diff --git a/mythril/laser/ethereum/instructions.py b/mythril/laser/ethereum/instructions.py
index 5d2b9e93..b0c63a3c 100644
--- a/mythril/laser/ethereum/instructions.py
+++ b/mythril/laser/ethereum/instructions.py
@@ -31,6 +31,7 @@ from mythril.laser.smt import symbol_factory
 
 import mythril.laser.ethereum.util as helper
 from mythril.laser.ethereum import util
+from mythril.laser.ethereum.keccak_function_manager import keccak_function_manager
 from mythril.laser.ethereum.call import get_call_parameters, native_call
 from mythril.laser.ethereum.evm_exceptions import (
     VmException,
@@ -947,33 +948,10 @@ class Instruction:
         else:
             # length is 0; this only matters for input of the BitVecFuncVal
             data = symbol_factory.BitVecVal(0, 1)
-
-        if data.symbolic:
-
-            annotations = set()  # type: Set[Any]
-
-            for b in state.memory[index : index + length]:
-                if isinstance(b, BitVec):
-                    annotations = annotations.union(b.annotations)
-
-            argument_hash = hash(state.memory[index])
-            result = symbol_factory.BitVecFuncSym(
-                "KECCAC[invhash({})]".format(hash(argument_hash)),
-                "keccak256",
-                256,
-                input_=data,
-                annotations=annotations,
-            )
-            log.debug("Created BitVecFunc hash.")
-
-        else:
-            keccak = utils.sha3(data.value.to_bytes(length, byteorder="big"))
-            result = symbol_factory.BitVecFuncVal(
-                util.concrete_int_from_bytes(keccak, 0), "keccak256", 256, input_=data
-            )
-            log.debug("Computed SHA3 Hash: " + str(binascii.hexlify(keccak)))
-
+        result, constraints = keccak_function_manager.create_keccak(data, length)
         state.stack.append(result)
+        state.constraints += constraints
+
         return [global_state]
 
     @StateTransition()
diff --git a/mythril/laser/ethereum/keccak_function_manager.py b/mythril/laser/ethereum/keccak_function_manager.py
new file mode 100644
index 00000000..ca7e406b
--- /dev/null
+++ b/mythril/laser/ethereum/keccak_function_manager.py
@@ -0,0 +1,58 @@
+from ethereum import utils
+from mythril.laser.smt import BitVec, Function, URem, symbol_factory, ULE, And, ULT, Or
+
+TOTAL_PARTS = 10 ** 40
+PART = (2 ** 256 - 1) // TOTAL_PARTS
+INTERVAL_DIFFERENCE = 10 ** 30
+
+
+class KeccakFunctionManager:
+    def __init__(self):
+        self.sizes = {}
+        self.size_index = {}
+        self.index_counter = TOTAL_PARTS - 34534
+        self.size_values = {}
+
+    def create_keccak(self, data: BitVec, length: int):
+        length = length * 8
+        assert length == data.size()
+        try:
+            func, inverse = self.sizes[length]
+        except KeyError:
+            func = Function("keccak256_{}".format(length), length, 256)
+            inverse = Function("keccak256_{}-1".format(length), 256, length)
+            self.sizes[length] = (func, inverse)
+            self.size_values[length] = []
+        constraints = []
+        if data.symbolic is False:
+            keccak = symbol_factory.BitVecVal(
+                utils.sha3(data.value.to_bytes(length // 8, byteorder="big")), 256
+            )
+            constraints.append(func(data) == keccak)
+
+        constraints.append(inverse(func(data)) == data)
+        if data.symbolic is False:
+            return func(data), constraints
+
+        constraints.append(URem(func(data), symbol_factory.BitVecVal(63, 256)) == 0)
+        try:
+            index = self.size_index[length]
+        except KeyError:
+            self.size_index[length] = self.index_counter
+            index = self.index_counter
+            self.index_counter -= INTERVAL_DIFFERENCE
+
+        lower_bound = index * PART
+        upper_bound = (index + 1) * PART
+
+        condition = And(
+            ULE(symbol_factory.BitVecVal(lower_bound, 256), func(data)),
+            ULT(func(data), symbol_factory.BitVecVal(upper_bound, 256)),
+        )
+        for val in self.size_values[length]:
+            condition = Or(condition, func(data) == val)
+        constraints.append(condition)
+        return func(data), constraints
+
+
+keccak_function_manager = KeccakFunctionManager()
diff --git a/mythril/laser/ethereum/state/account.py b/mythril/laser/ethereum/state/account.py
index c6afa0c3..6fee240e 100644
--- a/mythril/laser/ethereum/state/account.py
+++ b/mythril/laser/ethereum/state/account.py
@@ -55,7 +55,6 @@ class Storage:
             self._standard_storage = K(256, 256, 0)  # type: BaseArray
         else:
             self._standard_storage = Array("Storage", 256, 256)
-        self._map_storage = {}  # type: Dict[BitVec, BaseArray]
 
         self.printable_storage = {}  # type: Dict[BitVec, BitVec]
 
@@ -73,11 +72,8 @@ class Storage:
             return Concat(symbol_factory.BitVecVal(0, 512 - input_.size()), input_)
 
     def __getitem__(self, item: BitVec) -> BitVec:
-        storage, is_keccak_storage = self._get_corresponding_storage(item)
-        if is_keccak_storage:
-            sanitized_item = self._sanitize(cast(BitVecFunc, item).input_)
-        else:
-            sanitized_item = item
+        storage = self._standard_storage
+        sanitized_item = item
         if (
             self.address
             and self.address.value != 0
@@ -100,7 +96,6 @@ class Storage:
                 self.printable_storage[item] = storage[sanitized_item]
             except ValueError as e:
                 log.debug("Couldn't read storage at %s: %s", item, e)
-
         return simplify(storage[sanitized_item])
 
     @staticmethod
@@ -114,29 +109,12 @@ class Storage:
         index = Extract(255, 0, key.input_)
         return simplify(index)
 
-    def _get_corresponding_storage(self, key: BitVec) -> Tuple[BaseArray, bool]:
-        index = self.get_map_index(key)
-        if index is None:
-            storage = self._standard_storage
-            is_keccak_storage = False
-        else:
-            storage_map = self._map_storage
-            try:
-                storage = storage_map[index]
-            except KeyError:
-                if isinstance(self._standard_storage, Array):
-                    storage_map[index] = Array("Storage", 512, 256)
-                else:
-                    storage_map[index] = K(512, 256, 0)
-                storage = storage_map[index]
-            is_keccak_storage = True
-        return storage, is_keccak_storage
+    def _get_corresponding_storage(self, key: BitVec) -> BaseArray:
+        return self._standard_storage
 
     def __setitem__(self, key, value: Any) -> None:
-        storage, is_keccak_storage = self._get_corresponding_storage(key)
+        storage = self._get_corresponding_storage(key)
         self.printable_storage[key] = value
-        if is_keccak_storage:
-            key = self._sanitize(key.input_)
         storage[key] = value
         if key.symbolic is False:
             self.storage_keys_loaded.add(int(key.value))
@@ -147,7 +125,6 @@ class Storage:
             concrete=concrete, address=self.address, dynamic_loader=self.dynld
         )
         storage._standard_storage = deepcopy(self._standard_storage)
-        storage._map_storage = deepcopy(self._map_storage)
         storage.printable_storage = copy(self.printable_storage)
         storage.storage_keys_loaded = copy(self.storage_keys_loaded)
         return storage
diff --git a/mythril/laser/ethereum/svm.py b/mythril/laser/ethereum/svm.py
index 88b362c8..21e4c682 100644
--- a/mythril/laser/ethereum/svm.py
+++ b/mythril/laser/ethereum/svm.py
@@ -241,7 +241,6 @@ class LaserEVM:
             except NotImplementedError:
                 log.debug("Encountered unimplemented instruction")
                 continue
-
             new_states = [
                 state for state in new_states if state.mstate.constraints.is_possible
             ]
diff --git a/mythril/laser/smt/__init__.py b/mythril/laser/smt/__init__.py
index 6ab752ce..b0793562 100644
--- a/mythril/laser/smt/__init__.py
+++ b/mythril/laser/smt/__init__.py
@@ -22,6 +22,7 @@ from mythril.laser.smt.bitvecfunc import BitVecFunc
 from mythril.laser.smt.expression import Expression, simplify
 from mythril.laser.smt.bool import Bool, is_true, is_false, Or, Not, And
 from mythril.laser.smt.array import K, Array, BaseArray
+from mythril.laser.smt.function import Function
 from mythril.laser.smt.solver import Solver, Optimize, SolverStatistics
 from mythril.laser.smt.model import Model
 from mythril.laser.smt.bool import Bool as SMTBool
diff --git a/mythril/laser/smt/function.py b/mythril/laser/smt/function.py
new file mode 100644
index 00000000..93115c88
--- /dev/null
+++ b/mythril/laser/smt/function.py
@@ -0,0 +1,25 @@
+from typing import cast
+import z3
+
+from mythril.laser.smt.bitvec import BitVec
+
+
+class Function:
+    """An uninterpreted function."""
+
+    def __init__(self, name: str, domain: int, value_range: int):
+        """Initializes an uninterpreted function.
+
+        :param name: Name of the Function
+        :param domain: The domain for the Function (10 -> all the values that a bv of size 10 could take)
+        :param value_range: The range for the values of the function (10 -> all the values that a bv of size 10 could take)
+        """
+        self.domain = z3.BitVecSort(domain)
+        self.range = z3.BitVecSort(value_range)
+        self.raw = z3.Function(name, self.domain, self.range)
+
+    def __call__(self, item: BitVec) -> BitVec:
+        """Function accessor, item can be symbolic."""
+        return BitVec(
+            cast(z3.BitVecRef, self.raw(item.raw)), annotations=item.annotations
+        )  # type: ignore