From 112d0bd6a65f75d83556dbd5ced073466e745f35 Mon Sep 17 00:00:00 2001
From: enricobottazzi <85900164+enricobottazzi@users.noreply.github.com>
Date: Tue, 17 Jan 2023 16:34:05 +0100
Subject: [PATCH 1/3] add `SafeLessThan` template to comparators

---
 circuits/comparators.circom | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)

diff --git a/circuits/comparators.circom b/circuits/comparators.circom
index bfed0320..6ea44b9c 100644
--- a/circuits/comparators.circom
+++ b/circuits/comparators.circom
@@ -98,6 +98,23 @@ template LessThan(n) {
     out <== 1-n2b.out[n];
 }
 
+// Do Range checks on the inputs to avoid overflow
+template SafeLessThan(n) {
+    assert(n <= 252);
+    signal input in[2];
+    signal output out;
+
+    component aInRange = Num2Bits(252);
+    aInRange.in <== in[0];
+    component bInRange = Num2Bits(252);
+    bInRange.in <== in[1];
+
+    component n2b = Num2Bits(n+1);
+
+    n2b.in <== in[0]+ (1<<n) - in[1];
+
+    out <== 1-n2b.out[n];
+}
 
 
 // N is the number of bits the input  have.

From 4309a3c10c2ebb73e81735ffcf12d1711f11a431 Mon Sep 17 00:00:00 2001
From: enricobottazzi <85900164+enricobottazzi@users.noreply.github.com>
Date: Wed, 18 Jan 2023 13:45:57 +0100
Subject: [PATCH 2/3] use `LessThan` component inside `SafeLessThan` to save
 compatibility

---
 circuits/comparators.circom | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/circuits/comparators.circom b/circuits/comparators.circom
index 6ea44b9c..b327d42d 100644
--- a/circuits/comparators.circom
+++ b/circuits/comparators.circom
@@ -109,11 +109,12 @@ template SafeLessThan(n) {
     component bInRange = Num2Bits(252);
     bInRange.in <== in[1];
 
-    component n2b = Num2Bits(n+1);
+    component lt = LessThan(n);
 
-    n2b.in <== in[0]+ (1<<n) - in[1];
+    lt.in[0] <== in[0];
+    lt.in[1] <== in[1];
 
-    out <== 1-n2b.out[n];
+    out <== lt.out;
 }
 
 

From fb185d7a71dff613e770a9d7fcdb007f4233c555 Mon Sep 17 00:00:00 2001
From: enricobottazzi <85900164+enricobottazzi@users.noreply.github.com>
Date: Wed, 18 Jan 2023 13:54:43 +0100
Subject: [PATCH 3/3] Restrict `Num2Bits` component instantiation to n bits
 instead of 252

---
 circuits/comparators.circom | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/circuits/comparators.circom b/circuits/comparators.circom
index b327d42d..3977d246 100644
--- a/circuits/comparators.circom
+++ b/circuits/comparators.circom
@@ -98,15 +98,16 @@ template LessThan(n) {
     out <== 1-n2b.out[n];
 }
 
-// Do Range checks on the inputs to avoid overflow
+// Safely compare two n-bit numbers 
+// Performs range checks on the inputs to avoid overflow. Range is n <= 252
 template SafeLessThan(n) {
     assert(n <= 252);
     signal input in[2];
     signal output out;
 
-    component aInRange = Num2Bits(252);
+    component aInRange = Num2Bits(n);
     aInRange.in <== in[0];
-    component bInRange = Num2Bits(252);
+    component bInRange = Num2Bits(n);
     bInRange.in <== in[1];
 
     component lt = LessThan(n);