diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,18 @@
 # CHANGELOG for crypton
 
+## 1.1.5
+
+* fix(aead): reject undersized tags
+  [#80](https://github.com/kazu-yamamoto/crypton/pull/80)
+* fix(aes): refuse a zero-length AES-GCM IV
+  [#79](https://github.com/kazu-yamamoto/crypton/pull/79)
+* fix(p256): prevent crashes when validating valid points
+  [#78](https://github.com/kazu-yamamoto/crypton/pull/78)
+* feat(asn1): add SHA-3 HashAlgorithmASN1 instances for PKCS#1 v1.5
+  [#77](https://github.com/kazu-yamamoto/crypton/pull/77)
+* OCB3 conformance
+  [#76](https://github.com/kazu-yamamoto/crypton/pull/76)
+
 ## 1.1.4
 
 * Generic instance for RSA PublicKey and PrivateKey
diff --git a/Crypto/Cipher/AES.hs b/Crypto/Cipher/AES.hs
--- a/Crypto/Cipher/AES.hs
+++ b/Crypto/Cipher/AES.hs
@@ -55,7 +55,7 @@
     ; cbcEncrypt (CSTR aes) (IV iv) = encryptCBC aes (IV iv) \
     ; cbcDecrypt (CSTR aes) (IV iv) = decryptCBC aes (IV iv) \
     ; ctrCombine (CSTR aes) (IV iv) = encryptCTR aes (IV iv) \
-    ; aeadInit AEAD_GCM (CSTR aes) iv = CryptoPassed $ AEAD (gcmMode aes) (gcmInit aes iv) \
+    ; aeadInit AEAD_GCM (CSTR aes) iv = gcmAeadInit aes iv \
     ; aeadInit AEAD_OCB (CSTR aes) iv = CryptoPassed $ AEAD (ocbMode aes) (ocbInit aes iv) \
     ; aeadInit (AEAD_CCM n m l) (CSTR aes) iv = AEAD (ccmMode aes) <$> ccmInit aes iv n m l \
     ; aeadInit _        _          _  = CryptoFailed CryptoError_AEADModeNotSupported \
diff --git a/Crypto/Cipher/AES/Primitive.hs b/Crypto/Cipher/AES/Primitive.hs
--- a/Crypto/Cipher/AES/Primitive.hs
+++ b/Crypto/Cipher/AES/Primitive.hs
@@ -42,10 +42,13 @@
     -- * Incremental GCM
     gcmMode,
     gcmInit,
+    gcmAeadInit,
 
     -- * Incremental OCB
     ocbMode,
+    ocbModeWithTagLength,
     ocbInit,
+    ocbInitWithTagLength,
 
     -- * CCM
     ccmMode,
@@ -82,7 +85,7 @@
     cbcEncrypt = encryptCBC
     cbcDecrypt = decryptCBC
     ctrCombine = encryptCTR
-    aeadInit AEAD_GCM aes iv = CryptoPassed $ AEAD (gcmMode aes) (gcmInit aes iv)
+    aeadInit AEAD_GCM aes iv = gcmAeadInit aes iv
     aeadInit AEAD_OCB aes iv = CryptoPassed $ AEAD (ocbMode aes) (ocbInit aes iv)
     aeadInit (AEAD_CCM n m l) aes iv = AEAD (ccmMode aes) <$> ccmInit aes iv n m l
     aeadInit _ _ _ = CryptoFailed CryptoError_AEADModeNotSupported
@@ -90,6 +93,15 @@
     xtsEncrypt = encryptXTS
     xtsDecrypt = decryptXTS
 
+-- | Create an AES AEAD context for GCM, refusing the zero-length IV that
+-- SP 800-38D 5.2.1.1 forbids: any length other than 96 bits is fed to
+-- GHASH, and for the empty IV that makes J0 the GHASH of the empty
+-- string, which leaks the authentication key.
+gcmAeadInit :: ByteArrayAccess iv => AES -> iv -> CryptoFailable (AEAD c)
+gcmAeadInit aes iv
+    | B.length iv == 0 = CryptoFailed CryptoError_IvSizeInvalid
+    | otherwise = CryptoPassed $ AEAD (gcmMode aes) (gcmInit aes iv)
+
 -- | Create an AES AEAD implementation for GCM
 gcmMode :: AES -> AEADModeImpl AESGCM
 gcmMode aes =
@@ -110,6 +122,15 @@
         , aeadImplFinalize = ocbFinish aes
         }
 
+ocbModeWithTagLength :: AES -> Int -> AEADModeImpl AESOCB
+ocbModeWithTagLength aes taglen =
+    AEADModeImpl
+        { aeadImplAppendHeader = ocbAppendAAD aes
+        , aeadImplEncrypt = ocbAppendEncrypt aes
+        , aeadImplDecrypt = ocbAppendDecrypt aes
+        , aeadImplFinalize = \ocb _ -> ocbFinish aes ocb taglen
+        }
+
 -- | Create an AES AEAD implementation for CCM
 ccmMode :: AES -> AEADModeImpl AESCCM
 ccmMode aes =
@@ -529,9 +550,36 @@
 ocbInit ctx iv = unsafeDoIO $ do
     sm <- B.alloc sizeOCB $ \ocbStPtr ->
         withKeyAndIV ctx iv $ \k v ->
-            c_aes_ocb_init (castPtr ocbStPtr) k v (fromIntegral $ B.length iv)
+            c_aes_ocb_init
+                (castPtr ocbStPtr)
+                k
+                v
+                (fromIntegral $ B.length iv)
+                16
     return $ AESOCB sm
 
+-- | initialize an OCB context with a fixed authentication tag length.
+--
+-- The tag length is expressed in bytes and must be in [0..16].
+-- The IV length must be in [1..15] bytes per RFC 7253.
+{-# NOINLINE ocbInitWithTagLength #-}
+ocbInitWithTagLength :: ByteArrayAccess iv => AES -> iv -> Int -> CryptoFailable AESOCB
+ocbInitWithTagLength ctx iv taglen
+    | taglen < 0 || taglen > 16 = CryptoFailed CryptoError_AuthenticationTagSizeInvalid
+    | ivlen < 1 || ivlen > 15 = CryptoFailed CryptoError_IvSizeInvalid
+    | otherwise = CryptoPassed $ unsafeDoIO $ do
+        sm <- B.alloc sizeOCB $ \ocbStPtr ->
+            withKeyAndIV ctx iv $ \k v ->
+                c_aes_ocb_init
+                    (castPtr ocbStPtr)
+                    k
+                    v
+                    (fromIntegral ivlen)
+                    (fromIntegral taglen)
+        return $ AESOCB sm
+  where
+    ivlen = B.length iv
+
 -- | append data which is going to just be authenticated to the OCB context.
 --
 -- need to happen after initialization and before appending encryption/decryption data.
@@ -722,7 +770,8 @@
     c_aes_gcm_finish :: CString -> Ptr AESGCM -> Ptr AES -> IO ()
 
 foreign import ccall "crypton_aes.h crypton_aes_ocb_init"
-    c_aes_ocb_init :: Ptr AESOCB -> Ptr AES -> Ptr Word8 -> CUInt -> IO ()
+    c_aes_ocb_init
+        :: Ptr AESOCB -> Ptr AES -> Ptr Word8 -> CUInt -> CUInt -> IO ()
 
 foreign import ccall "crypton_aes.h crypton_aes_ocb_aad"
     c_aes_ocb_aad :: Ptr AESOCB -> Ptr AES -> CString -> CUInt -> IO ()
diff --git a/Crypto/Cipher/Types/AEAD.hs b/Crypto/Cipher/Types/AEAD.hs
--- a/Crypto/Cipher/Types/AEAD.hs
+++ b/Crypto/Cipher/Types/AEAD.hs
@@ -69,7 +69,22 @@
     (output, aeadFinal) = aeadEncrypt aead input
     tag = aeadFinalize aeadFinal taglen
 
+-- | The shortest authentication tag any mode here produces, four bytes
+-- (@CCM_M4@).  Modes that truncate their tag -- GCM and OCB3 -- will
+-- compute one of whatever length they are asked for, down to nothing, so
+-- 'aeadSimpleDecrypt' refuses a shorter tag than this rather than
+-- authenticate fewer bytes than any supported mode ever emits.
+minimumTagLength :: Int
+minimumTagLength = 4
+
 -- | Simple AEAD decryptio.
+--
+-- The number of bytes compared is the length of @authTag@.  That is the
+-- caller's choice of tag length, so a caller reading a tag off the wire
+-- must check its length against the one it expects: passing an
+-- attacker-supplied tag straight in lets the attacker pick how much of it
+-- is verified.  Tags shorter than 'minimumTagLength' are rejected
+-- outright.
 aeadSimpleDecrypt
     :: (ByteArrayAccess aad, ByteArray ba)
     => AEAD a
@@ -83,6 +98,7 @@
     -> Maybe ba
     -- ^ Plaintext
 aeadSimpleDecrypt aeadIni header input authTag
+    | B.length authTag < minimumTagLength = Nothing
     | tag == authTag = Just output
     | otherwise = Nothing
   where
diff --git a/Crypto/KDF/BCryptPBKDF.hs b/Crypto/KDF/BCryptPBKDF.hs
--- a/Crypto/KDF/BCryptPBKDF.hs
+++ b/Crypto/KDF/BCryptPBKDF.hs
@@ -13,7 +13,7 @@
 )
 where
 
-import Control.Exception (finally)
+import qualified Control.Exception as E
 import Control.Monad (when)
 import qualified Crypto.Cipher.Blowfish.Box as Blowfish
 import qualified Crypto.Cipher.Blowfish.Primitive as Blowfish
@@ -187,4 +187,4 @@
 
 finallyErase :: ForeignPtr Word8 -> Int -> IO () -> IO ()
 finallyErase fp len action =
-    action `finally` withForeignPtr fp (\ptr -> memSet ptr 0 len)
+    action `E.finally` withForeignPtr fp (\ptr -> memSet ptr 0 len)
diff --git a/Crypto/Number/ModArithmetic.hs b/Crypto/Number/ModArithmetic.hs
--- a/Crypto/Number/ModArithmetic.hs
+++ b/Crypto/Number/ModArithmetic.hs
@@ -21,7 +21,7 @@
     squareRoot,
 ) where
 
-import Control.Exception (Exception, throw)
+import qualified Control.Exception as E
 import Crypto.Number.Basic
 import Crypto.Number.Compat
 
@@ -29,7 +29,7 @@
 data CoprimesAssertionError = CoprimesAssertionError
     deriving (Show)
 
-instance Exception CoprimesAssertionError
+instance E.Exception CoprimesAssertionError
 
 -- | Compute the modular exponentiation of base^exponent using
 -- algorithms design to avoid side channels and timing measurement
@@ -109,7 +109,7 @@
 inverseCoprimes :: Integer -> Integer -> Integer
 inverseCoprimes g m =
     case inverse g m of
-        Nothing -> throw CoprimesAssertionError
+        Nothing -> E.throw CoprimesAssertionError
         Just i -> i
 
 -- | Computes the Jacobi symbol (a/n).
@@ -148,7 +148,7 @@
 data ModulusAssertionError = ModulusAssertionError
     deriving (Show)
 
-instance Exception ModulusAssertionError
+instance E.Exception ModulusAssertionError
 
 -- | Modular square root of @g@ modulo a prime @p@.
 --
@@ -159,7 +159,7 @@
 -- parameters only.
 squareRoot :: Integer -> Integer -> Maybe Integer
 squareRoot p
-    | p < 2 = throw ModulusAssertionError
+    | p < 2 = E.throw ModulusAssertionError
     | otherwise =
         case p `divMod` 8 of
             (v, 3) -> method1 (2 * v + 1)
@@ -167,7 +167,7 @@
             (u, 5) -> method2 u
             (_, 1) -> tonelliShanks p
             (0, 2) -> \a -> Just (if even a then 0 else 1)
-            _ -> throw ModulusAssertionError
+            _ -> E.throw ModulusAssertionError
   where
     x `eqMod` y = (x - y) `mod` p == 0
 
@@ -202,7 +202,7 @@
                             (expFast aa s p)
                             (expFast n s p)
                             e
-                | otherwise -> throw ModulusAssertionError
+                | otherwise -> E.throw ModulusAssertionError
   where
     aa = a `mod` p
     p1 = p - 1
diff --git a/Crypto/PubKey/RSA/PKCS15.hs b/Crypto/PubKey/RSA/PKCS15.hs
--- a/Crypto/PubKey/RSA/PKCS15.hs
+++ b/Crypto/PubKey/RSA/PKCS15.hs
@@ -247,6 +247,90 @@
             , 0x04
             , 0x20
             ]
+instance HashAlgorithmASN1 SHA3_224 where
+    hashDigestASN1 =
+        addDigestPrefix
+            [ 0x30
+            , 0x2b
+            , 0x30
+            , 0x0b
+            , 0x06
+            , 0x09
+            , 0x60
+            , 0x86
+            , 0x48
+            , 0x01
+            , 0x65
+            , 0x03
+            , 0x04
+            , 0x02
+            , 0x07
+            , 0x04
+            , 0x1c
+            ]
+instance HashAlgorithmASN1 SHA3_256 where
+    hashDigestASN1 =
+        addDigestPrefix
+            [ 0x30
+            , 0x2f
+            , 0x30
+            , 0x0b
+            , 0x06
+            , 0x09
+            , 0x60
+            , 0x86
+            , 0x48
+            , 0x01
+            , 0x65
+            , 0x03
+            , 0x04
+            , 0x02
+            , 0x08
+            , 0x04
+            , 0x20
+            ]
+instance HashAlgorithmASN1 SHA3_384 where
+    hashDigestASN1 =
+        addDigestPrefix
+            [ 0x30
+            , 0x3f
+            , 0x30
+            , 0x0b
+            , 0x06
+            , 0x09
+            , 0x60
+            , 0x86
+            , 0x48
+            , 0x01
+            , 0x65
+            , 0x03
+            , 0x04
+            , 0x02
+            , 0x09
+            , 0x04
+            , 0x30
+            ]
+instance HashAlgorithmASN1 SHA3_512 where
+    hashDigestASN1 =
+        addDigestPrefix
+            [ 0x30
+            , 0x4f
+            , 0x30
+            , 0x0b
+            , 0x06
+            , 0x09
+            , 0x60
+            , 0x86
+            , 0x48
+            , 0x01
+            , 0x65
+            , 0x03
+            , 0x04
+            , 0x02
+            , 0x0a
+            , 0x04
+            , 0x40
+            ]
 instance HashAlgorithmASN1 RIPEMD160 where
     hashDigestASN1 =
         addDigestPrefix
@@ -283,7 +367,7 @@
 --   Start Sequence
 --     ,Start Sequence
 --       ,OID oid
---       ,Null
+--       ,optional parameters (Null for SHA-2, absent for SHA-3)
 --     ,End Sequence
 --     ,OctetString digest
 --   ,End Sequence
diff --git a/Crypto/Random/Entropy/Unix.hs b/Crypto/Random/Entropy/Unix.hs
--- a/Crypto/Random/Entropy/Unix.hs
+++ b/Crypto/Random/Entropy/Unix.hs
@@ -11,10 +11,11 @@
     DevURandom,
 ) where
 
-import Control.Exception as E
+import qualified Control.Exception as E
 import Crypto.Random.Entropy.Source
 import Data.Word (Word8)
 import Foreign.Ptr
+import qualified System.IO.Error as E
 
 -- import System.Posix.Types (Fd)
 import System.IO
@@ -49,7 +50,7 @@
 
 openDev :: String -> IO (Maybe H)
 openDev filepath =
-    (Just `fmap` openAndNoBuffering) `E.catch` \(_ :: IOException) -> return Nothing
+    (Just `fmap` openAndNoBuffering) `E.catchIOError` \_ -> return Nothing
   where
     openAndNoBuffering = do
         h <- openBinaryFile filepath ReadMode
@@ -64,14 +65,14 @@
             Just fd -> f fd `E.finally` closeDev fd
 
 closeDev :: H -> IO ()
-closeDev h = hClose h `E.catch` \(_ :: IOException) -> return ()
+closeDev h = hClose h `E.catchIOError` \_ -> return ()
 
 gatherDevEntropy :: H -> Ptr Word8 -> Int -> IO Int
 gatherDevEntropy h ptr sz =
     (fromIntegral `fmap` hGetBufSome h ptr (fromIntegral sz))
-        `E.catch` \(_ :: IOException) -> return 0
+        `E.catchIOError` \_ -> return 0
 
 gatherDevEntropyNonBlock :: H -> Ptr Word8 -> Int -> IO Int
 gatherDevEntropyNonBlock h ptr sz =
     (fromIntegral `fmap` hGetBufNonBlocking h ptr (fromIntegral sz))
-        `E.catch` \(_ :: IOException) -> return 0
+        `E.catchIOError` \_ -> return 0
diff --git a/cbits/crypton_aes.c b/cbits/crypton_aes.c
--- a/cbits/crypton_aes.c
+++ b/cbits/crypton_aes.c
@@ -655,7 +655,7 @@
 #undef L_CACHED
 }
 
-void crypton_aes_ocb_init(aes_ocb *ocb, aes_key *key, uint8_t *iv, uint32_t len)
+void crypton_aes_ocb_init(aes_ocb *ocb, aes_key *key, uint8_t *iv, uint32_t len, uint32_t taglen)
 {
 	block128 tmp, nonce, ktop;
 	unsigned char stretch[24];
@@ -665,6 +665,9 @@
 	if (len > 15) {
 		len = 15;
 	}
+	if (taglen > 16) {
+		taglen = 16;
+	}
 
 	/* create L*, and L$,L0,L1,L2,L3 */
 	block128_zero(&tmp);
@@ -678,9 +681,11 @@
 
 	/* create strech from the nonce */
 	block128_zero(&nonce);
-	memcpy(nonce.b + 4, iv, 12);
-	nonce.b[0] = (unsigned char)(((16 * 8) % 128) << 1);
-	nonce.b[16-12-1] |= 0x01;
+	if (len > 0) {
+		memcpy(nonce.b + (16 - len), iv, len);
+		nonce.b[16 - len - 1] |= 0x01;
+	}
+	nonce.b[0] |= (unsigned char)(((taglen * 8) % 128) << 1);
 	bottom = nonce.b[15] & 0x3F;
 	nonce.b[15] &= 0xC0;
 	crypton_aes_encrypt_block(&ktop, key, &nonce);
diff --git a/cbits/crypton_aes.h b/cbits/crypton_aes.h
--- a/cbits/crypton_aes.h
+++ b/cbits/crypton_aes.h
@@ -109,7 +109,7 @@
 void crypton_aes_gcm_decrypt(uint8_t *output, aes_gcm *gcm, aes_key *key, uint8_t *input, uint32_t length);
 void crypton_aes_gcm_finish(uint8_t *tag, aes_gcm *gcm, aes_key *key);
 
-void crypton_aes_ocb_init(aes_ocb *ocb, aes_key *key, uint8_t *iv, uint32_t len);
+void crypton_aes_ocb_init(aes_ocb *ocb, aes_key *key, uint8_t *iv, uint32_t len, uint32_t taglen);
 void crypton_aes_ocb_aad(aes_ocb *ocb, aes_key *key, uint8_t *input, uint32_t length);
 void crypton_aes_ocb_encrypt(uint8_t *output, aes_ocb *ocb, aes_key *key, uint8_t *input, uint32_t length);
 void crypton_aes_ocb_decrypt(uint8_t *output, aes_ocb *ocb, aes_key *key, uint8_t *input, uint32_t length);
diff --git a/cbits/p256/p256.c b/cbits/p256/p256.c
--- a/cbits/p256/p256.c
+++ b/cbits/p256/p256.c
@@ -104,7 +104,9 @@
   borrow += top_c;
   borrow -= top_a;
   top_c = (crypton_p256_digit)borrow;
-  assert((borrow >> P256_BITSPERDIGIT) == 0);
+  /* A borrow out is a legitimate outcome: the quotient estimate in
+     crypton_p256_modmul can exceed the true quotient by one.  Report it in
+     the returned top digit (all ones) and let the caller correct. */
   return top_c;
 }
 
@@ -177,6 +179,13 @@
 
     // Subtract reducer from top | tmp.
     top = subTop(top_reducer, reducer, top, tmp + i);
+
+    // The quotient estimate above can exceed the true quotient by one --
+    // with 64-bit digits, whenever the low half of top is zero and the
+    // digits below it are small -- and the subtraction then borrows.  The
+    // deficit is always less than MOD, so adding MOD back once restores
+    // the invariant.
+    top = addM(MOD, top, tmp + i, 0 - (top >> (P256_BITSPERDIGIT - 1)));
 
     // top is now either 0 or 1. Make it 0, fixed-timing.
     assert(top <= 1);
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:            1.1.4
+version:            1.1.5
 license:            BSD3
 license-file:       LICENSE
 copyright:          Vincent Hanquez <vincent@snarc.org>
diff --git a/tests/BCrypt.hs b/tests/BCrypt.hs
--- a/tests/BCrypt.hs
+++ b/tests/BCrypt.hs
@@ -34,7 +34,7 @@
           \\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\
           \\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\
           \\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\
-          \\x00\x01\x02\x03\x04\x05" -- chars after 72 are ignored as usual
+          \chars after 72 are ignored as usual"
         )
     ,
         ( "$2a$05$/OK.fbVrR/bpIqNJ5ianF.R9xrDjiycxMbQE2bp.vgqlYpW5wx2yy"
diff --git a/tests/KAT_AES.hs b/tests/KAT_AES.hs
--- a/tests/KAT_AES.hs
+++ b/tests/KAT_AES.hs
@@ -5,6 +5,8 @@
 import BlockCipher
 import qualified Crypto.Cipher.AES as AES
 import Crypto.Cipher.Types
+import Crypto.Error
+import qualified Data.ByteArray as BA
 import qualified Data.ByteString as B
 import Data.Maybe
 import Imports
@@ -113,12 +115,55 @@
         , kat_AEAD = map toKatGCM KATGCM.vectors_aes256_enc
         }
 
+-- SP 800-38D 5.2.1.1: 1 <= len(IV) <= 2^64 - 1.  A zero-length IV makes
+-- J0 the GHASH of the empty string, which leaks the authentication key.
+aeadIVLengthTests :: TestTree
+aeadIVLengthTests =
+    testGroup
+        "AEAD IV length"
+        [ testCase "96-bit IV accepted" $
+            True @=? isRight (initWith (B.replicate 12 0))
+        , testCase "8-bit IV accepted" $
+            True @=? isRight (initWith (B.replicate 1 0))
+        , testCase "empty IV rejected" $
+            Left CryptoError_IvSizeInvalid @=? initWith B.empty
+        ]
+  where
+    ctx = throwCryptoError (cipherInit (B.replicate 16 0)) :: AES.AES128
+    initWith iv =
+        eitherCryptoError (() <$ aeadInit AEAD_GCM ctx (iv :: ByteString))
+    isRight = either (const False) (const True)
+
+aeadTagLengthTests :: TestTree
+aeadTagLengthTests =
+    testGroup
+        "AEAD tag length"
+        [ testCase "full tag verifies" $ Just message @=? openWith fullTag
+        , testCase "empty tag rejected" $ Nothing @=? openWith B.empty
+        , testCase "1-byte tag rejected" $ Nothing @=? openWith (B.take 1 fullTag)
+        , testCase "3-byte tag rejected" $ Nothing @=? openWith (B.take 3 fullTag)
+        , testCase "wrong tag rejected" $
+            Nothing @=? openWith (B.map (+ 1) fullTag)
+        ]
+  where
+    key = B.replicate 16 0
+    iv = B.replicate 12 0
+    aad = "additional data" :: ByteString
+    message = "authenticated message" :: ByteString
+    ctx = throwCryptoError (cipherInit key) :: AES.AES128
+    aead = throwCryptoError (aeadInit AEAD_GCM ctx iv)
+    (AuthTag tag, ciphertext) = aeadSimpleEncrypt aead aad message 16
+    fullTag = BA.convert tag :: ByteString
+    openWith t = aeadSimpleDecrypt aead aad ciphertext (AuthTag (BA.convert t))
+
 tests =
     testGroup
         "AES"
         [ testBlockCipher kats128 (undefined :: AES.AES128)
         , testBlockCipher kats192 (undefined :: AES.AES192)
         , testBlockCipher kats256 (undefined :: AES.AES256)
+        , aeadIVLengthTests
+        , aeadTagLengthTests
         {-
             , testProperty "genCtr" $ \(key, iv1) ->
                 let (bs1, iv2)    = AES.genCounter key iv1 32
diff --git a/tests/KAT_AES/KATOCB3.hs b/tests/KAT_AES/KATOCB3.hs
--- a/tests/KAT_AES/KATOCB3.hs
+++ b/tests/KAT_AES/KATOCB3.hs
@@ -18,7 +18,47 @@
 
 key1 = "\x00\x01\x02\x03\x04\x05\x06\x07\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f"
 nonce1 = "\x00\x01\x02\x03\x04\x05\x06\x07\x08\x09\x0a\x0b"
+key2 = "\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00"
+nonce2 = "\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x0d"
+nonce_rfc7253_00 = "\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x00"
+nonce_rfc7253_01 = "\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x01"
+nonce_rfc7253_02 = "\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x02"
+nonce_rfc7253_03 = "\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x03"
+nonce_rfc7253_04 = "\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x04"
+nonce_rfc7253_05 = "\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x05"
+nonce_rfc7253_06 = "\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x06"
+nonce_rfc7253_07 = "\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x07"
+nonce_rfc7253_08 = "\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x08"
+nonce_rfc7253_09 = "\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x09"
+nonce_rfc7253_0a = "\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x0a"
+nonce_rfc7253_0b = "\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x0b"
+nonce_rfc7253_0c = "\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x0c"
+nonce_rfc7253_0d = "\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x0d"
+nonce_rfc7253_0e = "\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x0e"
+nonce_rfc7253_0f = "\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x0f"
+nonce_dkg_120_00 = "\xee\xdd\xcc\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x00"
+nonce_dkg_120_01 = "\xee\xdd\xcc\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x01"
+nonce_dkg_120_02 = "\xee\xdd\xcc\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x02"
+nonce_dkg_120_03 = "\xee\xdd\xcc\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x03"
+nonce_dkg_120_04 = "\xee\xdd\xcc\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x04"
+nonce_dkg_120_05 = "\xee\xdd\xcc\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x05"
+nonce_dkg_120_06 = "\xee\xdd\xcc\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x06"
+nonce_dkg_120_07 = "\xee\xdd\xcc\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x07"
+nonce_dkg_120_08 = "\xee\xdd\xcc\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x08"
+nonce_dkg_120_09 = "\xee\xdd\xcc\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x09"
+nonce_dkg_120_0a = "\xee\xdd\xcc\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x0a"
+nonce_dkg_120_0b = "\xee\xdd\xcc\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x0b"
+nonce_dkg_120_0c = "\xee\xdd\xcc\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x0c"
+nonce_dkg_120_0d = "\xee\xdd\xcc\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x0d"
+nonce_dkg_120_0e = "\xee\xdd\xcc\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x0e"
+nonce_dkg_120_0f = "\xee\xdd\xcc\xbb\xaa\x99\x88\x77\x66\x55\x44\x33\x22\x11\x0f"
 
+bytes8 = "\x00\x01\x02\x03\x04\x05\x06\x07"
+bytes16 = "\x00\x01\x02\x03\x04\x05\x06\x07\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f"
+bytes24 = "\x00\x01\x02\x03\x04\x05\x06\x07\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17"
+bytes32 = "\x00\x01\x02\x03\x04\x05\x06\x07\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19\x1a\x1b\x1c\x1d\x1e\x1f"
+bytes40 = "\x00\x01\x02\x03\x04\x05\x06\x07\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19\x1a\x1b\x1c\x1d\x1e\x1f\x20\x21\x22\x23\x24\x25\x26\x27"
+
 vectors_aes128_enc :: [KATOCB3]
 vectors_aes128_enc =
     [
@@ -66,4 +106,289 @@
         , 16
         , "\x77\x6c\x99\x24\xd6\x72\x3a\x1f\xc4\x52\x45\x32\xac\x3e\x5b\xeb"
         )
+    {- Disabled: 96-bit tag vector
+    , ( key2
+      , nonce2
+      , "\x00\x01\x02\x03\x04\x05\x06\x07\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19\x1a\x1b\x1c\x1d\x1e\x1f\x20\x21\x22\x23\x24\x25\x26\x27"
+      , "\x00\x01\x02\x03\x04\x05\x06\x07\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19\x1a\x1b\x1c\x1d\x1e\x1f\x20\x21\x22\x23\x24\x25\x26\x27"
+      , "\x17\x92\xa4\xe3\x1e\x07\x55\xfb\x03\xe3\x1b\x22\x11\x6e\x6c\x2d\xdf\x9e\xfd\x6e\x33\xd5\x36\xf1\xa0\x12\x4b\x0a\x55\xba\xe8\x84\xed\x93\x48\x15\x29\xc7\x6b\x6a"
+      , 12
+      , "\xd0\xc5\x15\xf4\xd1\xcd\xd4\xfd\xac\x4f\x02\xaa"
+      )
+    -}
+    ] ++ vectors_rfc7253_aes128_tag128
+        ++ vectors_dkg_nonce120_aes128
+
+vectors_rfc7253_aes128_tag128 :: [KATOCB3]
+vectors_rfc7253_aes128_tag128 =
+    [ ( key1
+      , nonce_rfc7253_00
+      , ""
+      , ""
+      , ""
+      , 16
+      , "\x78\x54\x07\xbf\xff\xc8\xad\x9e\xdc\xc5\x52\x0a\xc9\x11\x1e\xe6"
+      )
+    , ( key1
+      , nonce_rfc7253_01
+      , bytes8
+      , bytes8
+      , "\x68\x20\xb3\x65\x7b\x6f\x61\x5a"
+      , 16
+      , "\x57\x25\xbd\xa0\xd3\xb4\xeb\x3a\x25\x7c\x9a\xf1\xf8\xf0\x30\x09"
+      )
+    , ( key1
+      , nonce_rfc7253_02
+      , bytes8
+      , ""
+      , ""
+      , 16
+      , "\x81\x01\x7f\x82\x03\xf0\x81\x27\x71\x52\xfa\xde\x69\x4a\x0a\x00"
+      )
+    , ( key1
+      , nonce_rfc7253_03
+      , ""
+      , bytes8
+      , "\x45\xdd\x69\xf8\xf5\xaa\xe7\x24"
+      , 16
+      , "\x14\x05\x4c\xd1\xf3\x5d\x82\x76\x0b\x2c\xd0\x0d\x2f\x99\xbf\xa9"
+      )
+    , ( key1
+      , nonce_rfc7253_04
+      , bytes16
+      , bytes16
+      , "\x57\x1d\x53\x5b\x60\xb2\x77\x18\x8b\xe5\x14\x71\x70\xa9\xa2\x2c"
+      , 16
+      , "\x3a\xd7\xa4\xff\x38\x35\xb8\xc5\x70\x1c\x1c\xce\xc8\xfc\x33\x58"
+      )
+    , ( key1
+      , nonce_rfc7253_05
+      , bytes16
+      , ""
+      , ""
+      , 16
+      , "\x8c\xf7\x61\xb6\x90\x2e\xf7\x64\x46\x2a\xd8\x64\x98\xca\x6b\x97"
+      )
+    , ( key1
+      , nonce_rfc7253_06
+      , ""
+      , bytes16
+      , "\x5c\xe8\x8e\xc2\xe0\x69\x27\x06\xa9\x15\xc0\x0a\xeb\x8b\x23\x96"
+      , 16
+      , "\xf4\x0e\x1c\x74\x3f\x52\x43\x6b\xdf\x06\xd8\xfa\x1e\xca\x34\x3d"
+      )
+    , ( key1
+      , nonce_rfc7253_07
+      , bytes24
+      , bytes24
+      , "\x1c\xa2\x20\x73\x08\xc8\x7c\x01\x07\x56\x10\x4d\x88\x40\xce\x19\x52\xf0\x96\x73\xa4\x48\xa1\x22"
+      , 16
+      , "\xc9\x2c\x62\x24\x10\x51\xf5\x73\x56\xd7\xf3\xc9\x0b\xb0\xe0\x7f"
+      )
+    , ( key1
+      , nonce_rfc7253_08
+      , bytes24
+      , ""
+      , ""
+      , 16
+      , "\x6d\xc2\x25\xa0\x71\xfc\x1b\x9f\x7c\x69\xf9\x3b\x0f\x1e\x10\xde"
+      )
+    , ( key1
+      , nonce_rfc7253_09
+      , ""
+      , bytes24
+      , "\x22\x1b\xd0\xde\x7f\xa6\xfe\x99\x3e\xcc\xd7\x69\x46\x0a\x0a\xf2\xd6\xcd\xed\x0c\x39\x5b\x1c\x3c"
+      , 16
+      , "\xe7\x25\xf3\x24\x94\xb9\xf9\x14\xd8\x5c\x0b\x1e\xb3\x83\x57\xff"
+      )
+    , ( key1
+      , nonce_rfc7253_0a
+      , bytes32
+      , bytes32
+      , "\xbd\x6f\x6c\x49\x62\x01\xc6\x92\x96\xc1\x1e\xfd\x13\x8a\x46\x7a\xbd\x3c\x70\x79\x24\xb9\x64\xde\xaf\xfc\x40\x31\x9a\xf5\xa4\x85"
+      , 16
+      , "\x40\xfb\xba\x18\x6c\x55\x53\xc6\x8a\xd9\xf5\x92\xa7\x9a\x42\x40"
+      )
+    , ( key1
+      , nonce_rfc7253_0b
+      , bytes32
+      , ""
+      , ""
+      , 16
+      , "\xfe\x80\x69\x0b\xee\x8a\x48\x5d\x11\xf3\x29\x65\xbc\x9d\x2a\x32"
+      )
+    , ( key1
+      , nonce_rfc7253_0c
+      , ""
+      , bytes32
+      , "\x29\x42\xbf\xc7\x73\xbd\xa2\x3c\xab\xc6\xac\xfd\x9b\xfd\x58\x35\xbd\x30\x0f\x09\x73\x79\x2e\xf4\x60\x40\xc5\x3f\x14\x32\xbc\xdf"
+      , 16
+      , "\xb5\xe1\xdd\xe3\xbc\x18\xa5\xf8\x40\xb5\x2e\x65\x34\x44\xd5\xdf"
+      )
+    , ( key1
+      , nonce_rfc7253_0d
+      , bytes40
+      , bytes40
+      , "\xd5\xca\x91\x74\x84\x10\xc1\x75\x1f\xf8\xa2\xf6\x18\x25\x5b\x68\xa0\xa1\x2e\x09\x3f\xf4\x54\x60\x6e\x59\xf9\xc1\xd0\xdd\xc5\x4b\x65\xe8\x62\x8e\x56\x8b\xad\x7a"
+      , 16
+      , "\xed\x07\xba\x06\xa4\xa6\x94\x83\xa7\x03\x54\x90\xc5\x76\x9e\x60"
+      )
+    , ( key1
+      , nonce_rfc7253_0e
+      , bytes40
+      , ""
+      , ""
+      , 16
+      , "\xc5\xcd\x9d\x18\x50\xc1\x41\xe3\x58\x64\x99\x94\xee\x70\x1b\x68"
+      )
+    , ( key1
+      , nonce_rfc7253_0f
+      , ""
+      , bytes40
+      , "\x44\x12\x92\x34\x93\xc5\x7d\x5d\xe0\xd7\x00\xf7\x53\xcc\xe0\xd1\xd2\xd9\x50\x60\x12\x2e\x9f\x15\xa5\xdd\xbf\xc5\x78\x7e\x50\xb5\xcc\x55\xee\x50\x7b\xcb\x08\x4e"
+      , 16
+      , "\x47\x9a\xd3\x63\xac\x36\x6b\x95\xa9\x8c\xa5\xf3\x00\x0b\x14\x79"
+      )
+    ]
+
+vectors_dkg_nonce120_aes128 :: [KATOCB3]
+vectors_dkg_nonce120_aes128 =
+    [ ( key1
+      , nonce_dkg_120_00
+      , ""
+      , ""
+      , ""
+      , 16
+      , "\x75\x2a\xcd\x21\x32\xc4\x1e\x02\x0e\x41\xfb\x22\x3e\xfd\x77\xb6"
+      )
+    , ( key1
+      , nonce_dkg_120_01
+      , bytes8
+      , bytes8
+      , "\x20\x1f\xe4\xd8\x9e\xa7\xbd\x1e"
+      , 16
+      , "\xb5\xb1\x57\x7d\xb1\x62\x83\xb8\xae\xd1\x71\x5a\xd6\xbe\x51\x49"
+      )
+    , ( key1
+      , nonce_dkg_120_02
+      , bytes8
+      , ""
+      , ""
+      , 16
+      , "\x71\x09\x60\xb9\xee\x00\xb8\xf4\x4d\x2e\x81\x20\xaa\xba\x63\xae"
+      )
+    , ( key1
+      , nonce_dkg_120_03
+      , ""
+      , bytes8
+      , "\x08\x4e\x86\x95\x70\x19\x4b\xd2"
+      , 16
+      , "\x50\x32\xfe\x9e\x53\x28\xe4\x5d\x50\x7e\x74\xf3\x36\x6e\x20\xd2"
+      )
+    , ( key1
+      , nonce_dkg_120_04
+      , bytes16
+      , bytes16
+      , "\x96\x76\xee\x37\xfd\x64\x5c\x07\xc0\xd4\xf7\x0a\xab\xf6\x86\x68"
+      , 16
+      , "\x8e\x39\xb2\xfb\x3f\xc4\xff\x30\xdc\xd1\x82\x7b\x36\xa2\x98\xd3"
+      )
+    , ( key1
+      , nonce_dkg_120_05
+      , bytes16
+      , ""
+      , ""
+      , 16
+      , "\x9d\x51\x0f\x56\xed\xf7\x2f\xfa\x34\x96\x9b\xce\xf9\x1e\x6d\xe9"
+      )
+    , ( key1
+      , nonce_dkg_120_06
+      , ""
+      , bytes16
+      , "\xd5\xe1\x5a\xa1\xd2\x32\xab\x57\xf2\x34\x36\x6d\xff\xb2\x55\x74"
+      , 16
+      , "\xa3\x63\x6a\x5f\x3e\x34\x33\xea\x45\x90\xcb\xf4\xf9\xac\x1f\x4d"
+      )
+    , ( key1
+      , nonce_dkg_120_07
+      , bytes24
+      , bytes24
+      , "\x1c\x4b\x67\x77\xb7\xf1\x37\xc3\x09\x71\xa9\x3d\xe3\xc5\x6c\xc7\x35\x68\x6a\x6f\x77\x03\x14\x2f"
+      , 16
+      , "\xab\x8a\xcc\x98\x7c\x14\x06\xdf\xf9\x62\x73\xc5\x37\x6e\x62\x10"
+      )
+    , ( key1
+      , nonce_dkg_120_08
+      , bytes24
+      , ""
+      , ""
+      , 16
+      , "\x96\xe6\x70\xc0\x23\x8f\xb9\x69\xb7\xac\xe4\xab\xaf\x74\x38\xc7"
+      )
+    , ( key1
+      , nonce_dkg_120_09
+      , ""
+      , bytes24
+      , "\x12\x90\xa6\x86\xd8\x25\xf7\x12\xe5\x94\xbe\x40\x39\xc0\x4d\x3e\x44\xf7\xd1\x34\x2b\x84\xff\xca"
+      , 16
+      , "\xd6\x8b\xbd\xfa\x04\xb5\x80\xea\x9a\x01\xe2\xf4\x56\x53\x99\xc3"
+      )
+    , ( key1
+      , nonce_dkg_120_0a
+      , bytes32
+      , bytes32
+      , "\xfb\xdf\xc1\x1f\x74\x92\x17\xbb\x7f\xae\x5d\x40\x36\xb8\xf2\x28\x03\x71\x2e\xff\x9e\xf9\x43\x42\xfe\x1b\x68\x49\x68\xd0\xe3\xe3"
+      , 16
+      , "\x81\xa2\x77\xda\xab\x83\x57\x94\x06\xa0\x1e\x26\x75\xa0\x82\xc9"
+      )
+    , ( key1
+      , nonce_dkg_120_0b
+      , bytes32
+      , ""
+      , ""
+      , 16
+      , "\x90\xcd\xa8\xa0\x51\x61\xd2\x87\x33\x61\x37\x4b\x76\xf9\x54\x30"
+      )
+    , ( key1
+      , nonce_dkg_120_0c
+      , ""
+      , bytes32
+      , "\xd1\x32\x0a\xf4\xb6\xff\x8a\xfe\xec\xee\x79\x21\x39\x5d\x4e\x86\x92\x71\x77\x53\xee\x15\xf5\x03\x8e\xb6\x74\xda\x43\xd6\xea\x8d"
+      , 16
+      , "\xbe\x78\x31\xe7\x23\xbe\x47\x1f\x62\xd9\xe7\xf4\x9a\x7d\x3b\x32"
+      )
+    , ( key1
+      , nonce_dkg_120_0d
+      , bytes40
+      , bytes40
+      , "\x5c\x79\xf1\xc4\xb9\xa2\x04\xed\x33\x23\x61\x6d\x57\x6f\xc5\x00\xe4\xa7\x19\x39\xf0\x3a\x3c\x3d\xe2\xc0\x97\xaf\x2c\x6c\x81\xdc\x3f\x03\x09\xe7\x60\x82\xb1\xf5"
+      , 16
+      , "\x0f\xf8\x52\x29\x59\xff\xe4\x1f\x37\xef\x50\x7e\x90\x76\xd3\x2c"
+      )
+    , ( key1
+      , nonce_dkg_120_0e
+      , bytes40
+      , ""
+      , ""
+      , 16
+      , "\x3b\xf1\x58\xb7\xde\x76\xc5\x15\x1e\xf6\x08\x6a\x82\x5d\x0c\xc4"
+      )
+    , ( key1
+      , nonce_dkg_120_0f
+      , ""
+      , bytes40
+      , "\x34\xda\x59\xd2\xeb\x08\xf4\x78\x22\xd4\x8c\x85\xb6\xa1\xd2\x36\x94\xe1\xd3\xde\x68\x0d\x61\x6d\x7b\x1b\x59\x47\x2c\x13\xe3\x69\xc6\x8d\xca\x69\x9d\xa1\x68\x6a"
+      , 16
+      , "\x33\x9d\x54\x52\x80\x36\x32\x81\x0b\x08\x40\xe6\x80\x4a\xb0\x20"
+      )
+    {- Disabled: 96-bit tag vector
+    , ( key2
+      , nonce_dkg_120_0d
+      , bytes40
+      , bytes40
+      , "\x07\xe9\x03\xbf\xc4\x95\x52\x41\x1a\xbc\x86\x5f\x5e\xce\x60\xf6\xfa\xd1\xf5\xa9\xf1\x4d\x30\x70\xfa\x2f\x13\x08\xa5\x63\x20\x7f\xfe\x14\xc1\xee\xa4\x4b\x22\x05"
+      , 12
+      , "\x9c\x74\x84\x31\x9d\x8a\x2c\x53\xc2\x36\xa7\xb3"
+      )
+    -}
     ]
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
@@ -73,6 +73,14 @@
 xR = 0x72b13dd4354b6b81745195e98cc5ba6970349191ac476bd4553cf35a545a067e
 yR = 0x8d585cbb2e1327d75241a8a122d7620dc33b13315aa5c9d46d013011744ac264
 
+-- Two points on the curve whose validation reduces a product whose top
+-- digit has a zero low half: x = 2^96, and an x with a repeating bit
+-- pattern.  Wycheproof ecdh_secp256r1_ecpoint tcId 74 and 93.
+xU = 0x0000000000000000000000000000000000000001000000000000000000000000
+yU = 0x7d12de58d54423eb85ae8d157ae416fb004a7eb522ac1b67047ef3cdf9acdc3f
+xV = 0x8000003ffffff0000007fffffe000000ffffffc000001ffffff8000003fffffc
+yV = 0x0c3527bd081c1c07b313bc1a0c3f845fb2fe22557699ccc8f1354e61a27b7f88
+
 tests =
     testGroup
         "P256"
@@ -142,6 +150,12 @@
             , testCase "valid-point-1" $ casePointIsValid (xS, yS)
             , testCase "valid-point-2" $ casePointIsValid (xR, yR)
             , testCase "valid-point-3" $ casePointIsValid (xT, yT)
+            , -- The quotient estimate in crypton_p256_modmul can exceed the
+              -- true quotient, and the resulting borrow used to abort the
+              -- process on an assertion inside the reduction rather than
+              -- being corrected.  Both points below are on the curve.
+              testCase "valid-point-reduction-1" $ casePointIsValid (xU, yU)
+            , testCase "valid-point-reduction-2" $ casePointIsValid (xV, yV)
             , testCase "point-add-1" $
                 let s = P256.pointFromIntegers (xS, yS)
                     t = P256.pointFromIntegers (xT, yT)
