{"id":6616,"date":"2024-12-27T07:10:00","date_gmt":"2024-12-27T06:10:00","guid":{"rendered":"https:\/\/wsj-crypto.com\/?p=6616"},"modified":"2024-12-27T07:10:00","modified_gmt":"2024-12-27T06:10:00","slug":"decoding-the-verkle-tree-a-game-changer-for-ethereums-future","status":"publish","type":"post","link":"https:\/\/wsj-crypto.com\/index.php\/2024\/12\/27\/decoding-the-verkle-tree-a-game-changer-for-ethereums-future\/","title":{"rendered":"Decoding the Verkle Tree: A Game-Changer for Ethereum&#8217;s Future"},"content":{"rendered":"<p><\/p>\n<div id=\"\">\n<p class=\"chakra-text css-gi02ar\">A Verkle tree is a commitment framework that operates similarly to a Merkle tree, yet has significantly smaller witnesses. It functions by substituting the hashes in a Merkle tree with a vector commitment, rendering broader branching factors more effective.<!-- --><\/p>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\"><em class=\"chakra-text css-0\">Gratitude to Kevaundray Wedderburn for the insights regarding the post.<!-- --><\/em><\/p>\n<p><!-- --><\/p>\n<h2 class=\"chakra-heading css-1w54o5f\" id=\"overview\">Overview<!-- --><\/h2>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">Refer to the following for information on how verkle trees function:<!-- --><\/p>\n<p><!-- --><br \/>\n<!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">The purpose of this post is to elucidate the specific configuration of the <!-- --><a target=\"_blank\" rel=\"noopener\" class=\"chakra-link css-ug8vf0\" href=\"https:\/\/notes.ethereum.org\/@vbuterin\/verkle_tree_eip\">draft verkle tree EIP<!-- --><\/a>. It targets client developers seeking to implement verkle trees and looking for a primer before exploring the EIP in greater detail.<!-- --><\/p>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">Verkle trees bring forth a variety of modifications to the tree architecture. The most notable alterations are:<!-- --><\/p>\n<p><!-- --><\/p>\n<ul role=\"list\" class=\"css-1onhfjo\">\n<li class=\"css-cvpopp\">a transition from 20-byte keys to 32-byte keys (not to be confused with 32-byte addresses, which constitutes a different modification);<!-- --><\/li>\n<li class=\"css-cvpopp\">the amalgamation of the account and storage tries; and ultimately<!-- --><\/li>\n<li class=\"css-cvpopp\">the arrival of the verkle trie itself, which employs vector commitments in lieu of hashes.<!-- --><\/li>\n<\/ul>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">For the vector commitment mechanism used in the verkle tree, we utilize <!-- --><em class=\"chakra-text css-0\">Pedersen commitments<!-- --><\/em>. Pedersen commitments rely on elliptic curves. For an introduction to Pedersen commitments and their application as polynomial or vector commitments utilizing Inner Product Arguments, refer to <!-- --><a target=\"_blank\" rel=\"noopener\" class=\"chakra-link css-ug8vf0\" href=\"https:\/\/dankradfeist.de\/ethereum\/2021\/07\/27\/inner-product-arguments.html\">here<!-- --><\/a>.<!-- --><\/p>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">The curve we are implementing is <!-- --><a target=\"_blank\" rel=\"noopener\" class=\"chakra-link css-ug8vf0\" href=\"https:\/\/ethresear.ch\/t\/introducing-bandersnatch-a-fast-elliptic-curve-built-over-the-bls12-381-scalar-field\/9957\">Bandersnatch<!-- --><\/a>. This curve was selected due to its performance, as well as for its capability to facilitate efficient SNARKs in BLS12_381 to reason about the verkle tree in the future. This could prove beneficial for rollups and also allow an enhancement where all witnesses can be condensed into a single SNARK once that becomes feasible, without the necessity of another commitment update.<!-- --><\/p>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">The curve order\/scalar field size of Bandersnatch is <!-- --><em class=\"chakra-text css-0\">p = 13108968793781547619861935127046491459309155893440570251786403306729687672801<!-- --><\/em>, which is a 253-bit prime number. Consequently, we can only safely commit to bit strings of up to 252 bits, else the field will overflow. We opted for a branching factor (width) of 256 for the verkle tree, meaning each commitment can commit to a maximum of 256 values of 252 bits each (or more accurately, integers up to <!-- --><em class=\"chakra-text css-0\">p &#8211; 1<!-- --><\/em>). We express this as <!-- --><em class=\"chakra-text css-0\">Commit(v\u2080, v\u2081, &#8230;, v\u2082\u2085\u2085)<!-- --><\/em> to commit to the array <!-- --><em class=\"chakra-text css-0\">v<!-- --><\/em> of length 256.<!-- --><\/p>\n<p><!-- --><\/p>\n<h2 class=\"chakra-heading css-1w54o5f\" id=\"layout-of-the-verkle-tree\">Layout of the verkle tree<!-- --><\/h2>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">A primary design objective of the verkle tree EIP is to make access to nearby positions (e.g., storage with nearly identical addresses or adjacent code segments) inexpensive. To achieve this, a key comprises a <!-- --><em class=\"chakra-text css-0\">stem<!-- --><\/em> of 31 bytes and a <!-- --><em class=\"chakra-text css-0\">suffix<!-- --><\/em> of one byte, culminating in a total of 32 bytes. The key strategy is devised so that &#8220;proximate&#8221; storage locations are linked to the same stem with distinct suffixes. For further information, please consult the <!-- --><a target=\"_blank\" rel=\"noopener\" class=\"chakra-link css-ug8vf0\" href=\"https:\/\/notes.ethereum.org\/@vbuterin\/verkle_tree_eip\">EIP draft<!-- --><\/a>.<!-- --><\/p>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">The verkle tree itself is ultimately comprised of two categories of nodes:<!-- --><\/p>\n<p><!-- --><\/p>\n<ul role=\"list\" class=\"css-1onhfjo\">\n<li class=\"css-cvpopp\"><em class=\"chakra-text css-0\">Extension nodes<!-- --><\/em>, which symbolize 256 values sharing the same stem but differing suffixes<!-- --><\/li>\n<li class=\"css-cvpopp\"><em class=\"chakra-text css-0\">Inner nodes<!-- --><\/em>, which can accommodate up to 256 children, comprised of either other inner nodes or extension nodes.<!-- --><\/li>\n<\/ul>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">The commitment to an extension node is a commitment to a 4 element vector; the remaining positions will be 0. It is:<!-- --><\/p>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">C\u2081 and C\u2082 are two additional commitments that secure all values with a stem equivalent to <!-- --><em class=\"chakra-text css-0\">stem<!-- --><\/em>. The rationale for requiring two commitments is that values encompass 32 bytes, but we can only hold 252 bits in one field element. A single commitment would therefore be insufficient to store 256 values. Thus, C\u2081 retains the values for suffix 0 to 127, while C\u2082 encompasses 128 to 255, with the values divided in two to fit within the field size (we&#8217;ll discuss this later).<!-- --><\/p>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">The extension, together with the commitments C\u2081 and C\u2082, is known as the &#8220;extension-and-suffix tree&#8221; (EaS for brevity).<!-- --><\/p>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\"><img decoding=\"async\" alt=\"\" src=\"https:\/\/blog.ethereum.org\/images\/posts\/upload_11c3da539634c3490428842b8e330fee.jpg\" class=\"chakra-image css-hw6q2r\"\/><br \/>\n<!-- --><strong>Figure 1<!-- --><\/strong> <!-- --><em class=\"chakra-text css-0\">Illustration of a path through a verkle tree for the key <!-- --><span class=\"chakra-text css-ons8vw\">0xfe0002abcd..ff04<\/span>: the route traverses 3 internal nodes with 256 children each (254, 0, 2), a single extension node representing <!-- --><span class=\"chakra-text css-ons8vw\">abcd..ff<\/span>, and the two suffix tree commitments, including the value for <!-- --><span class=\"chakra-text css-ons8vw\">04<\/span>, v\u2084. It is important to note that <!-- --><span class=\"chakra-text css-ons8vw\">stem<\/span> is actually the first 31 bytes of the key, including the path through the internal nodes.<!-- --><\/em><\/p>\n<p><!-- --><\/p>\n<h3 class=\"chakra-heading css-145upk7\" id=\"commitment-to-the-values-leaf-nodes\">Commitment to the values leaf nodes<!-- --><\/h3>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">Each extension and suffix tree node encapsulates 256 values. Given that a value is 256 bits wide, and we can only safely accommodate 252 bits in a single field element, four bits would be forfeited if we merely attempted to store one value in one field element.<!-- --><\/p>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">To address this issue, we decided to divide the cluster of 256 values into two sets of 128 values each. Each 32-byte value within a set is partitioned into two 16-byte values. Hence, a value v\u1d62\u2208 \ud835\udd39\u2083\u2082 transforms into v\u207d\u02e1\u1d52\u02b7\u1d49\u02b3\u207e\u1d62 \u2208 \ud835\udd39\u2081\u2086 and v\u207d\u1d58\u1d56\u1d56\u1d49\u02b3\u207e\u1d62\u2208 \ud835\udd39\u2081\u2086 such that v\u207d\u02e1\u1d52\u02b7\u1d49\u02b3\u207e\u1d62 ++ v\u207d\u1d58\u1d56\u1d56\u1d49\u02b3\u207e\u1d62= v\u1d62.<!-- --><\/p>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">A &#8220;leaf marker&#8221; is appended to the v\u207d\u02e1\u1d52\u02b7\u1d49\u02b3\u207e\u1d62, to distinguish between a leaf that has never been accessed and a leaf that has been overwritten with zeros. <!-- --><strong>No value is ever removed from a verkle tree<!-- --><\/strong>. This is essential for forthcoming state expiry frameworks. That marker is established at the 129th bit, i.e., v\u207d\u02e1\u1d52\u02b7\u1d49\u02b3 \u1d50\u1d52\u1d48\u2071\u1da0\u2071\u1d49\u1d48\u207e\u1d62 = v\u207d\u02e1\u1d52\u02b7\u1d49\u02b3\u207e\u1d62 + 2\u00b9\u00b2\u2078 if v\u1d62 has been accessed prior, and v\u207d\u02e1\u1d52\u02b7\u1d49\u02b3 \u1d50\u1d52\u1d48\u2071\u1da0\u2071\u1d49\u1d48\u207e\u1d62= 0 if v\u1d62 has not been accessed before.<!-- --><\/p>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">The two obligations C\u2081 and C\u2082 are then characterized as<!-- --><\/p>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\"><img decoding=\"async\" alt=\"\" src=\"https:\/\/blog.ethereum.org\/images\/posts\/c1-c2.png\" class=\"chakra-image css-hw6q2r\"\/><\/p>\n<p><!-- --><\/p>\n<h3 class=\"chakra-heading css-145upk7\" id=\"commitment-of-extension-nodes\">Commitment of extension nodes<!-- --><\/h3>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">The commitment to an extension node consists of an &#8220;extension indicator&#8221;, which is simply the numeral 1, the two subtree commitments C\u2081 and C\u2082, along with the <!-- --><em class=\"chakra-text css-0\">stem<!-- --><\/em> of the key that leads to this extension node.<!-- --><\/p>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\"><img decoding=\"async\" alt=\"\" src=\"https:\/\/blog.ethereum.org\/images\/posts\/commitment.png\" class=\"chakra-image css-hw6q2r\"\/><\/p>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">In contrast to extension nodes in the Merkle-Patricia tree, which only include the segment of the key that connects the parent internal node to the child internal node, the stem incorporates the entire key up to that moment. This is because verkle trees are created with stateless proofs in consideration: if a new key is added that &#8220;splits&#8221; the extension into two, the older sibling does not need to be revised, facilitating a more compact proof.<!-- --><\/p>\n<p><!-- --><\/p>\n<h3 class=\"chakra-heading css-145upk7\" id=\"commitment-of-internal-nodes\">Commitment of Internal nodes<!-- --><\/h3>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">Internal nodes feature a more straightforward calculation approach for their commitments: the node is perceived as a vector of 256 values, representing the (field rendition of the) root commitment of each of their 256 subtrees. The commitment for an empty subtree is 0. Should the subtree not be void, then the commitment for the internal node is<!-- --><\/p>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\"><img decoding=\"async\" alt=\"\" src=\"https:\/\/blog.ethereum.org\/images\/posts\/internal.png\" class=\"chakra-image css-hw6q2r\"\/><\/p>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">where the C\u1d62 denote the offspring of the internal node, and 0 if an offspring is absent.<!-- --><\/p>\n<p><!-- --><\/p>\n<h2 class=\"chakra-heading css-1w54o5f\" id=\"insertion-into-the-tree\">Insertion into the tree<!-- --><\/h2>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">Figure 2 is an example of the procedure for inserting a new value into the tree, which becomes intriguing when the stems intersect at multiple initial bytes.<!-- --><\/p>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\"><img decoding=\"async\" alt=\"\" src=\"https:\/\/blog.ethereum.org\/images\/posts\/upload_5196292ae56f82a63cf260429315b736.png\" class=\"chakra-image css-hw6q2r\"\/><\/p>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\"><strong>Figure 2<!-- --><\/strong> <!-- --><em class=\"chakra-text css-0\">Value v\u2081\u2089\u2082 is added at location <!-- --><span class=\"chakra-text css-ons8vw\">0000010000&#8230;0000<\/span> in a verkle tree that holds only value v\u2081\u2082\u2087 at location <!-- --><span class=\"chakra-text css-ons8vw\">0000000000&#8230;0000<\/span>. As the stems vary at the third byte, two internal nodes are appended until the differing byte. Following this, another &#8220;extension-and-suffix&#8221; tree is added, which includes a complete 31-byte stem. The initial node remains unaltered, and C\u00b2\u2080 retains the same value as C\u2070\u2080 prior to the addition.<!-- --><\/em><\/p>\n<p><!-- --><\/p>\n<h2 class=\"chakra-heading css-1w54o5f\" id=\"shallower-trees-smaller-proofs\">Shallower trees, smaller proofs<!-- --><\/h2>\n<p><!-- --><\/p>\n<p class=\"chakra-text css-gi02ar\">The verkle tree architecture enables shallower trees, leading to a reduction in the volume of stored data. Its real strength, however, lies in the capability to generate smaller proofs, i.e., witnesses. This will be elaborated in the subsequent article.<!-- --><\/p>\n<\/div>\n<p><br \/>\n<br \/><a href=\"https:\/\/blog.ethereum.org\/en\/2021\/12\/02\/verkle-tree-structure\">Source link <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A Verkle tree is a commitment framework that operates similarly to a Merkle tree, yet has significantly smaller witnesses. It functions by substituting the hashes in a Merkle tree with a vector commitment, rendering broader branching factors more effective. Gratitude to Kevaundray Wedderburn for the insights regarding the post. Overview Refer to the following for<\/p>\n","protected":false},"author":3,"featured_media":6617,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[23],"tags":[608],"class_list":["post-6616","post","type-post","status-publish","format-standard","has-post-thumbnail","category-ethereum","tag-return-a-list-of-comma-separated-tags-from-this-title-verkle-tree-structure-ethereum-foundation-blog"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Decoding the Verkle Tree: A Game-Changer for Ethereum&#039;s Future - WSJ-Crypto<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/wsj-crypto.com\/index.php\/2024\/12\/27\/decoding-the-verkle-tree-a-game-changer-for-ethereums-future\/\" \/>\n<meta property=\"og:locale\" content=\"it_IT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Decoding the Verkle Tree: A Game-Changer for Ethereum&#039;s Future - WSJ-Crypto\" \/>\n<meta property=\"og:description\" content=\"A Verkle tree is a commitment framework that operates similarly to a Merkle tree, yet has significantly smaller witnesses. 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It functions by substituting the hashes in a Merkle tree with a vector commitment, rendering broader branching factors more effective. Gratitude to Kevaundray Wedderburn for the insights regarding the post. 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