deploy: d3feb4d

background.html

@@ -176,7 +176,7 @@ <h1 class="menu-title">Polygon Miden VM</h1>
 
                 <div id="content" class="content">
                     <main>
-                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous">
+                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.4/dist/katex.min.css">
 <h1 id="background-material"><a class="header" href="#background-material">Background Material</a></h1>
 <p>Proofs of execution generated by Miden VM are based on STARKs. A STARK is a novel proof-of-computation scheme that allows you to create an efficiently verifiable proof that a computation was executed correctly. The scheme was developed by Eli Ben-Sasson, Michael Riabzev et al. at Technion - Israel Institute of Technology. STARKs do not require an initial trusted setup, and rely on very few cryptographic assumptions.</p>
 <p>Here are some resources to learn more about STARKs:</p>

design/chiplets/bitwise.html

@@ -176,7 +176,7 @@ <h1 class="menu-title">Polygon Miden VM</h1>
 
                 <div id="content" class="content">
                     <main>
-                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous">
+                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.4/dist/katex.min.css">
 <h1 id="bitwise-chiplet"><a class="header" href="#bitwise-chiplet">Bitwise chiplet</a></h1>
 <p>In this note we describe how to compute bitwise AND and XOR operations on 32-bit values and the constraints required for proving correct execution.</p>
 <p>Assume that <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">a</span></span></span></span> and <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">b</span></span></span></span> are field elements in a 64-bit prime field. Assume also that <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">a</span></span></span></span> and <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">b</span></span></span></span> are known to contain values smaller than <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">32</span></span></span></span></span></span></span></span></span></span></span></span>. We want to compute <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span></span></span></span>, where <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">⊕</span></span></span></span> is either bitwise AND or XOR, and <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span></span></span></span> is a field element containing the result of the corresponding bitwise operation.</p>

design/chiplets/hasher.html

@@ -176,7 +176,7 @@ <h1 class="menu-title">Polygon Miden VM</h1>
 
                 <div id="content" class="content">
                     <main>
-                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous">
+                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.4/dist/katex.min.css">
 <h1 id="hash-chiplet"><a class="header" href="#hash-chiplet">Hash chiplet</a></h1>
 <p>Miden VM "offloads" all hash-related computations to a separate <em>hash processor</em>. This chiplet supports executing the <a href="https://eprint.iacr.org/2022/1577">Rescue Prime Optimized</a> hash function (or rather a <a href="https://docs.rs/miden-crypto/latest/miden_crypto/hash/rpo/struct.Rpo256.html">specific instantiation</a> of it) in the following settings:</p>
 <ul>

design/chiplets/kernel_rom.html

@@ -176,7 +176,7 @@ <h1 class="menu-title">Polygon Miden VM</h1>
 
                 <div id="content" class="content">
                     <main>
-                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous">
+                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.4/dist/katex.min.css">
 <h1 id="kernel-rom-chiplet"><a class="header" href="#kernel-rom-chiplet">Kernel ROM chiplet</a></h1>
 <p>The kernel ROM enables executing predefined kernel procedures. These procedures are always executed in the root context and can only be accessed by a <code>SYSCALL</code> operation. The chiplet tracks and enforces correctness of all kernel procedure calls as well as maintaining a list of all the procedures defined for the kernel, whether they are executed or not. More background about Miden VM execution contexts can be found <a href="../../user_docs/assembly/execution_contexts.html">here</a>.</p>
 <h2 id="kernel-rom-trace"><a class="header" href="#kernel-rom-trace">Kernel ROM trace</a></h2>

design/chiplets/main.html

@@ -176,7 +176,7 @@ <h1 class="menu-title">Polygon Miden VM</h1>
 
                 <div id="content" class="content">
                     <main>
-                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous">
+                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.4/dist/katex.min.css">
 <h1 id="chiplets"><a class="header" href="#chiplets">Chiplets</a></h1>
 <p>The Chiplets module contains specialized components dedicated to accelerating complex computations. Each chiplet specializes in executing a specific type of computation and is responsible for proving both the correctness of its computations and its own internal consistency.</p>
 <p>Currently, Miden VM relies on 4 chiplets:</p>

design/chiplets/memory.html

@@ -176,7 +176,7 @@ <h1 class="menu-title">Polygon Miden VM</h1>
 
                 <div id="content" class="content">
                     <main>
-                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous">
+                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.4/dist/katex.min.css">
 <h1 id="memory-chiplet"><a class="header" href="#memory-chiplet">Memory chiplet</a></h1>
 <p>Miden VM supports linear read-write random access memory. This memory is word-addressable, meaning, four values are located at each address, and we can read and write values to/from memory in batches of four. Each value is a field element in a <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">64</span></span></span></span>-bit prime field with modulus <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8974em;vertical-align:-0.0833em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">64</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8974em;vertical-align:-0.0833em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">32</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span>. Memory address can be any field element.</p>
 <p>In this note we describe the rationale for selecting the above design and describe AIR constraints needed to support it.</p>

design/decoder/constraints.html

@@ -176,7 +176,7 @@ <h1 class="menu-title">Polygon Miden VM</h1>
 
                 <div id="content" class="content">
                     <main>
-                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous">
+                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.4/dist/katex.min.css">
 <h1 id="miden-vm-decoder-air-constraints"><a class="header" href="#miden-vm-decoder-air-constraints">Miden VM decoder AIR constraints</a></h1>
 <p>In this section we describe AIR constraint for Miden VM program decoder. These constraints enforce that the execution trace generated by the prover when executing a particular program complies with the rules described in the <a href="./main.html">previous section</a>.</p>
 <p>To refer to decoder execution trace columns, we use the names shown on the diagram below (these are the same names as in the previous section). Additionally, we denote the register containing the value at the top of the stack as <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>.</p>

design/decoder/main.html

@@ -176,7 +176,7 @@ <h1 class="menu-title">Polygon Miden VM</h1>
 
                 <div id="content" class="content">
                     <main>
-                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous">
+                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.4/dist/katex.min.css">
 <h1 id="miden-vm-program-decoder"><a class="header" href="#miden-vm-program-decoder">Miden VM Program decoder</a></h1>
 <p>Miden VM program decoder is responsible for ensuring that a program with a given <a href="../programs.html">MAST root</a> is executed by the VM. As the VM executes a program, the decoder does the following:</p>
 <ol>

design/lookups/logup.html

@@ -176,7 +176,7 @@ <h1 class="menu-title">Polygon Miden VM</h1>
 
                 <div id="content" class="content">
                     <main>
-                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous">
+                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.4/dist/katex.min.css">
 <h1 id="logup-multivariate-lookups-with-logarithmic-derivatives"><a class="header" href="#logup-multivariate-lookups-with-logarithmic-derivatives">LogUp: multivariate lookups with logarithmic derivatives</a></h1>
 <p>The description of LogUp can be found <a href="https://eprint.iacr.org/2022/1530.pdf">here</a>. In MidenVM, LogUp is used to implement efficient <a href="./main.html#communication-buses-in-miden-vm">communication buses</a>.</p>
 <p>Using the LogUp construction instead of a simple <a href="./multiset.html">multiset check</a> with running products reduces the computational effort for the prover and the verifier. Given two columns <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">a</span></span></span></span> and <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">b</span></span></span></span> in the main trace where <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">a</span></span></span></span> contains duplicates and <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">b</span></span></span></span> does not (i.e. <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">b</span></span></span></span> is part of the lookup table), LogUp allows us to compute two logarithmic derivatives and check their equality.</p>

design/lookups/main.html

@@ -176,9 +176,9 @@ <h1 class="menu-title">Polygon Miden VM</h1>
 
                 <div id="content" class="content">
                     <main>
-                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous">
+                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.4/dist/katex.min.css">
 <h1 id="lookup-arguments-in-miden-vm"><a class="header" href="#lookup-arguments-in-miden-vm">Lookup arguments in Miden VM</a></h1>
-<p>Zero knowledge virtual machines frequently make use of lookup arguments to enable performance optimizations. Miden VM uses two types of arguments: multiset checks and a multivariate lookup based on logarithmic derivatives known as LogUp. A brief introduction to multiset checks can be found <a href="https://hackmd.io/@arielg/ByFgSDA7D">here</a>. The description of LogUp can be found <a href="https://eprint.iacr.org/2022/1530.pdf">here</a>.</p>
+<p>Zero knowledge virtual machines frequently make use of lookup arguments to enable performance optimizations. Miden VM uses two types of arguments: multiset checks and a multivariate lookup based on logarithmic derivatives known as LogUp. A brief introduction to multiset checks can be found <a href="./multiset.html">here</a>. The description of LogUp can be found <a href="https://eprint.iacr.org/2022/1530.pdf">here</a>.</p>
 <p>In Miden VM, lookup arguments are used for two purposes:</p>
 <ol>
 <li>To prove the consistency of intermediate values that must persist between different cycles of the trace without storing the full data in the execution trace (which would require adding more columns to the trace).</li>

design/lookups/multiset.html

@@ -176,7 +176,7 @@ <h1 class="menu-title">Polygon Miden VM</h1>
 
                 <div id="content" class="content">
                     <main>
-                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous">
+                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.4/dist/katex.min.css">
 <h1 id="multiset-checks"><a class="header" href="#multiset-checks">Multiset checks</a></h1>
 <p>A brief introduction to multiset checks can be found <a href="https://hackmd.io/@arielg/ByFgSDA7D">here</a>. In Miden VM, multiset checks are used to implement <a href="#virtual-tables">virtual tables</a> and efficient <a href="./main.html#communication-buses-in-miden-vm">communication buses</a>.</p>
 <h2 id="running-product-columns"><a class="header" href="#running-product-columns">Running product columns</a></h2>

design/main.html

@@ -176,7 +176,7 @@ <h1 class="menu-title">Polygon Miden VM</h1>
 
                 <div id="content" class="content">
                     <main>
-                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous">
+                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.4/dist/katex.min.css">
 <h1 id="design"><a class="header" href="#design">Design</a></h1>
 <p>In the following sections, we provide in-depth descriptions of Miden VM internals, including all AIR constraints for the proving system. We also provide rationale for making specific design choices.</p>
 <p>Throughout these sections we adopt the following notations and assumptions:</p>

design/programs.html

@@ -176,7 +176,7 @@ <h1 class="menu-title">Polygon Miden VM</h1>
 
                 <div id="content" class="content">
                     <main>
-                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous">
+                        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.4/dist/katex.min.css">
 <h1 id="programs-in-miden-vm"><a class="header" href="#programs-in-miden-vm">Programs in Miden VM</a></h1>
 <p>Miden VM consumes programs in a form of a Merkelized Abstract Syntax Tree (MAST). This tree is a binary tree where each node is a <em>code block</em>. The VM starts execution at the root of the tree, and attempts to recursively execute each required block according to its semantics. If the execution of a code block fails, the VM halts at that point and no further blocks are executed. A set of currently available blocks and their execution semantics are described below.</p>
 <h2 id="code-blocks"><a class="header" href="#code-blocks">Code blocks</a></h2>