CBMC: Add proofs on top of native functions (polymat_permute_bitrev_to_custom_native)

- This commit adds CBMC proofs for the native function `mld_poly_permute_bitrev_to_custom`,
  called `polymat_permute_bitrev_to_custom_native`

- This following changes are include:
  - Apply the same harness file and construct function contract,
    reference from `polymat_permute_bitrev_to_custom`.
  - Use the following function contracts:
    - `mld_poly_permute_bitrev_to_custom`
  - Add `MLD_USE_NATIVE_NTT_CUSTOM_ORDER` in dummy_backend.h

- Also, for makeing this CBMC proof work, this commit refactor
  `mld_polymat_permute_bitrev_to_custom` from double loop to single loop.

Co-authored-by: Matthias J. Kannwischer <matthias@kannwischer.eu>
Signed-off-by: willieyz <willie.zhao@chelpis.com>

Author: willieyz

mldsa/src/native/api.h

@@ -116,7 +116,17 @@ set if there are native implementations for NTT and INTT."
  * Arguments:   - int32_t p[MLDSA_N]: pointer to in/output polynomial
  *
  **************************************************/
-static MLD_INLINE void mld_poly_permute_bitrev_to_custom(int32_t p[MLDSA_N]);
+static MLD_INLINE void mld_poly_permute_bitrev_to_custom(int32_t p[MLDSA_N])
+__contract__(
+  /* We don't specify that this should be a permutation, but only
+   * that it does not change the bound established at the end of
+   * mld_polyvec_matrix_expand.
+   */
+  requires(memory_no_alias(p, sizeof(int32_t) * MLDSA_N))
+  requires(array_bound(p, 0, MLDSA_N, 0, MLDSA_Q))
+  assigns(memory_slice(p, sizeof(int32_t) * MLDSA_N))
+  ensures(array_bound(p, 0, MLDSA_N, 0, MLDSA_Q))
+);
 #endif /* MLD_USE_NATIVE_NTT_CUSTOM_ORDER */
 
 

mldsa/src/polyvec.c

@@ -49,13 +49,17 @@ __contract__(
 {
 #if defined(MLD_USE_NATIVE_NTT_CUSTOM_ORDER)
   /* TODO: proof */
-  unsigned int i, j;
-  for (i = 0; i < MLDSA_K; i++)
+  unsigned int i;
+  for (i = 0; i < MLDSA_K * MLDSA_L; i++)
+  __loop__(
+    assigns(i, memory_slice(mat, sizeof(mld_polymat)))
+    invariant(i <= MLDSA_K * MLDSA_L)
+    invariant(forall(k1, 0, MLDSA_K, forall(l1, 0, MLDSA_L,
+      array_bound(mat->vec[k1].vec[l1].coeffs, 0, MLDSA_N, 0, MLDSA_Q))))
+  )
   {
-    for (j = 0; j < MLDSA_L; j++)
-    {
-      mld_poly_permute_bitrev_to_custom(mat->vec[i].vec[j].coeffs);
-    }
+    mld_poly_permute_bitrev_to_custom(
+        mat->vec[i / MLDSA_L].vec[i % MLDSA_L].coeffs);
   }
 
 #else /* MLD_USE_NATIVE_NTT_CUSTOM_ORDER */

proofs/cbmc/polymat_permute_bitrev_to_custom_native/Makefile

@@ -0,0 +1,55 @@
+# Copyright (c) The mldsa-native project authors
+# SPDX-License-Identifier: Apache-2.0 OR ISC OR MIT
+
+include ../Makefile_params.common
+
+HARNESS_ENTRY = harness
+HARNESS_FILE = polymat_permute_bitrev_to_custom_native_harness
+
+# This should be a unique identifier for this proof, and will appear on the
+# Litani dashboard. It can be human-readable and contain spaces if you wish.
+PROOF_UID = polymat_permute_bitrev_to_custom_native
+
+DEFINES += -DMLD_CONFIG_USE_NATIVE_BACKEND_ARITH -DMLD_CONFIG_ARITH_BACKEND_FILE="\"dummy_backend.h\""
+INCLUDES +=
+
+REMOVE_FUNCTION_BODY +=
+UNWINDSET +=
+
+PROOF_SOURCES += $(PROOFDIR)/$(HARNESS_FILE).c
+PROJECT_SOURCES += $(SRCDIR)/mldsa/src/polyvec.c
+
+CHECK_FUNCTION_CONTRACTS=mld_polymat_permute_bitrev_to_custom
+USE_FUNCTION_CONTRACTS=mld_poly_permute_bitrev_to_custom
+APPLY_LOOP_CONTRACTS=on
+USE_DYNAMIC_FRAMES=1
+
+# Disable any setting of EXTERNAL_SAT_SOLVER, and choose SMT backend instead
+EXTERNAL_SAT_SOLVER=
+CBMCFLAGS=--smt2 --slice-formula --no-array-field-sensitivity
+
+FUNCTION_NAME = polymat_permute_bitrev_to_custom_native
+
+# If this proof is found to consume huge amounts of RAM, you can set the
+# EXPENSIVE variable. With new enough versions of the proof tools, this will
+# restrict the number of EXPENSIVE CBMC jobs running at once. See the
+# documentation in Makefile.common under the "Job Pools" heading for details.
+# EXPENSIVE = true
+
+# This function is large enough to need...
+CBMC_OBJECT_BITS = 12
+
+# If you require access to a file-local ("static") function or object to conduct
+# your proof, set the following (and do not include the original source file
+# ("mldsa/poly.c") in PROJECT_SOURCES).
+# REWRITTEN_SOURCES = $(PROOFDIR)/<__SOURCE_FILE_BASENAME__>.i
+# include ../Makefile.common
+# $(PROOFDIR)/<__SOURCE_FILE_BASENAME__>.i_SOURCE = $(SRCDIR)/mldsa/poly.c
+# $(PROOFDIR)/<__SOURCE_FILE_BASENAME__>.i_FUNCTIONS = foo bar
+# $(PROOFDIR)/<__SOURCE_FILE_BASENAME__>.i_OBJECTS = baz
+# Care is required with variables on the left-hand side: REWRITTEN_SOURCES must
+# be set before including Makefile.common, but any use of variables on the
+# left-hand side requires those variables to be defined. Hence, _SOURCE,
+# _FUNCTIONS, _OBJECTS is set after including Makefile.common.
+
+include ../Makefile.common

proofs/cbmc/polymat_permute_bitrev_to_custom_native/polymat_permute_bitrev_to_custom_native_harness.c

@@ -0,0 +1,12 @@
+// Copyright (c) The mldsa-native project authors
+// SPDX-License-Identifier: Apache-2.0 OR ISC OR MIT
+
+#include "polyvec.h"
+
+void mld_polymat_permute_bitrev_to_custom(mld_polymat *mat);
+
+void harness(void)
+{
+  mld_polymat *mat;
+  mld_polymat_permute_bitrev_to_custom(mat);
+}

scripts/check-contracts

@@ -43,6 +43,9 @@ def gen_contracts():
 def is_exception(funcname):
     # The functions passing this filter are known not to have a proof
 
+    if funcname == 'poly_permute_bitrev_to_custom':
+        return True
+    
     if funcname.endswith("_native") or funcname.endswith("_asm"):
         # CBMC proofs are axiomatized against contracts of the backends
         return True