From ac51d27a64f7a699bd8cbab468389cc3f4ad063a Mon Sep 17 00:00:00 2001 From: Yu Guo Date: Sun, 29 Sep 2024 20:39:53 +0800 Subject: [PATCH] fix(binius): add authors --- fri-binius/binius-01.md | 3 +++ fri-binius/binius-01.zh.md | 3 +++ 2 files changed, 6 insertions(+) diff --git a/fri-binius/binius-01.md b/fri-binius/binius-01.md index 1e6df46..6913b6f 100644 --- a/fri-binius/binius-01.md +++ b/fri-binius/binius-01.md @@ -1,5 +1,8 @@ # Notes on FRI-Binius (Part I): Binary Towers +- Yu Guo +- Jade Xie + Binary fields possess elegant internal structures, and Binius aims to fully utilize these internal structures to construct efficient SNARK proof systems. This article mainly discusses the Binary Fields that Binius relies on at its core and the construction methods of Extension Towers based on Binary Fields. Binary Fields provide smaller fields and are compatible with various tool constructions in traditional cryptography while also being able to fully utilize optimization of special instructions on hardware. There are two main advantages to choosing Extension Towers: one is that the recursive Extension construction provides a consistent and incremental Basis selection, allowing Small Fields to be embedded into Large Fields in a very natural way; the other advantage is that multiplication and inversion operations have efficient recursive algorithms. ## Extension Fields diff --git a/fri-binius/binius-01.zh.md b/fri-binius/binius-01.zh.md index f3de891..ede5b30 100644 --- a/fri-binius/binius-01.zh.md +++ b/fri-binius/binius-01.zh.md @@ -1,5 +1,8 @@ # Notes on FRI-Binius (Part I): Binary Towers +- Yu Guo +- Jade Xie + 二进制域拥有优美的内部结构，而 Binius 是意图充分利用这些内部结构，构造高效的 SNARK 证明系统。本文主要讨论 Binius 底层所依赖的 Binary Fields 以及 基于 Binary Fields 的 Extension Tower 的构造方法。Binary Fields 提供了更小的 Fields，并且兼容传统密码学中的各种工具构造，同时也可以充分利用硬件上的特殊指令的优化。选用 Extension Tower 优点主要有两个，一个是递归的 Extension 构造提供了一致的、增量式的 Basis 选择，从而使得 Small Field 可以以非常自然的方式嵌入到一个 Large Field 中，另一个优点是乘法和求逆运算存在高效的递归算法。 ## Extension Fields