From 7d746a7408ad9e274d0d7eb8fb868953c0cf3925 Mon Sep 17 00:00:00 2001
From: Paul Miller <paul@paulmillr.com>
Date: Thu, 15 Dec 2022 22:11:40 +0000
Subject: [PATCH] Add modular division

---
 README.md      |  7 ++++---
 src/modular.ts | 10 ++++++++++
 2 files changed, 14 insertions(+), 3 deletions(-)

diff --git a/README.md b/README.md
index be14f67..4c35010 100644
--- a/README.md
+++ b/README.md
@@ -69,12 +69,13 @@ secp256k1.sign(randomBytes(32), secp256k1.utils.randomPrivateKey());
 
 import { twistedEdwards } from '@noble/curves/edwards'; // Twisted Edwards curve
 import { sha512 } from '@noble/hashes/sha512';
+import { div } from '@noble/curves/modular';
 
 const ed25519 = twistedEdwards({
   a: -1n,
-  d: 37095705934669439343138083508754565189542113879843219016388785533085940283555n,
-  P: 57896044618658097711785492504343953926634992332820282019728792003956564819949n,
-  n: 7237005577332262213973186563042994240857116359379907606001950938285454250989n,
+  d: div(-121665n, 121666n, 2n ** 255n - 19n), // -121665n/121666n
+  P: 2n ** 255n - 19n,
+  n: 2n ** 252n + 27742317777372353535851937790883648493n,
   h: 8n,
   Gx: 15112221349535400772501151409588531511454012693041857206046113283949847762202n,
   Gy: 46316835694926478169428394003475163141307993866256225615783033603165251855960n,
diff --git a/src/modular.ts b/src/modular.ts
index 575d1fd..0ff6208 100644
--- a/src/modular.ts
+++ b/src/modular.ts
@@ -64,6 +64,16 @@ export function invert(number: bigint, modulo: bigint): bigint {
   return mod(x, modulo);
 }
 
+/**
+ * Division over finite field.
+ * `a/b mod p == a * invert(b) mod p`
+ */
+export function div(numerator: bigint, denominator: bigint, modulo: bigint): bigint {
+  const num = mod(numerator, modulo);
+  const iden = invert(denominator, modulo);
+  return mod(num * iden, modulo);
+}
+
 /**
  * Takes a list of numbers, efficiently inverts all of them.
  * @param nums list of bigints