$\newcommand{\coinheads}{\mathsf{HEADS}}$ $\newcommand{\cointails}{\mathsf{TAILS}}$ $\newcommand{\varalice}{\class{var var_Alice}{\text{Alice}}}$ $\newcommand{\varbob}{\class{var var_Bob}{\text{Bob}}}$ $\newcommand{\alicebob}[3]{#1 & \ra{#2} & #3\\[-5pt]}$ $\newcommand{\bobalice}[3]{#1 & \la{#2} & #3\\[-5pt]}$ $\newcommand{\alicework}[1]{#1 & &\\[-5pt]}$ $\newcommand{\bobwork}[1]{ & & #1\\[-5pt]}$ $\newcommand{\work}[2]{#1 & & #2\\}$ $\newcommand{\allwork}[1]{ & #1 & \\}$ $\newcommand{\dupwork}[1]{#1 & & #1\\}$ $\newcommand{\aliceseparator}{-------&&\\}$ $\newcommand{\bobseparator}{&&-------\\}$ $\newcommand{\foo}{\phantom{\text{bigarrowfitsallthis}}}$ $\newcommand{\ra}[1]{% \vphantom{\xrightarrow{asd}}% \smash{\xrightarrow[\foo]{#1}}% }$ $\newcommand{\la}[1]{% \vphantom{\xleftarrow{asd}}% \smash{\xleftarrow[\foo]{#1}}% }$ $\newcommand{\z}[1]{\mathbb{Z}_{#1}}$ $\newcommand{\zq}{\mathbb{Z}_\varq}$ $\newcommand{\zqs}{\mathbb{Z}_q^\ast}$ $\newcommand{\zps}{\mathbb{Z}_p^\ast}$ $\newcommand{\zns}[1]{\mathbb{Z}_{#1}^\ast}$ $\require{action} \newcommand{\sampleSymb}{ {\overset{\$}{\leftarrow}} }$ $\newcommand{\field}[1]{\mathbb{F}_{#1}}$ $\newcommand{\sample}[1]{#1\sampleSymb\zq}$ $\newcommand{\sampleGeneric}[2]{#1\sampleSymb#2}$ $\newcommand{\sampleInterval}[2]{#1\sampleSymb\interval{#2}}$ $\newcommand{\sampleRange}[2]{#1\sampleSymb\range{#2}}$ $\newcommand{\sampleCgroup}[1]{#1\sampleSymb\cgroup}$ $\newcommand{\samplezqs}[1]{\class{hover}{#1\sampleSymb\zqs}}$ $\newcommand{\sampleN}[2]{\class{hover}{#1\sampleSymb\z{#2}}}$ $\newcommand{\sampleNs}[2]{\class{hover}{#1\sampleSymb\z{#2}^\ast}}$ $\newcommand{\equalQ}{\overset{?}{=}}$ $\newcommand{\gQ}{\overset{?}{>}}$ $\newcommand{\inQ}{\overset{?}{\in}}$ $\newcommand{\cgroup}{\mathbb{G}}$ $\newcommand{\Hash}{\mathsf{Hash}}$ $\newcommand{\hash}[1]{\Hash({#1})}$ $\newcommand{\HashToField}{\mathsf{HashToField}}$ $\newcommand{\hashtofield}[1]{\HashToField({#1})}$ $\newcommand{\HashToGroup}{\mathsf{HashToGroup}}$ $\newcommand{\hashtogroup}[1]{\HashToGroup({#1})}$ $\newcommand{\hashbit}[2]{\mathsf{Hash}({#1})\verb+[0:#2]+}$ $\newcommand{\hmac}[2]{\mathsf{HMAC}_{#1}\left(#2\right)}$ $\newcommand{\naturals}{\mathbb{N}}$ $\newcommand{\sqfree}{L_\mathsf{square-free}}$ $\newcommand{\ceil}[1]{\lceil #1 \rceil}$ $\newcommand{\sampleSet}[2]{\class{hover}{#1\sampleSymb#2}}$ $\newcommand{\bunch}[1]{\{ #1_i\}_{i=1}^m}$ $\newcommand{\bunchi}[1]{\{ #1\}_{i=1}^m}$ $\newcommand{\forb}{\text{ for }i=1,\ldots,m}$ $\newcommand{\interval}[1]{[0, #1[}$ $\newcommand{\range}[1]{[#1]}$ $\newcommand{\rangeone}[1]{\{1, \dots,#1 -1 \}}$ $\newcommand{\vara}{\class{var var_a}{a}}$ $\newcommand{\varb}{\class{var var_b}{b}}$ $\newcommand{\varc}{\class{var var_c}{c}}$ $\newcommand{\vard}{\class{var var_d}{d}}$ $\newcommand{\varh}{\class{var var_h}{h}}$ $\newcommand{\varH}{\class{var var_H}{H}}$ $\newcommand{\varg}{\class{var var_g}{g}}$ $\newcommand{\varG}{\class{var var_G}{G}}$ $\newcommand{\vari}{\class{var var_i}{i}}$ $\newcommand{\varj}{\class{var var_j}{j}}$ $\newcommand{\vars}{\class{var var_s}{s}}$ $\newcommand{\vart}{\class{var var_t}{t}}$ $\newcommand{\varu}{\class{var var_u}{u}}$ $\newcommand{\varU}{\class{var var_U}{U}}$ $\newcommand{\varl}{\class{var var_l}{l}}$ $\newcommand{\varm}{\class{var var_m}{m}}$ $\newcommand{\varn}{\class{var var_n}{n}}$ $\newcommand{\varx}{\class{var var_x}{x}}$ $\newcommand{\varX}{\class{var var_X}{X}}$ $\newcommand{\varz}{\class{var var_z}{z}}$ $\newcommand{\varr}{\class{var var_r}{r}}$ $\newcommand{\varq}{\class{var var_q}{q}}$ $\newcommand{\varp}{\class{var var_p}{p}}$ $\newcommand{\vare}{\class{var var_e}{e}}$ $\newcommand{\vary}{\class{var var_y}{y}}$ $\newcommand{\varv}{\class{var var_v}{v}}$ $\newcommand{\varw}{\class{var var_w}{w}}$ $\newcommand{\varC}{\class{var var_C}{C}}$ $\newcommand{\varf}{\class{var var_f}{f}}$ $\newcommand{\varA}{\class{var var_A}{A}}$ $\newcommand{\varB}{\class{var var_B}{B}}$ $\newcommand{\varC}{\class{var var_C}{C}}$ $\newcommand{\varL}{\class{var var_L}{L}}$ $\newcommand{\varP}{\class{var var_P}{P}}$ $\newcommand{\varR}{\class{var var_R}{R}}$ $\newcommand{\varT}{\class{var var_T}{T}}$ $\newcommand{\varX}{\class{var var_X}{X}}$ $\newcommand{\varalpha}{\class{var var_alpha}{\alpha}}$ $\newcommand{\varprover}{\class{var var_Prover}{\text{Prover}}}$ $\newcommand{\varprover}{\class{var var_Prover}{\text{Prover}}}$ $\newcommand{\varverifier}{\class{var var_Verifier}{\text{Verifier}}}$ $\newcommand{\varN}{\class{var var_N}{N}}$ $\newcommand{\rhovar}{\class{var var_ρ}{\rho}}$ $\newcommand{\sigmavar}{\class{var var_σ}{\sigma}}$ $\newcommand{\thetavar}{\class{var var_θ}{\theta}}$ $\newcommand{\muvar}{\class{var var_μ}{\mu}}$ $\renewcommand{\vec}[1]{\mathbf{#1}}$ $\newcommand{\veca}{\vec{\class{var var_vec_a}{a}}}$ $\newcommand{\vecb}{\vec{\class{var var_vec_b}{b}}}$ $\newcommand{\vecc}{\vec{\class{var var_vec_c}{c}}}$ $\newcommand{\vecs}{\vec{\class{var var_vec_s}{s}}}$ $\newcommand{\vecG}{\vec{\class{var var_vec_G}{G}}}$ $\newcommand{\vecH}{\vec{\class{var var_vec_H}{H}}}$ $\newcommand{\vecg}{\vec{\class{var var_vec_g}{g}}}$ $\newcommand{\vech}{\vec{\class{var var_vec_h}{h}}}$ $\newcommand{\true}{\mathsf{true}}$ $\newcommand{\false}{\mathsf{false}}$ $\newcommand{\ctx}{\mathsf{ctx}}$ $\newcommand{\coloneqq}{≔}$ $\newcommand{\ip}[2]{\left\langle #1, #2 \right\rangle}$ $\newcommand{\uwork}[2]{\underline{#1} & & \underline{#2}\\}$ $\newcommand{\aliceworks}[1]{#1 & &\\[-2pt]}$ $\newcommand{\bobworks}[1]{ & & #1\\[-2pt]}$ $\newcommand{\Halving}{\text{Halving}}$ $\newcommand{\HalveProof}{\text{HalveProof}}$ $\newcommand{\HalveVerify}{\text{HalveVerify}}$ $\newcommand{\indent}{\qquad}$ $\newcommand{\append}{\mathrm{append}}$ $\newcommand{\schnorrvalidate}{\mathsf{schnorr}\_\mathsf{validate}}$
Introduction

ZKDocs #

Zero-knowledge protocols #

ZKDocs provides comprehensive, detailed, and interactive documentation on zero-knowledge proof systems and related primitives.

At Trail of Bits, we audit many implementations of non-standardized cryptographic protocols and often find the same issues. As we discovered more instances of these bugs, we wanted to find a way to prevent them in the future. Unfortunately, for these protocols, the burden is on the developers to figure out all of the low-level implementation details and security pitfalls.

We hope that ZKDocs can fill in this gap and benefit the larger cryptography community.

Comprehensive #

We aim to be both self-contained and comprehensive in the topics related to zero-knowledge proof systems, from descriptions of simple systems like Schnorr’s identification protocol, to complex proof systems like Paillier-Blum modulus. We also cover cryptographic primitives such as: random sampling, Fiat-Shamir transformation, and Shamir’s Secret Sharing.

Detailed #

We describe each protocol in great detail, including all necessary setup, sanity-checks, auxiliary algorithms, further references, and potential security pitfalls with their associated severity.

Interactive #

The protocol descriptions are interactive, letting you modify variable names. This allows you to match the variable names in ZKdocs’ specification to the variable names in your code, making it easier to find bugs and missing assertions.

Interactivity features:

  • Click on $\varX$ to highlight the variable across the document. Try it!
  • Type or paste with $\varX$ highlighted to edit $\varX$’s name. Press Enter or Escape to stop editing.
  • Press the button to reset the names of all variables on the current page (variable names are independent across different pages)
Basic interactivity usage

Contribute #

We will continue to add more proof systems like Range proofs, STARK, and Bulletproofs.

Feel free to open issues and suggest new protocols that you would like to see added in ZKDocs.