコル(VOLE-based ZK)を構築できる。 +このパラダイムに基づく代表的なプロトコルとしてQuickSilverがある。 +VOLEベースの証明は、事前にVOLE相関をバッチ生成(pre-processing)しておき、オンラインフェーズでは軽い計算のみで証明を生成できるため、証明者・検証者ともに非常に高速である。 + +しかし、従来のVOLE-ZKプロトコルは、その健全性(Soundness)を保証するために、検証者がグローバルキー$\Delta$の値を秘密に保つ必要があった。 +このため、証明を検証できるのが特定の検証者に限定される\textbf{指定検証者証明(Designated Verifier Proof)}となり、第三者が検証できる\textbf{公開検証可能性(Public Verifiability)}を持たないという課題があった。 \subsection{VOLE-in-the-Head} -VOLEitHは、MPC-in-the-Headの開示構造にQuickSilver型のVOLE検査を組み込み、指定検証者型VOLEを公開検証可能に拡張した手法である。 -VOLEitHは、MPCitHの「開示しない1パーティ」を、VOLEのグローバル鍵 $\mathbf{\Delta}$ に対応付けることで、指定検証者型のVOLE系プロトコルを公開検証可能にする。 -鍵となるのが、長さ倍増PRGから構成するGGM treeに基づく All-but-One Vector Commitmentである。 -\begin{itemize} - \item 高さ $h=\log N$ のGGM木の根シードから $N$ 個の葉シード $sd_i$ を生成し、各葉にVOLE用の乱数列 $r_i$ を割り当てる。 - \item 開示しないインデックス $j^*$ を除き、$P$ は各葉への経路で必要な兄弟ノードのシードを開示するだけで $N-1$ 個の $r_i$ を再現させられる(通信量は $O(\log N)$)。 - \item 開示されない $r_{j^*}$ が $\mathbf{\Delta}$ に対応し、$V$ は公開された $r_i$ の線形結合から $\mathbf{q}=\mathbf{u}\circ\mathbf{\Delta}-\mathbf{v}$ を再構成する。 -\end{itemize} -この構成により、OTを用いずに非対話でVOLE相関を生成し、MACのbinding性を保ったままFiat--Shamir変換を適用できる。 +VOLE-in-the-Head(VOLEitH)は、上記のような指定検証者型のVOLE-ZKプロトコルを、非対話かつ公開検証可能なゼロ知識証明(NIZK)に変換するためのコンパイラである。 +VOLEitHは、MPC-in-the-HeadパラダイムとVOLEを組み合わせたもので、証明の健全性を単一の証明者の計算能力に帰着させる。 + +VOLEitHの核となるアイデアは、検証者が秘密情報($\Delta$)を持つ代わりに、証明者自身がコミットし、後からFiat-Shamir変換によって$\Delta$を導出する点にある。 +\begin{enumerate} + \item \textbf{コミットメント}: 証明者は、VOLE相関の元となるシード(seed)のベクトルにコミットする。このコミットメントには、GGMツリー(擬似乱数生成器を再帰的に適用する構成)に基づく\textbf{All-but-One ベクトルコミットメント}が用いられ、単一のハッシュ値で多数のシードをコミットできる。 + \item \textbf{チャレンジ生成}: 証明の主要部分が生成された後、Fiat-Shamir変換を用いて、証明全体のトランスクリプトからチャレンジとしてグローバルキー$\Delta$が導出される。$\Delta$が事前にわかると拘束性が破られるため、この「遅延」が重要である。 + \item \textbf{開示と検証}: $\Delta$が定まった後、証明者はコミットメントを開示する。All-but-Oneコミットメントの性質により、$N$個のシードのうち$N-1$個を$O(\log N)$の通信量で開示できる。開示されなかった1つのシードに対応する部分が、VOLEにおける$\Delta$の役割を果たす。 +\end{enumerate} +検証者は、開示された情報と自身で計算した$\Delta$を用いてVOLE相関式を検証する。これにより、検証者が事前に秘密を共有することなく、誰でも証明を検証できる公開検証可能性が実現される。 \subsection{Groth16} Groth16は、現在最も広く利用されているzk-SNARKsの一つであり、特にその証明サイズの小ささと検証の速さで知られている。 diff --git a/vole.md b/vole.md new file mode 100644 index 0000000..c71ac19 --- /dev/null +++ b/vole.md @@ -0,0 +1,65 @@ +VOLE in the Head(VOLEitH)に関する解説を、指定された流れと学術的な要件に従い、以下に記述します。 + +--- + +## 予備知識:Vector Oblivious Linear Evaluation (VOLE) および VOLE-in-the-Head + +本稿では、ゼロ知識証明システムを構築するために用いられる、Vector Oblivious Linear Evaluation(VOLE)、VOLEベースゼロ知識(VOLE-ZK)、および VOLE-in-the-Head(VOLEitH)の概念について解説する。 + +### 1. Vector Oblivious Linear Evaluation (VOLE) + +VOLE は、情報理論的安全性を基盤としたゼロ知識証明の構成要素として重要な役割を果たす。特に、VOLEは線形準同型コミットメントスキームの一種として利用される。 + +$k$ をセキュリティパラメータとし、$\mathbb{F}_{2^k}$ を有限体とする。VOLE(Vector Oblivious Linear Evaluation)相関は、長さ $\ell$ のベクトルに対して定義される。VOLE相関は、以下のパラメータによって特徴づけられる: + +1. **グローバルキー** ($\Delta \in \mathbb{F}_{2^k}$): ランダムに選択される。 +2. **ランダムビット**($u_i \in \mathbb{F}_2$)の集合。 +3. **VOLEタグ**($v_i \in \mathbb{F}_{2^k}$)の集合。 +4. **VOLEキー**($q_i \in \mathbb{F}_{2^k}$)の集合。 + +これらの要素は、以下の**VOLE相関式**を満たす: + +$$ +q_i = u_i \cdot \Delta + v_i \quad \text{for } i = 0, \ldots, \ell-1 \quad (1) +$$ + +ここで、**証明者(Prover, P)**は $u_i$ および $v_i$ の値を知り、**検証者(Verifier, V)**は $q_i$ および $\Delta$ の値を持つ。 + +このVOLE相関は、証明者がランダムビット $u_i$ にコミットするための**線形準同型コミットメントスキーム**として機能する。 + +* **秘匿性(Hiding)**: 検証者の持つ $q_i$ の値において、ランダムな $v_i$ が $u_i$ をマスクするため、秘匿性が保証される。 +* **拘束性(Binding)**: 証明者が $\Delta$ の知識なしに、コミットした値 $u_i$ と異なる値 $u'_i$ に開示するためには、$\Delta$ を推測する必要がある。これは $\mathbb{F}_{2^k}$ において確率 $2^{-k}$ でしか起こり得ないため、拘束性が保証される。 + +### 2. VOLEベースゼロ知識証明 (VOLE-ZK) の課題 + +VOLE相関の線形準同型性(加法準同型性)は、効率的なゼロ知識証明(VOLE-ZK)を構築する上で特に有用である。VOLE-ZKプロトコルは、事前に準備されたランダムなVOLE相関を用いて、コミット・アンド・プルーフ型の構造で、非常に効率的な証明を可能にする。例えば、QuickSilverプロトコル は、このパラダイムに基づいている。 + +しかし、従来のVOLE-ZKプロトコルは本質的に**指定検証者証明**(designated verifier proofs)であった。これは、プロトコルの健全性(Soundness)を確保するために、**検証者(V)が秘密の状態**、すなわち $\Delta$ と $q_i$ の値を保持し続ける必要があったためである。この制約により、証明が第三者による検証を可能とする**公開検証可能性**(public verifiability)を持たなかった。 + +### 3. VOLE-in-the-Head (VOLEitH) による公開検証可能性の獲得 + +VOLE-in-the-Head(VOLEitH)は、VOLE-ZKプロトコルを非対話形式に変換し、公開検証可能性を達成するための新しい手法である。 + +VOLEitHは、指定検証者設定のゼロ知識プロトコルを、非対話型かつ公開検証可能(NIZK)なプロトコルへと変換する**コンパイラ**として機能する。この変換は、OT(Oblivious Transfer)ベースのZKプロトコルをコンパイルする一般的なアプローチに基づいており、VOLE相関を生成するプロセスを、**計算的に秘匿性があり、直線的に抽出可能なオール・バット・ワンベクトルコミットメント**に基づいたメカニズムで置き換えることにより実現される。 + +#### VOLEitHのメカニズム:秘密のコミットメントと遅延されたチャレンジ + +VOLEitHが公開検証可能性を獲得する鍵は、検証者と秘密の状態を共有することなく、証明者が自己完結的にVOLE相関をコミットメントできる点にある。 + +1. **シード生成とコミットメント**: 証明者(P)はまず、自身の値 $u_i$ と $v_i$ を生成する。これらの値は、擬似乱数シードのベクトルコミットメント(**オール・バット・ワンベクトルコミットメント**)を用いてコミットされる。 + * このコミットメントは、長さ倍増PRGの木構造(GGM構成)を利用して構築される。 + * 証明者(P)は、単一のハッシュ値(コミットメント)を送信する。これにより、Pは $N$ 個のシード(擬似乱数)にコミットする。 +2. **VOLE相関への変換**: Pは、このベクトルコミットメントをVOLE相関に変換する。 +3. **チャレンジの遅延と非対話化**: 重要な点として、VOLE相関の**グローバルキー $\Delta$ は、ゼロ知識証明の主要なステップが実行された後でなければ、Pに与えられてはならない**。 + * $\Delta$ が事前に知られると、VOLEコミットメントの**拘束性**が破られてしまうためである。 + * VOLEitHでは、検証者(V)からのチャレンジ $\Delta$ は、Fiat-Shamir変換を用いて、証明のトランスクリプトのハッシュ値から導出される。 +4. **開示と検証**: チャレンジ $\Delta$ が確定した後、Pはベクトルコミットメントの開示(opening)を送信する。この開示は、コミットされた $N$ 個のシードのうち $N-1$ 個を、わずか $O(\log N)$ の通信量で開示する。 + * Vは、この開示と $\Delta$ を用いて、VOLE相関式 (1) を満たす $q_i$ の値を再構築し、Pの計算が正しいことを検証できる。 + +このようにして、VOLEitHは、検証者が秘密の状態を事前に保持することなく、プロトコル全体を非対話型に変換することを可能とし、**誰でも検証可能な公開検証可能性**を実現する。 + +### 4. VOLE in the Headの応用 + +VOLEitHは、その効率性と公開検証可能性から、様々な暗号学的構成要素に応用されている。 + +VOLEitHの重要な応用の一つとして、**FAEST**が挙げられる。FAESTは、VOLEitH構成に基づくポスト量子署名スキームであり、VOLEitHとQuickSilver情報理論的証明システムを組み合わせることにより、非対話型署名アルゴリズムを構築している。FAESTは、AES(Advanced Encryption Standard)のプリイメージの知識を証明することに基づいて設計されており、対称鍵プリミティブのみに依存する保守的なセキュリティ仮定を用いている。FAESTは、その効率的な設計により、他のポスト量子署名スキームと比較して、署名サイズが最小クラスとなることを実現している。FAESTのゼロ知識証明システムは、VOLEitHにより、公開検証可能となっている。 From deb4f4b0415ec26a8b741d6c8a68928b89cf7ea2 Mon Sep 17 00:00:00 2001 From: adust09 Date: Sun, 23 Nov 2025 15:28:48 +0900 Subject: [PATCH 04/21] Revise Groth16 subsection and update references in VOLEitH research paper - Reintroduced the Groth16 subsection in the preliminaries section, detailing its algorithms and significance in zk-SNARKs. - Enhanced the explanation of Groth16's efficiency and its trade-offs regarding Trusted Setup. - Added new references to QuickSilver and Fiat-Shamir, expanding the bibliography to support the discussions on zero-knowledge proofs. - Improved 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zBd*PF#9?C0#m3Ff#l;3N;o{;n;o@fHVdpe6WH&Zs1MqMP{@+LFGArBLJHxa7TSA#x z#?H*1l4jepyA{kg)rDQ^o%Ertz}m zjEY=#xo+%FgXlL2ngqs@Aon=Y+*+#FKZOair8IIlI?Ze!5lp%%BVL`i&ClcZorhdg z8BUJGXmN391Zd{Z5&BmR3xANP~KS~AQLGiPu@w-dJPbJ6zhFmKv5freRfpGpR(M( zgEP4P#*T!;ZDXD3^d zc522{SVkgQiB84k8C+00NV6d1jHfy~ZJuzTIa=+)iG_tL&-DLnU(hV)i~jUTlXvh5%Xvn?mQ7uf`Cs9dtG-%WSR4$!F3gk zxju0ezHt=!fg9F?8)1l>3oP^?|AbKg=k$L)DNfFYAZK@wsTn*Q4}gn@9iECxLO~M# FzX0>IChGtI diff --git a/paper/preliminaries.tex b/paper/preliminaries.tex index 2bd45b3..cf725e7 100644 --- a/paper/preliminaries.tex +++ b/paper/preliminaries.tex @@ -35,23 +35,6 @@ \subsection{VOLE-in-the-Head} \end{enumerate} 検証者は、開示された情報と自身で計算した$\Delta$を用いてVOLE相関式を検証する。これにより、検証者が事前に秘密を共有することなく、誰でも証明を検証できる公開検証可能性が実現される。 -\subsection{Groth16} -Groth16は、現在最も広く利用されているzk-SNARKsの一つであり、特にその証明サイズの小ささと検証の速さで知られている。 -ブロックチェーンのように検証コストが重視される環境において、特に強力な選択肢となる。 - -Groth16プロトコルは主に3つのアルゴリズムから構成される: -\begin{description} - \item[Setup] 回路(通常はR1CS形式)から、証明鍵(Proving Key, pk)と検証鍵(Verification Key, vk)を生成する。 - このプロセスは回路ごとに一度だけ実行する必要があり、信頼できる第三者または複数当事者によるセレモニー(Trusted Setup)を必要とする。 - このセットアップで用いられた乱数("toxic waste")が漏洩すると、不正な証明が生成可能になるという課題がある。 - \item[Prove] 証明者は、証明鍵、公開入力(witness)、および秘密入力を用いて、証明(proof, $\pi$)を生成する。 - \item[Verify] 検証者は、検証鍵、公開入力、および証明$\pi$を受け取り、その正当性を検証する。 -\end{description} - -Groth16の証明は、特定の楕円曲線(例: BN254)上の3つの群要素($\mathbb{G}_1$の元2つ、$\mathbb{G}_2$の元1つ)で構成され、回路の規模に関わらず常に一定のサイズである。 -検証は、数回のペアリング演算によって行われ、極めて高速に完了する。 -この効率性の代償として、回路ごとに異なるTrusted Setupが必要であり、汎用性(universality)に欠けるというトレードオフが存在する。 - \subsection{オンチェーン検証} オンチェーン検証とは、ブロックチェーン上で暗号学的証明の正当性を検証するプロセスを指す。本稿では特に、Ethereum仮想マシン(EVM)上でzk-SNARKの証明を検証するケースを扱う。 @@ -77,3 +60,20 @@ \subsection{オンチェーン検証} このようなオンチェーンZKアプリケーション開発において、\textbf{Circom}は算術回路を記述するためのドメイン固有言語(DSL)であり、そのツールチェーン(`snarkjs`を含む)は、回路記述の容易さに加え、コンパイルされた回路からGroth16の検証鍵を抽出し、それに基づいた\textbf{Solidity製の検証コントラクト(`Verifier.sol`)を自動生成する機能}を持つ。 これにより、開発者は複雑なペアリング演算のロジックを自ら実装することなく、効率的にオンチェーン検証用のスマートコントラクトを準備することが可能となる。 + +\subsection{Groth16} +Groth16は、現在最も広く利用されているzk-SNARKsの一つであり、特にその証明サイズの小ささと検証の速さで知られている。 +ブロックチェーンのように検証コストが重視される環境において、特に強力な選択肢となる。 + +Groth16プロトコルは主に3つのアルゴリズムから構成される: +\begin{description} + \item[Setup] 回路(通常はR1CS形式)から、証明鍵(Proving Key, pk)と検証鍵(Verification Key, vk)を生成する。 + このプロセスは回路ごとに一度だけ実行する必要があり、信頼できる第三者または複数当事者によるセレモニー(Trusted Setup)を必要とする。 + このセットアップで用いられた乱数("toxic waste")が漏洩すると、不正な証明が生成可能になるという課題がある。 + \item[Prove] 証明者は、証明鍵、公開入力(witness)、および秘密入力を用いて、証明(proof, $\pi$)を生成する。 + \item[Verify] 検証者は、検証鍵、公開入力、および証明$\pi$を受け取り、その正当性を検証する。 +\end{description} + +Groth16の証明は、特定の楕円曲線(例: BN254)上の3つの群要素($\mathbb{G}_1$の元2つ、$\mathbb{G}_2$の元1つ)で構成され、回路の規模に関わらず常に一定のサイズである。 +検証は、数回のペアリング演算によって行われ、極めて高速に完了する。 +この効率性の代償として、回路ごとに異なるTrusted Setupが必要であり、汎用性(universality)に欠けるというトレードオフが存在する。 diff --git a/paper/references.tex b/paper/references.tex index 6ca6bfe..604692c 100644 --- a/paper/references.tex +++ b/paper/references.tex @@ -46,4 +46,16 @@ \section*{参考文献 (References)} One Tree to Rule Them All: Optimizing GGM Trees and OWFs for Post-Quantum Signatures. \textit{Cryptology ePrint Archive}, Paper 2024/490, 2024. \url{https://eprint.iacr.org/2024/490}. + +\bibitem{quicksilver} +Yang, K., Kohl, P., and Song, D. +QuickSilver: Efficient and Affordable Zero-Knowledge Proofs for Circuits and Polynomials. +In \textit{Proceedings of the ACM SIGSAC Conference on Computer and Communications Security (CCS '21)}, pp. 233-250, 2021. +DOI: \url{10.1145/3460120.3484550}. + +\bibitem{fiatshamir} +Fiat, A., and Shamir, A. +How to Prove Yourself: Practical Solutions to Identification and Signature Problems. +In \textit{Advances in Cryptology -- CRYPTO '86}, pp. 186-194, 1987. +DOI: \url{10.1007/3-540-47721-7_12}. \end{thebibliography} From d5b5cee7a847323369a767d17e75d3bd596f5407 Mon Sep 17 00:00:00 2001 From: adust09 Date: Sun, 23 Nov 2025 15:54:51 +0900 Subject: [PATCH 05/21] Revise introduction and preliminaries sections to address challenges in blockchain ZKP - Updated the introduction to highlight two key challenges in blockchain ZKP: on-chain verification constraints and client-side proving requirements. - Expanded the preliminaries section with a new subsection on client-side proving, emphasizing the importance of lightweight proof generation for user experience. - Enhanced the discussion on on-chain verification, focusing on the need for succinct proof sizes and efficient verification calculations in blockchain environments. - Improved overall coherence and structure to better articulate the implications of these challenges for the adoption of zero-knowledge proofs in decentralized applications. --- paper/intro.tex | 16 ++++++++++----- paper/out/main.pdf | Bin 313060 -> 333439 bytes paper/preliminaries.tex | 43 ++++++++++++++++++++++++++++++---------- 3 files changed, 43 insertions(+), 16 deletions(-) diff --git a/paper/intro.tex b/paper/intro.tex index bd36bb6..218734f 100644 --- a/paper/intro.tex +++ b/paper/intro.tex @@ -1,9 +1,15 @@ \section{序論} -\subsection{ゼロ知識証明の進化とオンチェーン検証の課題} -ゼロ知識証明は、ある計算が正しく実行されたことを、その計算に関する入力情報を一切明らかにすることなく検証者に証明する暗号学的プロトコルである。 -この性質はプライバシー保護が強く求められる現代のデジタル社会において極めて重要であり、ブロックチェーン技術の分野でもその応用が期待されている。 -特にスマートコントラクトプラットフォームにおいては、計算の正当性をトランザクションとしてオンチェーンで検証する能力が、スケーラビリティとプライバシーの両方を向上させる鍵となる。 -しかし、ZKPをオンチェーンで検証する際には、証明サイズ、検証計算量、そしてそれに伴うガス代という、ブロックチェーン特有の厳しい制約が大きな課題となる。 +\subsection{ブロックチェーンZKPにおける二つの課題:オンチェーン検証とクライアントサイドプルービング} +ゼロ知識証明(ZKP)は、ある計算が正しく実行されたことを、その計算に関する情報を一切明らかにすることなく証明する暗号学的プロトコルである。 +このプライバシー保護の性質は、ブロックチェーン技術の文脈で特に重要視される。 +しかし、ZKPを実世界のアプリケーション、特にエンドユーザーが直接利用する分散型アプリケーションに導入するには、二つの大きな課題が存在する。 + +第一の課題は、\textbf{オンチェーン検証の制約}である。スマートコントラクト上で証明を検証する際には、証明サイズ、検証計算量、そしてそれに伴うガス代という、ブロックチェーン特有の厳しい制約に直面する。証明が大きすぎたり、検証が複雑すぎたりすると、コストが現実的でなくなり、実用性が失われる。 + +第二の課題は、\textbf{クライアントサイドプルービングの要求}である。アプリケーションが広く普及するためには、エンドユーザーが自身のデバイス(スマートフォンやPCなど)で証明を生成できなければならない。しかし、多くのzk-SNARKsは検証の軽量性と引き換えに、証明生成に膨大な計算リソースを要求する。この「証明生成の重さ」はユーザー体験を著しく損ない、技術の普及を妨げる大きな障壁となっている。 + +したがって、理想的な証明システムは、これら二つの課題を同時に解決する必要がある。すなわち、クライアントにとっては\textbf{軽量な証明生成}を、ブロックチェーンにとっては\textbf{効率的なオンチェーン検証}を両立させなければならない。 +VOLE-in-the-Head(VOLEitH)のような対称鍵暗号ベースの証明システムは、特に証明生成の軽量性に優れていることから、このクライアントサイドプルービングの課題に対する有望な解決策として注目されている。 \subsection{VOLEベースZKPとVOLE-in-the-Head} この課題に対し、証明者の計算効率を大幅に向上させる新しいZKPの系統として、VOLE(Vector Oblivious Linear Evaluation)ベースのプロトコルが登場した。 diff --git a/paper/out/main.pdf b/paper/out/main.pdf index 67d33268a8e69b92cf9d2f7f952013afac3f309a..8368837ab66301fcafd721ae039d95a68401064f 100644 GIT binary patch delta 329806 zcmZU)LwKMKu&o;#9oy{Kwr$(C{l)6oPRAWP>DcVpwr%75_nyh#&zaSzrt4j+RvpBm zeOIB^DL{ZRvnMM-PylQk90CGxu5K>o#`bVtYbDxkaTnu=lb;x$;6W?-j*cW@M$Ta+qt>P88nSr)D~`Zc0T)Pz%93E!%Rkyr znrLlrf6X9Q1Ep0Bl=6%F11CS-5++o%D^+5mvk!HbZBp{)rO6Oa<= zW0e7_z&6d|FGfWu_iYwFsZkxTnPbjKa$nI=S7rEFD4$rCcwJ%7L>^zLaVpFg(=K6+J!M9~v+|)@@Mq4DjNHG1F&TBZPxhj)} z62^{ZEf9gCfe1a|-#6iSUF3UIh{EyD!K__(hA&+8HbIci?t@T=4*DThsQUU^>XgYG zZ#s>>H#p}4JI^IOG=V={2_YE~GlR2kdzh&$L|y&8!wZ6Lzqk<@3^iDb-D^-&@*x?# 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technical terms. - Recommended structural improvements for navigation, such as summarizing sections and clarifying logical connections between them. - Proposed visual elements and automated reference management to enhance readability and academic rigor. --- improve.md | 58 +++++++++++++++++++++++++++++++++++++++++++++ paper/abstract.tex | 2 +- paper/intro.tex | 41 +++++++++++++++++++++++--------- paper/out/main.pdf | Bin 333761 -> 344589 bytes 4 files changed, 89 insertions(+), 12 deletions(-) create mode 100644 improve.md diff --git a/improve.md b/improve.md new file mode 100644 index 0000000..b73573e --- /dev/null +++ b/improve.md @@ -0,0 +1,58 @@ +# 論文「EthereumにおけるVOLE-in-the-Headの検証コスト評価」改善案 + +## 総合評価 + +本論文は、VOLE-in-the-HeadとSNARKを組み合わせたハイブリッドアーキテクチャの性能と課題を定量的に示した、技術的に価値の高い研究である。論理構成は明晰であり、データに基づく分析は詳細かつ説得力がある。 + +一方で、ターゲット読者として「Ethereumとゼロ知識証明の初心者」を想定する場合、専門用語の密度と概念の抽象度の高さが、読者の理解を妨げる可能性がある。研究の貢献をより広い読者層に的確に伝えるため、以下の改善を提案する。 + +## 優先的に取り組むべき改善点 + +### 1. 概念の段階的導入と具体例による補足 + +専門用語や抽象的な概念を提示する際に、読者の理解を助けるための工夫を導入する。 + +* **背景・目的の先行提示**: + 各技術概念(例:ゼロ知識証明, VOLE, コミットメント)を定義する前に、まず「なぜその技術が必要とされるのか」という動機付けや、解決しようとしている課題を平易な言葉で説明する。例えば、ゼロ知識証明であれば、プライバシーを保護したID検証や金融取引といった具体的なユースケースを先に示す。 + +* **機能的な比喩・具体例の活用**: + 抽象的な定義の後には、その概念の機能を説明する簡潔な具体例を添える。「コミットメント」であれば、「後から変更できないように、情報をデジタルな封筒に入れて封印し、必要に応じて開封して中身を示す仕組み」のように、その役割を直感的に理解できる表現を用いる。 + +* **基本用語の脚注による補足**: + 「ガス代」「スマートコントラクト」「有限体」など、特定の技術領域に固有の基本用語については、本文の記述の流れを維持しつつ、脚注(`\footnote`)を用いて簡潔な定義を補足する。 + +### 2. 論文構成のナビゲーション強化 + +読者が論文全体の論理構成や、各章・各節の役割を把握しやすくするための工夫を施す。 + +* **章・節の冒頭での要旨提示**: + 各章(`\section`)および主要な節(`\subsection`)の冒頭に、そのセクションで論じる内容、目的、そして導かれる結論を要約した短いパラグラフを設ける。これにより、読者は詳細な議論に入る前にその位置付けと要点を理解できる。 + +* **論理的接続の明確化**: + セクション間の繋がりを強化するため、「前節では〜という課題を明らかにした。本節では、この課題に対し〜というアプローチで評価を行う」といった、論理の流れを示す接続表現を効果的に使用する。 + +### 3. 視覚的要素と参考文献管理の高度化 + +論文の可読性と学術的な体裁を向上させる。 + +* **図・表の効果的な活用**: + * **アーキテクチャ図**: 提案するハイブリッドアーキテクチャ(VOLEitH + SNARK)の全体像を示す概念図は、システムの構成要素とデータフローを読者が直感的に理解するために不可欠である。 + * **結果の可視化**: 性能測定結果(例:SNARKの制約数と証明生成時間の関係)は、グラフを用いて視覚的に示すことで、数値データだけでは伝わりにくい傾向や相関関係を明確に伝えられる。 + +* **参考文献管理の自動化**: + 現在の手動による参考文献リスト(`thebibliography`)の管理は、項目数の増加に伴い、フォーマットの不統一やエラーを引き起こす可能性が高い。BibTeXやBibLaTeXといった文献管理システムを導入し、`.bib`ファイルで文献情報を一元管理することを強く推奨する。これにより、引用スタイルの一貫性が保証され、論文の学術的信頼性が向上する。 + +## セクションごとの具体的な改善案 + +* **Introduction (`intro.tex`)**: + * ゼロ知識証明、オンチェーン検証、クライアントサイドプルービングといった核心的な課題について、初学者にも理解可能な平易な言葉で説明を加える。 + +* **Preliminaries (`preliminaries.tex`)**: + * VOLE, VOLE-in-the-Head, Groth16などの技術解説において、数式や専門用語を提示する前に、それぞれの技術が「何をするためのものか」という目的・役割を記述する。 + +* **Results and Analysis (`results_analysis.tex`)**: + * 各サブセクションの冒頭で、「この分析から何が明らかになったか」という結論を簡潔に要約する。 + * 「Field Mappingに起因する制約数爆発」のような複雑な現象については、その原因と結果の関係性をより丁寧に解説する。 + +* **Conclusion (`conclusion.tex`)**: + * 研究全体の結論を再確認した上で、「今後の展望」で提示される各研究課題が、「なぜ重要なのか」という文脈(例:ポスト量子耐性の必要性)を補足する。 diff --git a/paper/abstract.tex b/paper/abstract.tex index 691211e..328c870 100644 --- a/paper/abstract.tex +++ b/paper/abstract.tex @@ -1,5 +1,5 @@ \begin{abstract} -Vector Oblivious Linear Evaluation (VOLE) を用いたゼロ知識証明 VOLE-in-the-Head (VOLE-itH) は、線形演算をVOLEプリプロセスに置き換えることで証明生成コストを大幅に削減する。 +Vector Oblivious Linear Evaluation (VOLE) は、二者間で線形関係を秘匿したまま、ある種の相関を生成するための暗号学的プリミティブであり、これを応用したゼロ知識証明 VOLE-in-the-Head (VOLE-itH) は、従来のゼロ知識証明と比較して線形演算をVOLEプリプロセスに置き換えることで証明生成コストを大幅に削減する。 一方、Ethereum での公開検証ではオンチェーン検証コストが実用性のボトルネックとなる。本研究は、VOLE-itH のオンチェーン適用に向けた実装ベースの評価として、(1) 証明生成・検証の計算量と証明サイズを測定し、(2) SNARK (Groth16) で圧縮した上で Ethereum verifier を実装し、そのガスコストを評価した。 SHA-256/Keccak-F/基本論理回路でベンチマークした結果、VOLE-itH の証明生成は Circom 実装より最大 15.5× 高速だが証明サイズは 6000× 増大した。SNARK で圧縮すると証明サイズを 1,055 バイトに固定でき、オンチェーン検証は実測で xxx gas で完了した。 これらの結果から、VOLE-itH をブロックチェーン応用に適用する際のコスト・圧縮トレードオフと実用条件を明らかにする。 diff --git a/paper/intro.tex b/paper/intro.tex index d37d32b..240df0a 100644 --- a/paper/intro.tex +++ b/paper/intro.tex @@ -1,22 +1,41 @@ \section{序論} -\subsection{ブロックチェーンZKPにおける二つの課題:オンチェーン検証とクライアントサイドプルービング} -ゼロ知識証明は、ある計算が正しく実行されたことを、その計算に関する情報を一切明らかにすることなく証明する暗号学的プロトコルである。 -このプライバシー保護の性質は、ブロックチェーン技術の文脈で特に重要視される。 -しかし、ZKPを実世界のアプリケーション、特にエンドユーザーが直接利用する分散型アプリケーションに導入するには、二つの大きな課題が存在する。 +\subsection{Ethereumにおけるプライバシーとゼロ知識証明の役割} +Ethereumは、\textbf{スマートコントラクト}\footnote{契約の条件確認や履行を自動的に強制するコンピュータプログラム。ブロックチェーン上で実行される。}と呼ばれるプログラムを実行できる分散型プラットフォームであり、世界中の誰もがアクセスできる巨大な共有コンピュータに例えられる。 +この透明性はシステムの信頼性を担保する一方で、すべての取引記録が公開台帳(ブロックチェーン)に恒久的に記録されることを意味する。 +これにより、どのアドレスからどのアドレスへ、いつ、どれだけの資産が移動したかを誰でも追跡できるため、ユーザーの金融活動におけるプライバシーが本質的に欠如するという深刻な課題を抱えている。 -第一の課題は、\textbf{オンチェーン検証の制約}である。スマートコントラクト上で証明を検証する際には、証明サイズ、検証計算量、そしてそれに伴うガス代という、ブロックチェーン特有の厳しい制約に直面する。 -証明が大きすぎたり、検証が複雑すぎたりすると、コストが現実的でなくなり、実用性が失われる。 +このプライバシーの欠如という課題に対する強力な解決策として、\textbf{ゼロ知識証明 (Zero-Knowledge Proof, ZKP)} が注目されている。 +ZKPは、「ある秘密の情報を知っている」という事実を、その秘密情報自体を一切明らかにすることなく相手に納得させることができる暗号学的なプロトコルである。 +この性質を利用することで、ユーザーは自身の取引の詳細を秘匿したまま、その取引が正当であることだけを証明できる。 -第二の課題は、\textbf{クライアントサイドプルービングの要求}である。アプリケーションが広く普及するためには、エンドユーザーが自身のデバイス(スマートフォンやPCなど)で証明を生成できなければならない。 -しかし、多くのzk-SNARKsは検証の軽量性と引き換えに、証明生成に膨大な計算リソースを要求する。この「証明生成の重さ」はユーザー体験を著しく損ない、技術の普及を妨げる大きな障壁となっている。 +Ethereum上でZKPを活用した代表的なアプリケーションに、プライバシーミキサーである\textbf{Tornado Cash}がある。 +Tornado Cashでは、ユーザーは資産を共通のプールに預け入れ、後で全く新しいアドレスから同額を引き出すことができる。 +このとき、ユーザーは「自分がある金額をプールに預け入れた正当な預金者である」ことをZKPを用いて証明する。 +この証明には、預け入れ時のどのアドレスとも結びつく情報が含まれないため、預け入れと引き出しの間の繋がりが暗号学的に断ち切られ、送金経路のプライバシーが保護される。 + +このようなアプリケーションを実現するには、Ethereum上でZKPを検証する仕組み、すなわち\textbf{オンチェーン検証}が不可欠である。 +オンチェーン検証のプロセスは、一般的に以下の手順で行われる。 +(1) ユーザーが自身のデバイスで、ある計算(例:「私はプールへの預金者である」)が正しいことを示す証明を生成する。 +(2) この証明を、Ethereum上にデプロイされた検証者スマートコントラクトにトランザクションとして送信する。 +(3) スマートコントラクトは、受け取った証明が有効であるかを検証し、有効であれば後続の処理(例:資産の引き出し許可)を実行する。 + +しかし、このオンチェーン検証には二つの大きな課題が存在する。 + +第一の課題は、\textbf{オンチェーン検証のコストと制約}である。 +スマートコントラクト上での計算実行には、\textbf{ガス代}\footnote{Ethereumネットワーク上でトランザクションを実行するために必要な手数料。計算が複雑であるほど高額になる。}と呼ばれる手数料が発生する。 +検証アルゴリズムが複雑であったり、証明のデータサイズが大きかったりすると、ガス代は著しく高騰し、アプリケーションの実用性が失われてしまう。 + +第二の課題は、\textbf{クライアントサイドでの証明生成の負荷}である。 +アプリケーションが広く普及するためには、ユーザーが特別な高性能ハードウェアを必要とせず、自身のデバイス(PCやスマートフォン)で証明を生成できることが望ましい。 +しかし、多くの既存のZKP技術(特にzk-SNARKs)は、検証の軽量性と引き換えに、証明生成に膨大な計算リソースと時間を要求する。この「証明生成の重さ」は、ユーザー体験を損なう大きな障壁となる。 したがって、理想的な証明システムは、これら二つの課題を同時に解決する必要がある。すなわち、クライアントにとっては\textbf{軽量な証明生成}を、ブロックチェーンにとっては\textbf{効率的なオンチェーン検証}を両立させなければならない。 VOLE-in-the-Head(VOLEitH)のような対称鍵暗号ベースの証明システムは、特に証明生成の軽量性に優れていることから、このクライアントサイドプルービングの課題に対する有望な解決策として注目されている。 \subsection{VOLEベースZKPとVOLE-in-the-Head} -この課題に対し、証明者の計算効率を大幅に向上させる新しいZKPの系統として、VOLE(Vector Oblivious Linear Evaluation)ベースのプロトコルが登場した。 -これらのプロトコルは、従来のSNARKs(Succinct Non-Interactive Argument of Knowledge)で主流であったR1CS(Rank-1 Constraint System)とは異なるアプローチを取り、特に証明者の計算負荷を軽減することに成功している。 -SNARKsは証明サイズが小さく検証が高速なためオンチェーン検証で広く利用されており、Groth16\cite{groth16}やPLONK\cite{plonk}のような多くの証明システムが提案されている。 +VOLE(Vector Oblivious Linear Evaluation)は、セキュア多者計算(MPC: Secure Multi-Party Computation)の分野、特にYao's Garbled Circuit (GC) とOblivious Transfer (OT) の研究から派生した暗号学的プリミティブである。 +これは、二者間で線形関係を秘匿したまま特定の相関を生成することを可能にする。その後、このVOLEの特性、特にその高い計算効率がゼロ知識証明に応用され、証明者の計算負荷を大幅に軽減する新しいZKPの系統が発展した。 +これにより、従来のSNARKs(Succinct Non-Interactive Argument of Knowledge)で主流であったR1CS(Rank-1 Constraint System)とは異なるアプローチを取り、特に証明者の計算負荷を軽減することに成功している。 その中でもVOLE-in-the-Head (VOLE itH) は、VOLEベースの対話型プロトコルにFiat-Shamir変換を適用することで、誰でも検証可能な公開証明(publicly verifiable proof)を生成可能にした画期的な手法である\cite{voleith}。 これにより、証明者側の高い計算効率という利点を維持しつつ、オンチェーン検証への道が拓かれた。 diff --git a/paper/out/main.pdf b/paper/out/main.pdf index 85fcaa8fe8bc7024be42995e71329b794da78f8f..70830148e42079c3a84b88a08a99041c5ab9f0df 100644 GIT binary patch delta 340514 zcmZs?V{@QwxNY09ZKq?iW7{@6w(TcQ$F@4Q&5mu`wvF?ys(q@~u5#m~wxe(s4LkjAewAN&KZ6>wO(P{L%R$UALC*^Qa>r<#|M zm#`|?F25I3@@jxBK*vT?1$I1oGD8m6?;ZD;iA0tFy-)sBa$wN-VqjRj2;7OkoL~}) zz0-V@GMKHeyl4^EPQ8V7?uy{21(~vIYHPHn1FPF4gWEG^ofnMvx7WTbDl+Q*1{w!$ 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z$_+b45BArfQbt%QCmhWU*;bFGTF~+h`__P_S`?dF#M2Gp)}ZGz{@L|U{@##h7(zon z{z20fU)g6cycaR6Vg(v@5Hu@@=iT2L_zcVAw&YUeOzl~Jf!=86qcKoWkT>ysT3&}x z4m@d(ma>?SRLahYi2oPNo6pLAvR6@1x=c9<*`_Ank%XJy@OZqJH;`eK;4(Y-pQL!W zVjH!yz4Glt^*7|{)PN78I~nglyo>%)%I8ye8ILc)=?I%;)4J^~ub5dKP`PO&alXFQe{?65|CL4XbtoU~FUbe Date: Sun, 23 Nov 2025 16:03:25 +0900 Subject: [PATCH 06/21] Update introduction and preliminaries sections to enhance clarity on blockchain ZKP challenges - Revised the introduction to clarify the definition of zero-knowledge proofs and the significance of privacy in blockchain applications. - Improved the discussion on on-chain verification constraints and client-side proving requirements, emphasizing the need for lightweight proof generation. - Enhanced the preliminaries section by adding citations for QuickSilver and Fiat-Shamir, providing better context for the discussed protocols. - Updated the references to include the Ethereum Yellow Paper, ensuring comprehensive coverage of relevant literature. --- paper/intro.tex | 8 +++++--- paper/out/main.pdf | Bin 333439 -> 333761 bytes paper/preliminaries.tex | 6 +++--- paper/references.tex | 6 ++++++ 4 files changed, 14 insertions(+), 6 deletions(-) diff --git a/paper/intro.tex b/paper/intro.tex index 218734f..d37d32b 100644 --- a/paper/intro.tex +++ b/paper/intro.tex @@ -1,12 +1,14 @@ \section{序論} \subsection{ブロックチェーンZKPにおける二つの課題:オンチェーン検証とクライアントサイドプルービング} -ゼロ知識証明(ZKP)は、ある計算が正しく実行されたことを、その計算に関する情報を一切明らかにすることなく証明する暗号学的プロトコルである。 +ゼロ知識証明は、ある計算が正しく実行されたことを、その計算に関する情報を一切明らかにすることなく証明する暗号学的プロトコルである。 このプライバシー保護の性質は、ブロックチェーン技術の文脈で特に重要視される。 しかし、ZKPを実世界のアプリケーション、特にエンドユーザーが直接利用する分散型アプリケーションに導入するには、二つの大きな課題が存在する。 -第一の課題は、\textbf{オンチェーン検証の制約}である。スマートコントラクト上で証明を検証する際には、証明サイズ、検証計算量、そしてそれに伴うガス代という、ブロックチェーン特有の厳しい制約に直面する。証明が大きすぎたり、検証が複雑すぎたりすると、コストが現実的でなくなり、実用性が失われる。 +第一の課題は、\textbf{オンチェーン検証の制約}である。スマートコントラクト上で証明を検証する際には、証明サイズ、検証計算量、そしてそれに伴うガス代という、ブロックチェーン特有の厳しい制約に直面する。 +証明が大きすぎたり、検証が複雑すぎたりすると、コストが現実的でなくなり、実用性が失われる。 -第二の課題は、\textbf{クライアントサイドプルービングの要求}である。アプリケーションが広く普及するためには、エンドユーザーが自身のデバイス(スマートフォンやPCなど)で証明を生成できなければならない。しかし、多くのzk-SNARKsは検証の軽量性と引き換えに、証明生成に膨大な計算リソースを要求する。この「証明生成の重さ」はユーザー体験を著しく損ない、技術の普及を妨げる大きな障壁となっている。 +第二の課題は、\textbf{クライアントサイドプルービングの要求}である。アプリケーションが広く普及するためには、エンドユーザーが自身のデバイス(スマートフォンやPCなど)で証明を生成できなければならない。 +しかし、多くのzk-SNARKsは検証の軽量性と引き換えに、証明生成に膨大な計算リソースを要求する。この「証明生成の重さ」はユーザー体験を著しく損ない、技術の普及を妨げる大きな障壁となっている。 したがって、理想的な証明システムは、これら二つの課題を同時に解決する必要がある。すなわち、クライアントにとっては\textbf{軽量な証明生成}を、ブロックチェーンにとっては\textbf{効率的なオンチェーン検証}を両立させなければならない。 VOLE-in-the-Head(VOLEitH)のような対称鍵暗号ベースの証明システムは、特に証明生成の軽量性に優れていることから、このクライアントサイドプルービングの課題に対する有望な解決策として注目されている。 diff --git a/paper/out/main.pdf b/paper/out/main.pdf index 8368837ab66301fcafd721ae039d95a68401064f..85fcaa8fe8bc7024be42995e71329b794da78f8f 100644 GIT binary patch delta 27131 zcmY&;V{oQjux*lwZQItwoY=OV2_~HQP4dJO+qTV#C$??dc5=Uaew|abyK2||)wQ~7 z)$Y~ns}i%P2D8=;65!+!5`zEj;%s4J2k)_3q|+LG{}*lY1M>r-;J^ng5DC!(iRU|O 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zT7Po>^6at~_RZxVEo4rg75^cIU#m9__*O-y37;ni;T;c#mRZPcEpzD1x&So^5PG{v~6JO zd;jX_;_XGqEZddJi=UNqv3xt{ie=8_UT$sj^ewv*z0SuR8V#wTSaS>>{09@ItA3N= z%oAKWGaxV^Z(?c+JUlN{d2nSfSW;zXFG)mOJT^HtV_`WsG-fh5Vqr2cGch?ZGG$_6 zH(@p~IXE~sVLm)IIW}WqIXEV~}r8~QuV-M`3B)w-AMq&g;V-&_>491}a2VuOD5(m9Y0=t-REC~~FFeWQ0FV>Yqa6M+=Av}zk zI25xm8)xAh%)wze59i}toQC;09CI-bm*Fm4j3aO)Zosp+0x#lpOu-qr1()M0T!X2& z7T4icEW&L#3X5?&?!Xe!~A1U!OA@fcR&37m)*um;cJd921sI1^`MDVE_LoQ&nT4=Zs$9>9Z`j#F?d zUcy&+4KL#ryo&XB9dF=Gti?LKg?I5b-oXZZhK+a+A7T^U#|QWXAK_zsiZAgwzJK69 za%0?zukjb<%>z@bFPuJ)ak@aNo%K(wB_r>TS8#P?U{?%K(v@k{bk*zJ>~ew1F1pE@+r=oIhhjKJVl>9$ zAdJUEOjh>Z86y7yg1WaH3T19&b98cLVQmU!Ze(v_Y6^37VRCeMa%E-;Gcz(cH#Q0- IB}Gq03iA Date: Tue, 2 Dec 2025 00:21:45 +0900 Subject: [PATCH 08/21] Enhance introduction, our approach, and preliminaries sections in VOLEitH research paper - Updated the introduction to include specific implementation details and challenges related to VOLEitH, emphasizing the need for lightweight proof generation and efficient on-chain verification. - Expanded the our approach section with a detailed four-step process for integrating VOLEitH with SNARK, highlighting the benefits of this hybrid architecture. - Revised the preliminaries section to clarify the implementation of VOLEitH using the Schmivitz library, ensuring better context for the discussed protocols. - Improved overall coherence and structure to enhance the readability and academic rigor of the document. --- paper/intro.tex | 6 +++++- paper/our_approach.tex | 36 ++++++++++++++++++++++++++++++++---- paper/out/main.pdf | Bin 344589 -> 348943 bytes paper/preliminaries.tex | 2 +- paper/references.tex | 8 ++++++++ 5 files changed, 46 insertions(+), 6 deletions(-) diff --git a/paper/intro.tex b/paper/intro.tex index 240df0a..9506d73 100644 --- a/paper/intro.tex +++ b/paper/intro.tex @@ -24,10 +24,14 @@ \subsection{Ethereumにおけるプライバシーとゼロ知識証明の役割 第一の課題は、\textbf{オンチェーン検証のコストと制約}である。 スマートコントラクト上での計算実行には、\textbf{ガス代}\footnote{Ethereumネットワーク上でトランザクションを実行するために必要な手数料。計算が複雑であるほど高額になる。}と呼ばれる手数料が発生する。 検証アルゴリズムが複雑であったり、証明のデータサイズが大きかったりすると、ガス代は著しく高騰し、アプリケーションの実用性が失われてしまう。 +todo:実測値を入れる +todo:precompiled contractを使うことができるが、全てのZKPで使えるわけではないことを明記する +todo:starkではsnark(groth16)で圧縮した証明を使うアプローチが一般的であることを述べる 第二の課題は、\textbf{クライアントサイドでの証明生成の負荷}である。 アプリケーションが広く普及するためには、ユーザーが特別な高性能ハードウェアを必要とせず、自身のデバイス(PCやスマートフォン)で証明を生成できることが望ましい。 しかし、多くの既存のZKP技術(特にzk-SNARKs)は、検証の軽量性と引き換えに、証明生成に膨大な計算リソースと時間を要求する。この「証明生成の重さ」は、ユーザー体験を損なう大きな障壁となる。 +todo: 実際、デリゲートプルービングというアプローチが一般的であることを述べる したがって、理想的な証明システムは、これら二つの課題を同時に解決する必要がある。すなわち、クライアントにとっては\textbf{軽量な証明生成}を、ブロックチェーンにとっては\textbf{効率的なオンチェーン検証}を両立させなければならない。 VOLE-in-the-Head(VOLEitH)のような対称鍵暗号ベースの証明システムは、特に証明生成の軽量性に優れていることから、このクライアントサイドプルービングの課題に対する有望な解決策として注目されている。 @@ -51,4 +55,4 @@ \subsection{研究の目的と貢献} \item 証明者と検証者の計算負荷(CPU、メモリ) \item 最終的なオンチェーン検証にかかるガス代 \end{itemize} -本研究は、VOLEitHのオンチェーン応用における実現可能性と技術的なトレードオフを明らかにすることで、将来的なZKPシステムの設計と最適化、そしてブロックチェーンアプリケーションにおけるプライバシーとスケーラビリティの向上に貢献することを目指す。 +本研究は、VOLEitHのオンチェーン応用における実現可能性と技術的なトレードオフを明らかにすることで、将来的なZKPシステムの設計と最適化、そしてブロックチェーンアプリケーションにおけるプライバシーの向上に貢献することを目指す。 diff --git a/paper/our_approach.tex b/paper/our_approach.tex index 8e30497..548ff43 100644 --- a/paper/our_approach.tex +++ b/paper/our_approach.tex @@ -1,6 +1,37 @@ \section{ベンチマーク設計} 本章では、VOLEitHとSNARKを組み合わせたアーキテクチャの性能を定量的に評価するために設計したベンチマークの詳細について述べる。 +\subsection{提案アーキテクチャ:VOLEitH証明のSNARKによる圧縮} +\label{subsec:our_approach} +本研究で評価するアーキテクチャは、VOLE-in-the-Head(VOLEitH)が生成する巨大な証明サイズの問題を解決し、オンチェーン検証に適した形式に圧縮することを目的としている。 +このため、証明者効率に優れたVOLEitHと、証明の簡潔性および検証効率に優れたzk-SNARK(本研究ではGroth16\cite{groth16}を採用)を組み合わせたハイブリッドアプローチを採用する。 +このアーキテクチャの究極的な目的は、VOLEitHの利点である「クライアントサイドでの高速な証明生成」と、SNARKの利点である「低コストなオンチェーン検証」を両立させることにある。 + +証明者が最終的なオンチェーン検証用の証明を生成するまでのプロセスは、以下の4つのステップで構成される。 + +\begin{enumerate} + \item \textbf{ステップ1:VOLEitH証明の生成} + まず、証明者は与えられた計算(算術回路)に対し、VOLEitHプロトコルを用いて証明\(\pi_{\text{VOLEitH}}\)を生成する。 + このプロセスは、対称鍵暗号ベースの軽い計算で構成されるため非常に高速だが、生成される証明\(\pi_{\text{VOLEitH}}\)のサイズは数MBオーダーと非常に大きい。 + + \item \textbf{ステップ2:VOLEitH検証回路のR1CS化} + 次に、ステップ1で生成された\(\pi_{\text{VOLEitH}}\)の正当性を検証するアルゴリズム自体を、一つの計算と見なす。 + この検証ロジックを、SNARKが扱うことができる形式であるR1CS(Rank-1 Constraint System)の算術回路として表現する。 + この「検証回路」は、\(\pi_{\text{VOLEitH}}\)を入力として受け取り、それが有効であれば真を、無効であれば偽を出力する。 + + \item \textbf{ステップ3:SNARK証明の生成} + 証明者は、ステップ2で構築した「VOLEitH検証回路」に対して、Groth16プロトコルを用いて証明\(\pi_{\text{SNARK}}\)を生成する。 + この\(\pi_{\text{SNARK}}\)は、「ある有効な\(\pi_{\text{VOLEitH}}\)を知っており、それに対する検証計算が正しく実行された」という事実を証明するものである。 + Groth16の特性により、\(\pi_{\text{SNARK}}\)は回路の複雑さに関わらず一定の小さなサイズ(約1KB)となる。 + + \item \textbf{ステップ4:オンチェーン検証} + 最終的に、コンパクトなSNARK証明\(\pi_{\text{SNARK}}\)と、計算の公開入力のみがEthereum上の検証者スマートコントラクトに送信される。 + スマートコントラクトは、事前にデプロイされた検証鍵を用いて\(\pi_{\text{SNARK}}\)を検証する。この検証は、数回のペアリング演算で完了するため、極めて少ないガス代で実行可能である。 +\end{enumerate} + +この一連のプロセスにより、クライアント側では証明生成の大部分を軽量なVOLEitHプロトコルが担い、ブロックチェーン側では検証コストの高い計算がコンパクトなSNARK証明の検証に置き換えられる。 +本研究では、このアーキテクチャをRust言語で実装した。VOLEitHの実装には\texttt{schmivitz}ライブラリを、SNARK回路の構築と証明生成には\texttt{arkworks}エコシステムを利用し、オンチェーン検証用のSolidityコントラクトは\texttt{ark-groth16}の機能を用いて生成した。 + \subsection{測定項目} 本研究では、証明システムの性能と実用性を多角的に評価するため、以下のメトリクスを測定対象とした。 \begin{table}[hbtp] @@ -38,10 +69,7 @@ \subsection{評価環境} \item \textbf{ソフトウェア}: \begin{itemize} \item 言語: Rust - \item ベンチマークツール: \texttt{cargo bench} - \item VOLEitH実装: \texttt{soft\_spoken} ライブラリ - \item スマートコントラクト開発・テスト: Foundryフレームワーク - \item Solidityバージョン: 0.8.20 + \item VOLEitH実装: \texttt{schmivitz} ライブラリ \end{itemize} \end{itemize} diff --git a/paper/out/main.pdf b/paper/out/main.pdf index 70830148e42079c3a84b88a08a99041c5ab9f0df..5053ce5d46d2a44d2484d225e997fa3631444c81 100644 GIT binary patch delta 345827 zcmY(KLzFHGtfkAgZQHhO+qV6eZQHi(Q?_l}r+ljVb`N^JH_OT(gRBhp{*uInq9>H2 zCvpNaCvi~%l+aEmf_?>^-BXUNEG-@3u|P#gt2Ps^u8PwE7%fNv7E!$;iR-BupPU5W 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z`h4ieB)x@o^OL?{Z;dyfpqX9@agLw(CUyO)SAIcL>PT*NCYadV>iT9hK~^<>s?e)d za+Ke_0NqtR{t>)mgg<8P+2qc+E9BJ;IHqs82%}Lo~q8}NcbSt8CIiU0i z;Q1@zg-_uH`mlVL63Tmv@KD*a?9Ia&(~eZHId3?V?R06xz}*!68Wir1M{S5N-({H^ zG~-A$-o42E5q<+k#}DGb#MI}X8Wo%x+~odQeS@SmD1n8DYs-l+s?33-qN^@77NBiJ zV^-2C!DXww zkZE4>NdKr;LaGNuZn=_=^^APi-YuDK!+WWAMLH`f&~((RFtpE3{-|7>AVDnM{>B== z$B^|v|EOm~A$aA2nY&{iT`|U0UJ{>7SWr@=v`>onli_gpZYBOreSdQSzMu-+pO3T6 i0+o=soeLcYZ0_{UrtB%h5+k#5ax)`QQi>^vBmEC>3>umM diff --git a/paper/preliminaries.tex b/paper/preliminaries.tex index d843566..34fbbfa 100644 --- a/paper/preliminaries.tex +++ b/paper/preliminaries.tex @@ -24,7 +24,7 @@ \subsection{VOLE-based ZK} このため、証明を検証できるのが特定の検証者に限定される\textbf{指定検証者証明(Designated Verifier Proof)}となり、第三者が検証できる\textbf{公開検証可能性(Public Verifiability)}を持たないという課題があった。 \subsection{VOLE-in-the-Head} -VOLE-in-the-Head(VOLEitH)は、上記のような指定検証者型のVOLE-ZKプロトコルを、非対話かつ公開検証可能なゼロ知識証明(NIZK)に変換するためのコンパイラである。 +VOLE-in-the-Head(VOLEitH)は、上記のような指定検証者型のVOLE-ZKプロトコルを、非対話かつ公開検証可能なゼロ知識証明(NIZK)に変換するためのコンパイラである。本研究では、このVOLEitHの具体的な実装として、Rustで記述されたライブラリであるSchmivitz\cite{schmivitz}を利用している。 VOLEitHは、MPC-in-the-HeadパラダイムとVOLEを組み合わせたもので、証明の健全性を単一の証明者の計算能力に帰着させる。 VOLEitHの核となるアイデアは、検証者が秘密情報($\Delta$)を持つ代わりに、証明者自身がコミットし、後からFiat-Shamir変換\cite{fiatshamir}によって$\Delta$を導出する点にある。 diff --git a/paper/references.tex b/paper/references.tex index 6c2b49c..7c8a220 100644 --- a/paper/references.tex +++ b/paper/references.tex @@ -64,4 +64,12 @@ \section*{参考文献 (References)} Ethereum: A Secure Decentralised Generalized Transaction Ledger. \textit{Ethereum Project Yellow Paper}, 2024. \url{https://ethereum.github.io/yellowpaper/paper.pdf}. + +\bibitem{schmivitz} +adust09. +Swanky: A suite of tools for developing zero-knowledge circuits and applications. +GitHub Repository. +\url{https://github.com/adust09/swanky}. +Accessed: 2025-12-01. + \end{thebibliography} From 17d47aa9f2bb80b6a9c771ce98b76b7da303be24 Mon Sep 17 00:00:00 2001 From: adust09 Date: Tue, 2 Dec 2025 00:40:30 +0900 Subject: [PATCH 09/21] Add GEMINI project overview and enhance preliminaries in VOLEitH research paper - Introduced a new GEMINI.md file detailing the project's structure, goals, and usage instructions for the Rust-based VOLEitH benchmarking tool. - Expanded the preliminaries section in the research paper to include additional explanations and clarifications on VOLE, VOLE-based ZK, and VOLE-in-the-Head concepts. - Added specific todos for further enhancements in the preliminaries, focusing on the foundational aspects of VOLE and its implications for zero-knowledge proofs. - Updated the main PDF output to reflect these changes, ensuring comprehensive documentation for both the project and the research paper. --- GEMINI.md | 71 ++++++++++++++++++++++++++++++++++++++++ paper/out/main.pdf | Bin 348943 -> 350141 bytes paper/preliminaries.tex | 4 +++ 3 files changed, 75 insertions(+) create mode 100644 GEMINI.md diff --git a/GEMINI.md b/GEMINI.md new file mode 100644 index 0000000..42704cd --- /dev/null +++ b/GEMINI.md @@ -0,0 +1,71 @@ +# Project Overview + +This is a Rust project for benchmarking the "VOLE in the Head" (VOLEitH) zero-knowledge proof system. The primary goal is to evaluate the feasibility and performance of on-chain verification for VOLEitH proofs. The project is structured as a Rust library and a command-line interface (CLI) application. It uses various cryptographic libraries, including `ark-groth16`, `ark-bn254`, and a custom `schmivitz` library, to implement and benchmark the proof system. + +The project also includes a benchmarking suite using `criterion` to measure performance metrics such as proof generation time, verification time, proof size, and computational load (CPU and memory usage). + +# Building and Running + +## Building the Project + +To build the project, use the standard Cargo command: + +```bash +cargo build --release +``` + +## Running the CLI + +The project includes a CLI for generating proofs. The following command can be used to generate a proof using the `keccak_f` algorithm: + +```bash +cargo run --release -- prove --algorithm keccak_f +``` + +## Running the Benchmarks + +To run the performance benchmarks, use the following command: + +```bash +cargo bench +``` + +The benchmark results, including detailed reports, will be available in the `target/criterion` directory. + +# Development Conventions + +## Code Style + +The project follows standard Rust conventions. Code is formatted using `rustfmt`. + +## Testing + +The project uses a combination of unit tests and integration tests. The core logic is tested through the benchmarking suite in the `benches` directory. + +## Dependencies + +The project's dependencies are managed using `Cargo.toml`. Key dependencies include: + +- `schmivitz` and `schmivitz-snark`: Core libraries for VOLEitH proofs. +- `arkworks` libraries (`ark-groth16`, `ark-bn254`, etc.): For zero-knowledge proof implementations. +- `criterion`: For performance benchmarking. +- `clap`: For the command-line interface. + +# Paper Writing Guidelines + +This section outlines the guidelines for writing the research paper located in the `paper/` directory. + +## Target Publication + +The paper is to be submitted to the **SCIS (Symposium on Cryptography and Information Security)**, a Japanese security conference. + +## Target Audience + +The intended audience is individuals who are **not deeply familiar with Ethereum or zero-knowledge proofs**. + +## Writing Style and Structure + +- The paper must be structured as a formal academic paper. +- The language and structure should be tailored to clearly convey the significance of this research to the target audience. +- Use logical explanations, mathematical formulas, and diagrams to explain complex concepts. +- The paper should be written in Japanese. diff --git a/paper/out/main.pdf b/paper/out/main.pdf index 5053ce5d46d2a44d2484d225e997fa3631444c81..7caa06b8fe18967bd698e8a1d39b39d0faa1feee 100644 GIT binary patch delta 257808 zcmV)KK)Sz=rWL)f6|l|{e>XWeK0XR_baG{3Z3=kW&05Kh>_`>e^A)+QCzS4(2fF$# zkZ2@!NN-0YwMT>yi(bI@bMB47VP`liOEeNHrR>ZKN8I7u*|%SA@+R;nZ(iNJi$jRF z`JedVkNEuU_WN(Q?|#%bDTipSx_#Sj#tuP++uhm0TYdYs{N-H;e`)ZM__(ikT*SL@ zUI-hVP+<|vwu(uQxc9op%#t%C?xivfA7vsA}k@TaS{6n-rs_w(U?p}`xx9Cy0`gCe;*;js#!Hvls+UCdBxzM zJ&YZb_*xa>{L5!p9cf(=hjc^K{wR~9ns!;}(cnzQe0zX`WJP=j2+`Y(*N#ewNzPbr zSVfVoX}2e*&E6r~4cf*wB=|FHp7?K5k;(00g%QIYE)iL24SGknp=fsT=5kEy^iA zJu`gTM+}*;?@3 z65(F%43gmkQM8|0CO${4$+8}e{ETeJv2^cV+jF|{E|!{D^D`=p<31-zSS^f25sCS3@LAi8Zo3T;V0s}Nm((DO870w!m3fM z%UZB;e-(nTacul(n3v>>GLqZ~KcZqn%{uL<0kD#UWDayzc#<->qEKZ*>$?EsQLr@T ziNcU)&1#sM7c0P-!dl^i_OS3j&L*ixAcpol`=CZrj{#e2HNb&YQRRqjipbbR$XUa| zvuVI7!hwHx}6 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