CBMC: State (not prove) poly_invntt_tomont + Prove polyvec_ntt and polyvec_invntt_tomont

cbmc/proofs/polyvec_invntt_tomont/Makefile

@@ -0,0 +1,54 @@
+# SPDX-License-Identifier: Apache-2.0
+
+include ../Makefile_params.common
+
+HARNESS_ENTRY = harness
+HARNESS_FILE = polyvec_invntt_tomont_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 = polyvec_invntt_tomont
+
+DEFINES +=
+INCLUDES +=
+
+REMOVE_FUNCTION_BODY +=
+UNWINDSET += $(MLKEM_NAMESPACE)polyvec_invntt_tomont.0:4 # Largest value of MLKEM_K
+
+PROOF_SOURCES += $(PROOFDIR)/$(HARNESS_FILE).c
+PROJECT_SOURCES += $(SRCDIR)/mlkem/polyvec.c
+
+CHECK_FUNCTION_CONTRACTS=$(MLKEM_NAMESPACE)polyvec_invntt_tomont
+USE_FUNCTION_CONTRACTS=$(MLKEM_NAMESPACE)poly_invntt_tomont
+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 = polyvec_invntt_tomont
+
+# 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
+# ("mlkem/poly.c") in PROJECT_SOURCES).
+# REWRITTEN_SOURCES = $(PROOFDIR)/<__SOURCE_FILE_BASENAME__>.i
+# include ../Makefile.common
+# $(PROOFDIR)/<__SOURCE_FILE_BASENAME__>.i_SOURCE = $(SRCDIR)/mlkem/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

cbmc/proofs/polyvec_invntt_tomont/cbmc-proof.txt

@@ -0,0 +1,3 @@
+# SPDX-License-Identifier: Apache-2.0
+
+# This file marks this directory as containing a CBMC proof.

cbmc/proofs/polyvec_invntt_tomont/polyvec_invntt_tomont_harness.c

@@ -0,0 +1,27 @@
+// Copyright Amazon.com, Inc. or its affiliates. All Rights Reserved.
+// SPDX-License-Identifier: MIT-0 AND Apache-2.0
+
+/*
+ * Insert copyright notice
+ */
+
+/**
+ * @file polyvec_invntt_tomont_harness.c
+ * @brief Implements the proof harness for polyvec_invntt_tomont function.
+ */
+#include "polyvec.h"
+
+/*
+ * Insert project header files that
+ *   - include the declaration of the function
+ *   - include the types needed to declare function arguments
+ */
+
+/**
+ * @brief Starting point for formal analysis
+ *
+ */
+void harness(void) {
+  polyvec *r;
+  polyvec_invntt_tomont(r);
+}

cbmc/proofs/polyvec_ntt/Makefile

@@ -0,0 +1,54 @@
+# SPDX-License-Identifier: Apache-2.0
+
+include ../Makefile_params.common
+
+HARNESS_ENTRY = harness
+HARNESS_FILE = polyvec_ntt_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 = polyvec_ntt
+
+DEFINES +=
+INCLUDES +=
+
+REMOVE_FUNCTION_BODY +=
+UNWINDSET += $(MLKEM_NAMESPACE)polyvec_ntt.0:4 # Largest value of MLKEM_K
+
+PROOF_SOURCES += $(PROOFDIR)/$(HARNESS_FILE).c
+PROJECT_SOURCES += $(SRCDIR)/mlkem/polyvec.c
+
+CHECK_FUNCTION_CONTRACTS=$(MLKEM_NAMESPACE)polyvec_ntt
+USE_FUNCTION_CONTRACTS=$(MLKEM_NAMESPACE)poly_ntt
+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 = polyvec_ntt
+
+# 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
+# ("mlkem/poly.c") in PROJECT_SOURCES).
+# REWRITTEN_SOURCES = $(PROOFDIR)/<__SOURCE_FILE_BASENAME__>.i
+# include ../Makefile.common
+# $(PROOFDIR)/<__SOURCE_FILE_BASENAME__>.i_SOURCE = $(SRCDIR)/mlkem/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

cbmc/proofs/polyvec_ntt/cbmc-proof.txt

@@ -0,0 +1,3 @@
+# SPDX-License-Identifier: Apache-2.0
+
+# This file marks this directory as containing a CBMC proof.

cbmc/proofs/polyvec_ntt/polyvec_ntt_harness.c

@@ -0,0 +1,28 @@
+// Copyright Amazon.com, Inc. or its affiliates. All Rights Reserved.
+// SPDX-License-Identifier: MIT-0 AND Apache-2.0
+
+/*
+ * Insert copyright notice
+ */
+
+/**
+ * @file polyvec_ntt_harness.c
+ * @brief Implements the proof harness for polyvec_ntt function.
+ */
+#include "ntt.h"
+#include "polyvec.h"
+
+/*
+ * Insert project header files that
+ *   - include the declaration of the function
+ *   - include the types needed to declare function arguments
+ */
+
+/**
+ * @brief Starting point for formal analysis
+ *
+ */
+void harness(void) {
+  polyvec *r;
+  polyvec_ntt(r);
+}

mlkem/ntt.h

@@ -55,7 +55,11 @@ ENSURES(ARRAY_IN_BOUNDS(0, MLKEM_N - 1, r->coeffs, -(NTT_BOUND - 1), NTT_BOUND -
  * Arguments:   - uint16_t *a: pointer to in/output polynomial
  **************************************************/
 #define poly_invntt_tomont MLKEM_NAMESPACE(poly_invntt_tomont)
-void poly_invntt_tomont(poly *r);
+void poly_invntt_tomont(poly *r)  // clang-format off
+REQUIRES(IS_FRESH(r, sizeof(poly)))
+ASSIGNS(OBJECT_UPTO(r, sizeof(poly)))
+ENSURES(ARRAY_IN_BOUNDS(0, MLKEM_N - 1, r->coeffs, -(INVNTT_BOUND - 1), INVNTT_BOUND - 1));
+// clang-format on
 
 #define basemul_cached MLKEM_NAMESPACE(basemul_cached)
 /************************************************************

mlkem/polyvec.c

@@ -202,28 +202,13 @@ void polyvec_frombytes(polyvec *r, const uint8_t a[MLKEM_POLYVECBYTES]) {
   }
 }
 
-/*************************************************
- * Name:        polyvec_ntt
- *
- * Description: Apply forward NTT to all elements of a vector of polynomials
- *
- * Arguments:   - polyvec *r: pointer to in/output vector of polynomials
- **************************************************/
 void polyvec_ntt(polyvec *r) {
   unsigned int i;
   for (i = 0; i < MLKEM_K; i++) {
     poly_ntt(&r->vec[i]);
   }
 }
 
-/*************************************************
- * Name:        polyvec_invntt_tomont
- *
- * Description: Apply inverse NTT to all elements of a vector of polynomials
- *              and multiply by Montgomery factor 2^16
- *
- * Arguments:   - polyvec *r: pointer to in/output vector of polynomials
- **************************************************/
 void polyvec_invntt_tomont(polyvec *r) {
   unsigned int i;
   for (i = 0; i < MLKEM_K; i++) {

mlkem/polyvec.h

@@ -89,16 +89,54 @@ ENSURES(FORALL(int, k0, 0, MLKEM_K - 1,
 ASSIGNS(OBJECT_WHOLE(r));  // clang-format on
 
 #define polyvec_ntt MLKEM_NAMESPACE(polyvec_ntt)
+/*************************************************
+ * Name:        polyvec_ntt
+ *
+ * Description: Apply forward NTT to all elements of a vector of polynomials.
+ *
+ *              The input is assumed to be in normal order and
+ *              coefficient-wise bound by MLKEM_Q in absolute value.
+ *
+ *              The output polynomial is in bitreversed order, and
+ *              coefficient-wise bound by NTT_BOUND in absolute value.
+ *
+ * Arguments:   - polyvec *r: pointer to in/output vector of polynomials
+ *
+ **************************************************/
 void polyvec_ntt(polyvec *r)  // clang-format off
   REQUIRES(IS_FRESH(r, sizeof(polyvec)))
+  REQUIRES(FORALL(int, j, 0, MLKEM_K - 1,
+    ARRAY_IN_BOUNDS(0, MLKEM_N - 1,
+                    r->vec[j].coeffs, -(MLKEM_Q - 1), (MLKEM_Q - 1))))
   ASSIGNS(OBJECT_WHOLE(r))
   ENSURES(FORALL(int, j, 0, MLKEM_K - 1,
     ARRAY_IN_BOUNDS(0, MLKEM_N - 1,
                     r->vec[j].coeffs, -(NTT_BOUND - 1), (NTT_BOUND - 1))));
 // clang-format on
 
 #define polyvec_invntt_tomont MLKEM_NAMESPACE(polyvec_invntt_tomont)
-void polyvec_invntt_tomont(polyvec *r);
+/*************************************************
+ * Name:        polyvec_invntt_tomont
+ *
+ * Description: Apply inverse NTT to all elements of a vector of polynomials
+ *              and multiply by Montgomery factor 2^16
+ *
+ *              The input is assumed to be in bitreversed order, and can
+ *              have arbitrary coefficients in int16_t.
+ *
+ *              The output polynomial is in normal order, and
+ *              coefficient-wise bound by INVNTT_BOUND in absolute value.
+ *
+ *
+ * Arguments:   - polyvec *r: pointer to in/output vector of polynomials
+ **************************************************/
+void polyvec_invntt_tomont(polyvec *r)  // clang-format off
+  REQUIRES(IS_FRESH(r, sizeof(polyvec)))
+  ASSIGNS(OBJECT_WHOLE(r))
+  ENSURES(FORALL(int, j, 0, MLKEM_K - 1,
+    ARRAY_IN_BOUNDS(0, MLKEM_N - 1,
+                    r->vec[j].coeffs, -(INVNTT_BOUND - 1), (INVNTT_BOUND - 1))));
+// clang-format on
 
 #define polyvec_basemul_acc_montgomery \
   MLKEM_NAMESPACE(polyvec_basemul_acc_montgomery)