From 3f7519bed410c1d673359b06899f0ea7d273da49 Mon Sep 17 00:00:00 2001
From: filifa <filifa.breath652@8alias.com>
Date: Thu, 11 Dec 2025 23:49:34 -0500
Subject: [PATCH] add function for legendre symbol

---
 modules/math.js | 13 +++++++++++--
 1 file changed, 11 insertions(+), 2 deletions(-)

diff --git a/modules/math.js b/modules/math.js
index e40d615..db1d21b 100644
--- a/modules/math.js
+++ b/modules/math.js
@@ -101,10 +101,19 @@ function isprime(n) {
 	return true;
 }
 
+function legendreSymbol(a, p) {
+	let r = modpow(a, (p - 1n)/2n, p);
+	if (r === p - 1n) {
+		r = -1n;
+	}
+
+	return r;
+}
+
 function quadraticNonResidue(p) {
 	// TODO: consider randomizing this
 	for (let a = 2n; a < p; a++) {
-		if (modpow(a, (p-1n)/2n, p) === p - 1n) {
+		if (legendreSymbol(a, p) === -1n) {
 			return a;
 		}
 	}
@@ -158,7 +167,7 @@ function modsqrt(n, modulus) {
 
 	if (n % modulus === 0n) {
 		return 0n;
-	} else if (modpow(n, (modulus-1n)/2n, modulus) !== 1n) {
+	} else if (legendreSymbol(n, modulus) !== 1n) {
 		throw new Error("radicand is not a quadratic residue of the modulus");
 	} else if (modulus === 2n) {
 		return n % 2n;