diff --git a/workers/math.js b/workers/math.js
index f1cc164..f610a93 100644
--- a/workers/math.js
+++ b/workers/math.js
@@ -184,17 +184,24 @@ function modsqrt(n, modulus) {
 		n += modulus;
 	}
 
+	let r = null;
 	if (n % modulus === 0n) {
-		return 0n;
+		r = 0n;
 	} else if (modulus === 2n) {
-		return n % 2n;
+		r = n % 2n;
 	} else if (legendreSymbol(n, modulus) !== 1n) {
 		throw new Error("radicand is not a quadratic residue of the modulus");
 	} else if (modulus % 4n === 3n) {
-		return modpow(n, (modulus+1n)/4n, modulus);
+		r = modpow(n, (modulus+1n)/4n, modulus);
+	} else {
+		r = tonelliShanks(n, modulus);
 	}
 
-	return tonelliShanks(n, modulus);
+	if (modulus - r <= r) {
+		r = modulus - r;
+	}
+
+	return r;
 }
 
 function ord(n, modulus) {