diff --git a/Crypto/PubKey/ECC/Prim.hs b/Crypto/PubKey/ECC/Prim.hs
--- a/Crypto/PubKey/ECC/Prim.hs
+++ b/Crypto/PubKey/ECC/Prim.hs
@@ -43,19 +43,34 @@
 -- | Elliptic Curve point doubling.
 --
 -- /WARNING:/ Vulnerable to timing attacks.
+--
+-- This perform the following calculation:
+-- > lambda = (3 * xp ^ 2 + a) / 2 yp
+-- > xr = lambda ^ 2 - 2 xp
+-- > yr = lambda (xp - xr) - yp
+--
+-- With binary curve:
+-- > xp == 0   => P = O
+-- > otherwise =>
+-- >    s = xp + (yp / xp)
+-- >    xr = s ^ 2 + s + a
+-- >    yr = xp ^ 2 + (s+1) * xr
+--
 pointDouble :: Curve -> Point -> Point
 pointDouble _ PointO = PointO
 pointDouble (CurveFP (CurvePrime pr cc)) (Point xp yp) = fromMaybe PointO $ do
-    l <- divmod (3 * xp ^ (2::Int) + a) (2 * yp) pr
-    let xr = (l ^ (2::Int) - 2 * xp) `mod` pr
-        yr = (l * (xp - xr) - yp) `mod` pr
+    lambda <- divmod (3 * xp ^ (2::Int) + a) (2 * yp) pr
+    let xr = (lambda ^ (2::Int) - 2 * xp) `mod` pr
+        yr = (lambda * (xp - xr) - yp) `mod` pr
     return $ Point xr yr
   where a = ecc_a cc
-pointDouble (CurveF2m (CurveBinary fx cc)) (Point xp yp) = fromMaybe PointO $ do
-    s <- return . addF2m xp =<< divF2m fx yp xp
-    let xr = mulF2m fx s s `addF2m` s `addF2m` a
-        yr = mulF2m fx xp xp `addF2m` mulF2m fx xr (s `addF2m` 1)
-    return $ Point xr yr
+pointDouble (CurveF2m (CurveBinary fx cc)) (Point xp yp)
+    | xp == 0   = PointO
+    | otherwise = fromMaybe PointO $ do
+        s <- return . addF2m xp =<< divF2m fx yp xp
+        let xr = mulF2m fx s s `addF2m` s `addF2m` a
+            yr = mulF2m fx xp xp `addF2m` mulF2m fx xr (s `addF2m` 1)
+        return $ Point xr yr
   where a = ecc_a cc
 
 -- | Elliptic curve point multiplication (double and add algorithm).
diff --git a/Tests/KAT/ECDSA.hs b/Tests/KAT/ECDSA.hs
--- a/Tests/KAT/ECDSA.hs
+++ b/Tests/KAT/ECDSA.hs
@@ -4,6 +4,8 @@
 
 import Data.ByteString (ByteString)
 
+import Crypto.Number.Serialize
+
 import qualified Crypto.PubKey.ECC.ECDSA as ECDSA
 import qualified Crypto.Types.PubKey.ECC as ECC
 import qualified Crypto.Hash.SHA1 as SHA1
@@ -33,16 +35,44 @@
         , r     = 1176954224688105769566774212902092897866168635793
         , s     = 299742580584132926933316745664091704165278518100
         }
+    -- from official ECDSA KATs
     , VectorECDSA
         { curve = ECC.getCurveByName ECC.SEC_t163k1
-        , msg   = "abc"
-        , d     = 5321230001203043918714616464614664646674949479949
-        , q     = ECC.Point 0x037d529fa37e42195f10111127ffb2bb38644806bc
-                            0x0447026eee8b34157f3eb51be5185d2be0249ed776
-        , k     = 936523985789236956265265265235675811949404040044
-        , r     = 875196600601491789979810028167552198674202899628
-        , s     = 1935199835333115956886966454901154618180070051199
+        , msg   = i2osp 0xa2c1a03fdd00521bb08fc88d20344321977aaf637ef9d5470dd7d2c8628fc8d0d1f1d3587c6b3fd02386f8c13db341b14748a9475cc63baf065df64054b27d5c2cdf0f98e3bbb81d0b5dc94f8cdb87acf75720f6163de394c8c6af360bc1acb85b923a493b7b27cc111a257e36337bd94eb0fab9d5e633befb1ae7f1b244bfaa
+        , d     = 0x00000011f2626d90d26cb4c0379043b26e64107fc
+        , q     = ECC.Point 0x0389fa5ad7f8304325a8c060ef7dcb83042c045bc
+                            0x0eefa094a5054da196943cc80509dcb9f59e5bc2e
+        , k     = 0x0000000c3a4ff97286126dab1e5089395fcc47ebb
+        , r     = 0x0dbe6c3a1dc851e7f2338b5c26c62b4b37bf8035c
+        , s     = 0x1c76458135b1ff9fbd23009b8414a47996126b56a
         }
+    , VectorECDSA
+        { curve = ECC.getCurveByName ECC.SEC_t163k1
+        , msg   = i2osp 0x67048080daaeb77d3ac31babdf8be23dbe75ceb4dfb94aa8113db5c5dcb6fe14b70f717b7b0ed0881835a66a86e6d840ffcb7d976c75ef2d1d4322fbbc86357384e24707aef88cea2c41a01a9a3d1b9e72ce650c7fdecc4f9448d3a77df6cdf13647ab295bb3132de0b1b2c402d8d2de7d452f1e003e0695de1470d1064eee16
+        , d     = 0x00000006a3803301daee9af09bb5b6c991a4f49a4
+        , q     = ECC.Point 0x4b500f555e857da8c299780130c5c3f48f02ee322 0x5c1c0ae25b47f06cc46fb86b12d2d8c0ba6a4bf07
+        , k     = 0x0000002f39fbf77f3e0dc046116de692b6cf91b16
+        , r     = 0x3d3eeda42f65d727f4a564f1415654356c6c57a6c
+        , s     = 0x35e4d43c5f08baddf138449db1ad0b7872552b7cd
+        }
+    , VectorECDSA
+        { curve = ECC.getCurveByName ECC.SEC_t163k1
+        , msg   = i2osp 0x77e007dc2acd7248256165a4b30e98986f51a81efd926b85f74c81bc2a6d2bcd030060a844091e22fbb0ff3db5a20caaefb5d58ccdcbc27f0ff8a4d940e78f303079ec1ca5b0ca3d4ecc7580f8b34a9f0496c9e719d2ec3e1614b7644bc11179e895d2c0b58a1da204fbf0f6e509f97f983eacb6487092caf6e8e4e6b3c458b2
+        , d     = 0x0000002e28676514bd93fea11b62db0f6e324b18d
+        , q     = ECC.Point 0x3f9c90b71f6a1de20a2716f38ef1b5f98c757bd42 0x2ff0a5d266d447ef62d43fbca6c34c08c1ce35a40
+        , k     = 0x00000001233ae699883e74e7f4dfb5279ff22280a
+        , r     = 0x39de3cd2cf04145e522b8fba3f23e9218226e0860
+        , s     = 0x2af62bfb3cfa202e2342606ee5bb0934c3b0375b6
+        }
+    , VectorECDSA
+        { curve = ECC.getCurveByName ECC.SEC_t163k1
+        , msg   = i2osp 0xfbacfcce4688748406ddf5c3495021eef8fb399865b649eb2395a04a1ab28335da2c236d306fcc59f7b65ea931cf0139571e1538ede5688958c3ac69f47a285362f5ad201f89cc735b7b465408c2c41b310fc8908d0be45054df2a7351fae36b390e842f3b5cdd9ad832940df5b2d25c2ed43ce86eaf2508bcf401ae58bb1d47
+        , d     = 0x000000361dd088e3a6d3c910686c8dce57e5d4d8e
+        , q     = ECC.Point 0x064f905c1da9d7e9c32d81890ae6f30dcc7839d32 0x06f1faedb6d9032016d3b681e7cf69c29d29eb27b
+        , k     = 0x00000022f723e9f5da56d3d0837d5dca2f937395f
+        , r     = 0x374cdc8571083fecfbd4e25e1cd69ecc66b715f2d
+        , s     = 0x313b10949222929b2f20b15d446c27d6dcae3f086
+        }
     ]
 
 vectorToPrivate :: VectorECDSA -> ECDSA.PrivateKey
@@ -58,7 +88,7 @@
 doVerifyTest (i, vector) = testCase (show i) (True @=? actual)
   where actual = ECDSA.verify SHA1.hash (vectorToPublic vector) (ECDSA.Signature (r vector) (s vector)) (msg vector)
 
-ecdsaTests = testGroup "DSA"
+ecdsaTests = testGroup "ECDSA"
     [ testGroup "SHA1"
         [ testGroup "signature" $ map doSignatureTest (zip [0..] vectorsSHA1)
         , testGroup "verify" $ map doVerifyTest (zip [0..] vectorsSHA1)
diff --git a/Tests/Tests.hs b/Tests/Tests.hs
--- a/Tests/Tests.hs
+++ b/Tests/Tests.hs
@@ -175,8 +175,8 @@
     ]
 
 main = defaultMain
-    [ asymEncryptionTests
+    [ testGroup "KATs" katTests
+    , asymEncryptionTests
     , asymSignatureTests
     , asymOtherTests
-    , testGroup "KATs" katTests
     ]
diff --git a/crypto-pubkey.cabal b/crypto-pubkey.cabal
--- a/crypto-pubkey.cabal
+++ b/crypto-pubkey.cabal
@@ -1,5 +1,5 @@
 Name:                crypto-pubkey
-Version:             0.2.6
+Version:             0.2.7
 Description:
     Public Key cryptography
     .
@@ -14,7 +14,7 @@
 Synopsis:            Public Key cryptography
 Category:            Cryptography
 Build-Type:          Simple
-Homepage:            http://github.com/vincenthz/hs-crypto-pubkey
+Homepage:            https://github.com/vincenthz/hs-crypto-pubkey
 Cabal-Version:       >=1.8
 Extra-Source-Files:  Tests/*.hs
                      Tests/KAT/*.hs
@@ -80,4 +80,4 @@
 
 source-repository head
   type:     git
-  location: git://github.com/vincenthz/hs-crypto-pubkey
+  location: https://github.com/vincenthz/hs-crypto-pubkey