CBMC: Add contract and proof for poly_pointwise_montgomery

Resolves #107

Signed-off-by: Matthias J. Kannwischer <[email protected]>

Author: mkannwischer

mldsa/poly.c

@@ -84,6 +84,9 @@ void poly_pointwise_montgomery(poly *c, const poly *a, const poly *b)
   unsigned int i;
 
   for (i = 0; i < MLDSA_N; ++i)
+  __loop__(
+    invariant(i <= MLDSA_N)
+    invariant(forall(k0, i, MLDSA_N, a->coeffs[k0] == loop_entry(*a).coeffs[k0])))
   {
     c->coeffs[i] = montgomery_reduce((int64_t)a->coeffs[i] * b->coeffs[i]);
   }

mldsa/poly.h

@@ -152,7 +152,14 @@ void poly_invntt_tomont(poly *a);
  *              - const poly *a: pointer to first input polynomial
  *              - const poly *b: pointer to second input polynomial
  **************************************************/
-void poly_pointwise_montgomery(poly *c, const poly *a, const poly *b);
+void poly_pointwise_montgomery(poly *c, const poly *a, const poly *b)
+__contract__(
+  requires(memory_no_alias(a, sizeof(poly)))
+  requires(memory_no_alias(b, sizeof(poly)))
+  requires(memory_no_alias(c, sizeof(poly)))
+  requires(array_bound(a->coeffs, 0, MLDSA_N, 0, MLDSA_Q))
+  assigns(memory_slice(c, sizeof(poly)))
+);
 
 #define poly_power2round MLD_NAMESPACE(poly_power2round)
 /*************************************************

proofs/cbmc/poly_pointwise_montgomery/Makefile

@@ -0,0 +1,54 @@
+# SPDX-License-Identifier: Apache-2.0
+
+include ../Makefile_params.common
+
+HARNESS_ENTRY = harness
+HARNESS_FILE = poly_pointwise_montgomery_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 = poly_pointwise_montgomery
+
+DEFINES +=
+INCLUDES +=
+
+REMOVE_FUNCTION_BODY +=
+UNWINDSET +=
+
+PROOF_SOURCES += $(PROOFDIR)/$(HARNESS_FILE).c
+PROJECT_SOURCES += $(SRCDIR)/mldsa/poly.c
+
+CHECK_FUNCTION_CONTRACTS=$(MLD_NAMESPACE)poly_pointwise_montgomery
+USE_FUNCTION_CONTRACTS=$(MLD_NAMESPACE)montgomery_reduce
+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
+
+FUNCTION_NAME = poly_pointwise_montgomery
+
+# 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 = 8
+
+# 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/poly_pointwise_montgomery/poly_pointwise_montgomery_harness.c

@@ -0,0 +1,10 @@
+// Copyright (c) 2025 The mldsa-native project authors
+// SPDX-License-Identifier: Apache-2.0
+
+#include "poly.h"
+
+void harness(void)
+{
+  poly *a, *b, *c;
+  poly_pointwise_montgomery(c, a, b);
+}