diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,10 @@
 # CHANGELOG for crypton
 
+## 1.1.3
+
+* Ensure that `pointAdd` in `PubKey.ECC.P256` treats the point at infinity as the additive identity.
+  [#73](https://github.com/kazu-yamamoto/crypton/pull/73)
+
 ## 1.1.2
 
 * Preparing `ram` v0.22.
diff --git a/Crypto/PubKey/ECC/P256.hs b/Crypto/PubKey/ECC/P256.hs
--- a/Crypto/PubKey/ECC/P256.hs
+++ b/Crypto/PubKey/ECC/P256.hs
@@ -110,9 +110,12 @@
 
 -- | Add a point to another point
 pointAdd :: Point -> Point -> Point
-pointAdd a b = withNewPoint $ \dx dy ->
-    withPoint a $ \ax ay -> withPoint b $ \bx by ->
-        ccrypton_p256e_point_add ax ay bx by dx dy
+pointAdd a b
+    | pointIsAtInfinity a = b
+    | pointIsAtInfinity b = a
+    | otherwise = withNewPoint $ \dx dy ->
+        withPoint a $ \ax ay -> withPoint b $ \bx by ->
+            ccrypton_p256e_point_add ax ay bx by dx dy
 
 -- | Negate a point
 pointNegate :: Point -> Point
diff --git a/crypton.cabal b/crypton.cabal
--- a/crypton.cabal
+++ b/crypton.cabal
@@ -1,6 +1,6 @@
 cabal-version:      1.18
 name:               crypton
-version:            1.1.2
+version:            1.1.3
 license:            BSD3
 license-file:       LICENSE
 copyright:          Vincent Hanquez <vincent@snarc.org>
diff --git a/tests/KAT_EdDSA.hs b/tests/KAT_EdDSA.hs
--- a/tests/KAT_EdDSA.hs
+++ b/tests/KAT_EdDSA.hs
@@ -3,6 +3,7 @@
 {-# LANGUAGE GADTs #-}
 {-# LANGUAGE OverloadedStrings #-}
 {-# LANGUAGE RecordWildCards #-}
+{-# LANGUAGE TypeOperators #-}
 
 module KAT_EdDSA (tests) where
 
diff --git a/tests/KAT_PubKey/P256.hs b/tests/KAT_PubKey/P256.hs
--- a/tests/KAT_PubKey/P256.hs
+++ b/tests/KAT_PubKey/P256.hs
@@ -40,7 +40,9 @@
 curveGen = ECC.ecc_g . ECC.common_curve $ curve
 
 pointP256ToECC :: P256.Point -> ECC.Point
-pointP256ToECC = uncurry ECC.Point . P256.pointToIntegers
+pointP256ToECC p
+    | P256.pointIsAtInfinity p = ECC.PointO
+    | otherwise = uncurry ECC.Point (P256.pointToIntegers p)
 
 i2ospScalar :: Integer -> Bytes
 i2ospScalar i =
@@ -145,8 +147,11 @@
                     t = P256.pointFromIntegers (xT, yT)
                     r = P256.pointFromIntegers (xR, yR)
                  in r @=? P256.pointAdd s t
+            , testProperty "point-add-infinity" casePointAddInfinity
             , testProperty "lift-to-curve" propertyLiftToCurve
             , testProperty "point-add" propertyPointAdd
+            , testProperty "point-add-infinity-identity" propertyPointAddInfinityIdentity
+            , testProperty "point-add-inverse" propertyPointAddInverse
             , testProperty "point-negate" propertyPointNegate
             , testProperty "point-mul" propertyPointMul
             , testProperty "infinity" $
@@ -198,4 +203,49 @@
          in propertyHold
                 [ eqTest "p256" pR (P256.pointMul (unP256Scalar s) p)
                 , eqTest "ecc" peR (pointP256ToECC pR)
+                ]
+
+    pointInfinity :: P256.Point
+    pointInfinity = P256.pointFromIntegers (0, 0)
+
+    casePointAddInfinity =
+        propertyHold
+            [ eqTest
+                "infinity + base"
+                P256.pointBase
+                (P256.pointAdd pointInfinity P256.pointBase)
+            , eqTest
+                "base + infinity"
+                P256.pointBase
+                (P256.pointAdd P256.pointBase pointInfinity)
+            , eqTest
+                "infinity + infinity"
+                pointInfinity
+                (P256.pointAdd pointInfinity pointInfinity)
+            ]
+
+    propertyPointAddInfinityIdentity r =
+        let p = P256.toPoint (unP256Scalar r)
+         in propertyHold
+                [ eqTest
+                    "infinity + p"
+                    p
+                    (P256.pointAdd pointInfinity p)
+                , eqTest
+                    "p + infinity"
+                    p
+                    (P256.pointAdd p pointInfinity)
+                ]
+
+    propertyPointAddInverse r =
+        let p = P256.toPoint (unP256Scalar r)
+         in propertyHold
+                [ eqTest
+                    "p + negate p"
+                    True
+                    (P256.pointIsAtInfinity (P256.pointAdd p (P256.pointNegate p)))
+                , eqTest
+                    "negate p + p"
+                    True
+                    (P256.pointIsAtInfinity (P256.pointAdd (P256.pointNegate p) p))
                 ]