From e739733c8ca2b89cfc49f35b161e81e16b5957d7 Mon Sep 17 00:00:00 2001 From: Pavel Kalinnikov Date: Fri, 13 May 2022 15:38:32 +0100 Subject: [PATCH] docs: Use SVG format for images (#26) Diagrams in the Markdown files are better rendered on any screen size if they are in vector format, such as SVG. This change also improves positioning and scaling of the diagrams, which is now easy to change with the vector image format. --- docs/compact_ranges.md | 28 +- docs/images/compact_ranges.png | Bin 33865 -> 0 bytes docs/images/compact_ranges.svg | 509 ++++++++++++++++++ docs/images/compact_ranges_merge.png | Bin 36768 -> 0 bytes docs/images/compact_ranges_merge.svg | 521 ++++++++++++++++++ docs/images/consistency_proof.png | Bin 21389 -> 0 bytes docs/images/consistency_proof.svg | 386 +++++++++++++ docs/images/distributed_tree.png | Bin 85851 -> 0 bytes docs/images/distributed_tree.svg | 707 ++++++++++++++++++++++++ docs/images/inclusion_proof.png | Bin 26276 -> 0 bytes docs/images/inclusion_proof.svg | 391 ++++++++++++++ docs/images/inclusion_proof_range.png | Bin 27035 -> 0 bytes docs/images/inclusion_proof_range.svg | 408 ++++++++++++++ docs/images/witness.png | Bin 112701 -> 0 bytes docs/images/witness.svg | 745 ++++++++++++++++++++++++++ 15 files changed, 3688 insertions(+), 7 deletions(-) delete mode 100644 docs/images/compact_ranges.png create mode 100644 docs/images/compact_ranges.svg delete mode 100644 docs/images/compact_ranges_merge.png create mode 100644 docs/images/compact_ranges_merge.svg delete mode 100644 docs/images/consistency_proof.png create mode 100644 docs/images/consistency_proof.svg delete mode 100644 docs/images/distributed_tree.png create mode 100644 docs/images/distributed_tree.svg delete mode 100644 docs/images/inclusion_proof.png create mode 100644 docs/images/inclusion_proof.svg delete mode 100644 docs/images/inclusion_proof_range.png create mode 100644 docs/images/inclusion_proof_range.svg delete mode 100644 docs/images/witness.png create mode 100644 docs/images/witness.svg diff --git a/docs/compact_ranges.md b/docs/compact_ranges.md index f1bf56c..99d0e59 100644 --- a/docs/compact_ranges.md +++ b/docs/compact_ranges.md @@ -27,7 +27,9 @@ example, in the picture below, the range `[2, 9)` is covered by perfect nodes `[1.1, 2.1, 8]`, and the range `[12, 16)` is covered by a single perfect node `2.3`. -![compact_ranges](images/compact_ranges.png) +

+ +

Note that, in the picture above, range `[0, 21)` could be covered by a single node `5.0`. However, we only use the perfect nodes for a compact range, so it @@ -48,7 +50,9 @@ The core property that makes compact ranges widely usable is that they are merged into an `[L, R)` range. Consider the picture below for an intuitive understanding of how it works. -![compact_ranges_merge](images/compact_ranges_merge.png) +

+ +

Given two compact ranges, `[2, 9)` and `[9, 16)`, each represented by a set of node hashes (three green and three cyan nodes correspondingly), we “merge” two @@ -103,7 +107,9 @@ middle range `[i, i+1)` formed simply as the hash of this leaf. The result will be a compact range `[0, N)`, which can be compared with the trusted root hash. -![inclusion_proof](images/inclusion_proof.png) +

+ +

In the example above, an inclusion proof for leaf `6` consists of compact ranges `[0, 6)` and `[7, 16)`. @@ -125,7 +131,9 @@ complementary part of the tree. For example, consider the case when we want to prove the authenticity of values within the range `[6, 13)`, as shown in the picture below. -![inclusion_proof_range](images/inclusion_proof_range.png) +

+ +

To do so, the server can provide two compact ranges: `[0, 6)` and `[13, 16)`. The client will then construct the middle compact range locally (based on the @@ -153,7 +161,9 @@ individual entry inclusion proofs which could cost `O(N log N)`. A consistency proof (or proof of the append-only property) proves to a client that one tree state is the result of appending some entries to another state. -![consistency_proof](images/consistency_proof.png) +

+ +

The definition of the consistency proof already contains a hint on how to model it with compact ranges. Suppose a client knows a compact range of the old tree, @@ -192,7 +202,9 @@ Since the Merkle tree is a highly regular recursive structure, its geometry can be split into pieces of a controllable size that a single server can handle. See the picture below for an intuition how. -![distributed_tree](images/distributed_tree.png) +

+ +

The construction work is split across a number of "leaf" workers, each piece of work is based on a relatively small range of leaves. When the corresponding @@ -241,7 +253,9 @@ range `[0, N)`. The benefit of storing a compact range is in the ability to incrementally update it as the tree state evolves. See the picture below. -![witness](images/witness.png) +

+ +

Similarly to the [updatable proofs](#updatable-proofs), the accumulated space / bandwidth complexity of updating the state `O(N)` times is `O(N)`, as opposed diff --git a/docs/images/compact_ranges.png b/docs/images/compact_ranges.png deleted file mode 100644 index 1a36832d64012f66e2bc3d120ec5d0c23cebdb2f..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 33865 zcmZ_02RxPU|3B^=Co6le?3KOuCVOwPXZGIf*rNy`WM*ZP8PP!@WQB}`vR76@#qTyo6SrHq3`iG_lKf}^UUsE2|ABSb-gm|{S|o$7*T zx!?!HS5H|UrGAWh8~l>yV4~`%sfof4t}#&1AZRG4$R;SDJ%sR|YY4ceM7ecy9|gq- zLiO*pC4}w2?Gv0)VE?pn1V52qD&QMD{m)O-V#t4cEQbE4HH@$r^*`4TQ{-b~On6D) z2d0;bsV@r3Z6f411SKz@90dh>+u6Xx&qPy0+|JXT+s5A0)`2_7-3$2?ie!*DxO8{$ zv!M%eck}QS50YZIX(0}-k+*pm=x&<$xk@pZXzI`@c=|Zd33Kyu^D;) z>nSSz^EmiTis6BupO-ifPhemmcc1{br;ig4pO}~!4=+CtKR*{}!Q~t5;b#-X<>AZt zx0C<$qv+sk=i}_<=j`c0hwRtJ*3;ilih%+7qJO{sj?>TC@xO2K@cn06V1hiz|KZ`| z=H>afZ}6xj@~*g^gRiHXKeBs64`)AVe#x80|9kttZ~Oa{wvV#|7%%cMX}*6R`M>x6 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