From 6f15d54a5c599684101a06754d86a24bfa3eea84 Mon Sep 17 00:00:00 2001 From: hirugohan Date: Mon, 16 Mar 2026 00:01:26 +0700 Subject: [PATCH] feat: add elliptic curve ch01 --- textbooks/elliptic-curves-prasma/ch01.md | 10 ++++++++++ textbooks/elliptic-curves-prasma/ch02.md | 0 textbooks/elliptic-curves-prasma/ch02_01.md | 0 textbooks/elliptic-curves-prasma/ch02_02.md | 0 textbooks/elliptic-curves-prasma/ch02_02_01.md | 0 textbooks/elliptic-curves-prasma/ch02_03.md | 0 textbooks/elliptic-curves-prasma/ch03.md | 0 textbooks/elliptic-curves-prasma/ch04.md | 0 textbooks/elliptic-curves-prasma/ch04_01.md | 0 textbooks/elliptic-curves-prasma/ch04_02.md | 0 textbooks/elliptic-curves-prasma/ch04_03.md | 0 textbooks/elliptic-curves-prasma/ch04_04.md | 0 textbooks/elliptic-curves-prasma/ch04_05.md | 0 textbooks/elliptic-curves-prasma/ch05.md | 0 textbooks/elliptic-curves-prasma/ch05_01.md | 0 textbooks/elliptic-curves-prasma/ch05_02.md | 0 textbooks/elliptic-curves-prasma/ch05_03.md | 0 textbooks/elliptic-curves-prasma/ch05_04.md | 0 textbooks/elliptic-curves-prasma/ch05_05.md | 0 textbooks/elliptic-curves-prasma/ch05_06.md | 0 textbooks/elliptic-curves-prasma/ch05_07.md | 0 textbooks/elliptic-curves-prasma/ch05_08.md | 0 textbooks/elliptic-curves-prasma/ch05_09.md | 0 textbooks/elliptic-curves-prasma/index.md | 5 +++++ 24 files changed, 15 insertions(+) create mode 100644 textbooks/elliptic-curves-prasma/ch01.md create mode 100644 textbooks/elliptic-curves-prasma/ch02.md create mode 100644 textbooks/elliptic-curves-prasma/ch02_01.md create mode 100644 textbooks/elliptic-curves-prasma/ch02_02.md create mode 100644 textbooks/elliptic-curves-prasma/ch02_02_01.md create mode 100644 textbooks/elliptic-curves-prasma/ch02_03.md create mode 100644 textbooks/elliptic-curves-prasma/ch03.md create mode 100644 textbooks/elliptic-curves-prasma/ch04.md create mode 100644 textbooks/elliptic-curves-prasma/ch04_01.md create mode 100644 textbooks/elliptic-curves-prasma/ch04_02.md create mode 100644 textbooks/elliptic-curves-prasma/ch04_03.md create mode 100644 textbooks/elliptic-curves-prasma/ch04_04.md create mode 100644 textbooks/elliptic-curves-prasma/ch04_05.md create mode 100644 textbooks/elliptic-curves-prasma/ch05.md create mode 100644 textbooks/elliptic-curves-prasma/ch05_01.md create mode 100644 textbooks/elliptic-curves-prasma/ch05_02.md create mode 100644 textbooks/elliptic-curves-prasma/ch05_03.md create mode 100644 textbooks/elliptic-curves-prasma/ch05_04.md create mode 100644 textbooks/elliptic-curves-prasma/ch05_05.md create mode 100644 textbooks/elliptic-curves-prasma/ch05_06.md create mode 100644 textbooks/elliptic-curves-prasma/ch05_07.md create mode 100644 textbooks/elliptic-curves-prasma/ch05_08.md create mode 100644 textbooks/elliptic-curves-prasma/ch05_09.md create mode 100644 textbooks/elliptic-curves-prasma/index.md diff --git a/textbooks/elliptic-curves-prasma/ch01.md b/textbooks/elliptic-curves-prasma/ch01.md new file mode 100644 index 0000000..e4a6aa6 --- /dev/null +++ b/textbooks/elliptic-curves-prasma/ch01.md @@ -0,0 +1,10 @@ +# Chapter 1: Introduction + +Since the construction of Miller's algorithm [Mil], the cryptography community has started to use elliptic curves and their pairing extensively; by now; many publicly available code libraries allow one to efficiently compute these mathematical objects. + +Compared to Machine Learning, where the mathematical pre-requisites consist of Linear Algebra, Calculus, and basic Statistics, elliptic curves require substantially more background and are usually taught at a master level in pure Mathematics. This state of affairs poses a challenge to engineers and others who wish to understand the mathematical building blocks. + +This notes aim to give a self-contained, rigorous and elementary account of most of the maths required for pairing-based cryptography. I sometimes formulated elementary arguments to replace non-elementary ones. I completely avoid relying on Galois theory or algebraic gemotery andeven ring theory is mostly skipped. + +Footnotes: +- Mil (Miller's algorithm): Miller, V.S., 2004. The Weil pairing, and its efficient calculation. Journal of cryptology, 17(4), pp.235-261 diff --git a/textbooks/elliptic-curves-prasma/ch02.md b/textbooks/elliptic-curves-prasma/ch02.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch02_01.md b/textbooks/elliptic-curves-prasma/ch02_01.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch02_02.md b/textbooks/elliptic-curves-prasma/ch02_02.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch02_02_01.md b/textbooks/elliptic-curves-prasma/ch02_02_01.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch02_03.md b/textbooks/elliptic-curves-prasma/ch02_03.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch03.md b/textbooks/elliptic-curves-prasma/ch03.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch04.md b/textbooks/elliptic-curves-prasma/ch04.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch04_01.md b/textbooks/elliptic-curves-prasma/ch04_01.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch04_02.md b/textbooks/elliptic-curves-prasma/ch04_02.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch04_03.md b/textbooks/elliptic-curves-prasma/ch04_03.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch04_04.md b/textbooks/elliptic-curves-prasma/ch04_04.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch04_05.md b/textbooks/elliptic-curves-prasma/ch04_05.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch05.md b/textbooks/elliptic-curves-prasma/ch05.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch05_01.md b/textbooks/elliptic-curves-prasma/ch05_01.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch05_02.md b/textbooks/elliptic-curves-prasma/ch05_02.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch05_03.md b/textbooks/elliptic-curves-prasma/ch05_03.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch05_04.md b/textbooks/elliptic-curves-prasma/ch05_04.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch05_05.md b/textbooks/elliptic-curves-prasma/ch05_05.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch05_06.md b/textbooks/elliptic-curves-prasma/ch05_06.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch05_07.md b/textbooks/elliptic-curves-prasma/ch05_07.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch05_08.md b/textbooks/elliptic-curves-prasma/ch05_08.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/ch05_09.md b/textbooks/elliptic-curves-prasma/ch05_09.md new file mode 100644 index 0000000..e69de29 diff --git a/textbooks/elliptic-curves-prasma/index.md b/textbooks/elliptic-curves-prasma/index.md new file mode 100644 index 0000000..6c86ce8 --- /dev/null +++ b/textbooks/elliptic-curves-prasma/index.md @@ -0,0 +1,5 @@ +--- +title: Elliptic curves over finite fields and their pairings - an elementary and rigorous account +author: Matan Prasma +year: December, 2024 +---