CBMC: Add spec + proof for polyvec_basemul_acc_montgomery_cached + poly_add

cbmc/proofs/poly_add/Makefile

@@ -0,0 +1,54 @@
+# SPDX-License-Identifier: Apache-2.0
+
+include ../Makefile_params.common
+
+HARNESS_ENTRY = harness
+HARNESS_FILE = poly_add_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_add
+
+DEFINES +=
+INCLUDES +=
+
+REMOVE_FUNCTION_BODY +=
+UNWINDSET +=
+
+PROOF_SOURCES += $(PROOFDIR)/$(HARNESS_FILE).c
+PROJECT_SOURCES += $(SRCDIR)/mlkem/poly.c
+
+CHECK_FUNCTION_CONTRACTS=$(MLKEM_NAMESPACE)poly_add
+USE_FUNCTION_CONTRACTS=
+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_add
+
+# 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/poly_add/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/poly_add/poly_add_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 poly_add_harness.c
+ * @brief Implements the proof harness for basemul_cached function.
+ */
+#include "poly.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) {
+  poly *r, *b;
+  poly_add(r, b);
+}

cbmc/proofs/polyvec_basemul_acc_montgomery_cached/Makefile

@@ -0,0 +1,54 @@
+# SPDX-License-Identifier: Apache-2.0
+
+include ../Makefile_params.common
+
+HARNESS_ENTRY = harness
+HARNESS_FILE = polyvec_basemul_acc_montgomery_cached_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_basemul_acc_montgomery_cached
+
+DEFINES +=
+INCLUDES +=
+
+REMOVE_FUNCTION_BODY +=
+UNWINDSET += $(MLKEM_NAMESPACE)polyvec_basemul_acc_montgomery_cached.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_basemul_acc_montgomery_cached
+USE_FUNCTION_CONTRACTS=$(MLKEM_NAMESPACE)poly_basemul_montgomery_cached $(MLKEM_NAMESPACE)poly_add
+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_basemul_acc_montgomery_cached
+
+# 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_basemul_acc_montgomery_cached/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_basemul_acc_montgomery_cached/polyvec_basemul_acc_montgomery_cached_harness.c

@@ -0,0 +1,30 @@
+// Copyright Amazon.com, Inc. or its affiliates. All Rights Reserved.
+// SPDX-License-Identifier: MIT-0 AND Apache-2.0
+
+/*
+ * Insert copyright notice
+ */
+
+/**
+ * @file polyvec_basemul_acc_montgomery_cached_harness.c
+ * @brief Implements the proof harness for basemul_cached 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) {
+  poly *r;
+  polyvec *a, *b;
+  polyvec_mulcache *b_cached;
+
+  polyvec_basemul_acc_montgomery_cached(r, a, b, b_cached);
+}

mlkem/indcpa.c

@@ -321,7 +321,7 @@ void indcpa_keypair_derand(uint8_t pk[MLKEM_INDCPA_PUBLICKEYBYTES],
   }
 
   // Arithmetic cannot overflow, see static assertion at the top
-  polyvec_add(&pkpv, &pkpv, &e);
+  polyvec_add(&pkpv, &e);
   polyvec_reduce(&pkpv);
   polyvec_reduce(&skpv);
 
@@ -395,9 +395,9 @@ void indcpa_enc(uint8_t c[MLKEM_INDCPA_BYTES],
   poly_invntt_tomont(&v);
 
   // Arithmetic cannot overflow, see static assertion at the top
-  polyvec_add(&b, &b, &ep);
-  poly_add(&v, &v, &epp);
-  poly_add(&v, &v, &k);
+  polyvec_add(&b, &ep);
+  poly_add(&v, &epp);
+  poly_add(&v, &k);
 
   polyvec_reduce(&b);
   poly_reduce(&v);

mlkem/poly.c

@@ -496,20 +496,19 @@ void poly_reduce(poly *r) {
 }
 #endif /* MLKEM_USE_NATIVE_POLY_REDUCE */
 
-/*************************************************
- * Name:        poly_add
- *
- * Description: Add two polynomials; no modular reduction is performed
- *
- * Arguments: - poly *r: pointer to output polynomial
- *            - const poly *a: pointer to first input polynomial
- *            - const poly *b: pointer to second input polynomial
- **************************************************/
-void poly_add(poly *r, const poly *a, const poly *b) {
-  unsigned int i;
-  for (i = 0; i < MLKEM_N; i++) {
-    r->coeffs[i] = a->coeffs[i] + b->coeffs[i];
-  }
+void poly_add(poly *r, const poly *b) {
+  int i;
+  for (i = 0; i < MLKEM_N; i++)
+      // clang-format off
+    ASSIGNS(i, OBJECT_WHOLE(r))
+    INVARIANT(i >= 0 && i <= MLKEM_N)
+    INVARIANT(FORALL(int, k0, i, MLKEM_N - 1, r->coeffs[k0] == LOOP_ENTRY(*r).coeffs[k0]))
+    INVARIANT(FORALL(int, k1, 0, i - 1, r->coeffs[k1] == LOOP_ENTRY(*r).coeffs[k1] + b->coeffs[k1]))
+    DECREASES(MLKEM_N - i)
+    // clang-format on
+    {
+      r->coeffs[i] = r->coeffs[i] + b->coeffs[i];
+    }
 }
 
 /*************************************************

mlkem/poly.h

@@ -432,7 +432,31 @@ ENSURES(ARRAY_IN_BOUNDS(int, k, 0, MLKEM_N - 1, r->coeffs, 0, MLKEM_Q - 1));
 // clang-format on
 
 #define poly_add MLKEM_NAMESPACE(poly_add)
-void poly_add(poly *r, const poly *a, const poly *b);
+/************************************************************
+ * Name: poly_add
+ *
+ * Description: Adds two polynomials in place
+ *
+ * Arguments: - r: Pointer to input-output polynomial to be added to.
+ *            - b: Pointer to input polynomial that should be added
+ *                 to r. Must be disjoint from r.
+ *
+ * The coefficients of r and b must be so that the addition does
+ * not overflow. Otherwise, the behaviour of this function is undefined.
+ *
+ ************************************************************/
+// REF-CHANGE:
+// The reference implementation uses a 3-argument poly_add.
+// We specialize to the accumulator form to avoid reasoning about aliasing.
+void poly_add(poly *r, const poly *b)  // clang-format off
+REQUIRES(IS_FRESH(r, sizeof(poly)))
+REQUIRES(IS_FRESH(b, sizeof(poly)))
+REQUIRES(FORALL(int, k0, 0, MLKEM_N - 1, (int32_t) r->coeffs[k0] + b->coeffs[k0] <= INT16_MAX))
+REQUIRES(FORALL(int, k1, 0, MLKEM_N - 1, (int32_t) r->coeffs[k1] + b->coeffs[k1] >= INT16_MIN))
+ENSURES(FORALL(int, k, 0, MLKEM_N - 1, r->coeffs[k] == OLD(*r).coeffs[k] + b->coeffs[k]))
+ASSIGNS(OBJECT_WHOLE(r));
+// clang-format on
+
 #define poly_sub MLKEM_NAMESPACE(poly_sub)
 void poly_sub(poly *r, const poly *a, const poly *b);
 

mlkem/polyvec.c

@@ -226,18 +226,35 @@ void polyvec_basemul_acc_montgomery_cached(poly *r, const polyvec *a,
   POLYVEC_BOUND(b, NTT_BOUND);
   POLYVEC_BOUND(b_cache, MLKEM_Q);
 
-  unsigned int i;
+  int i;
   poly t;
 
   poly_basemul_montgomery_cached(r, &a->vec[0], &b->vec[0], &b_cache->vec[0]);
-  for (i = 1; i < MLKEM_K; i++) {
-    poly_basemul_montgomery_cached(&t, &a->vec[i], &b->vec[i],
-                                   &b_cache->vec[i]);
-    poly_add(r, r, &t);
-    // abs bounds: < (i+1) * 3/2 * q
-  }
 
-  // abs bounds: < MLKEM_K * 3/2 * q <= 4 * 3/2 * q = 19974
+  for (i = 1; i < MLKEM_K; i++)
+      // clang-format off
+    ASSIGNS(i, t, OBJECT_WHOLE(r))
+    INVARIANT(i >= 1 && i <= MLKEM_K)
+    INVARIANT(ARRAY_IN_BOUNDS(int, k, 0, MLKEM_N - 1, r->coeffs,
+                              i * (-3 * HALF_Q + 1), i * (3 * HALF_Q - 1)))
+    DECREASES(MLKEM_K - i)
+    // clang-format on
+    {
+      poly_basemul_montgomery_cached(&t, &a->vec[i], &b->vec[i],
+                                     &b_cache->vec[i]);
+      poly_add(r, &t);
+      // abs bounds: < (i+1) * 3/2 * q
+    }
+
+  // Those bounds are true for the C implementation, but not needed
+  // in the higher level bounds reasoning. It is thus best to omit
+  // them from the spec to not unnecessarily constraint native implementations.
+  ASSERT(
+      ARRAY_IN_BOUNDS(int, k, 0, MLKEM_N - 1, r->coeffs,
+                      MLKEM_K * (-3 * HALF_Q + 1), MLKEM_K * (3 * HALF_Q - 1)),
+      "polyvec_basemul_acc_montgomery_cached output bounds");
+  // TODO: Integrate CBMC assertion into POLY_BOUND if CBMC is set
+  POLY_BOUND(r, MLKEM_K * 3 * HALF_Q);
 }
 #else  /* !MLKEM_USE_NATIVE_POLYVEC_BASEMUL_ACC_MONTGOMERY_CACHED */
 void polyvec_basemul_acc_montgomery_cached(poly *r, const polyvec *a,
@@ -310,9 +327,9 @@ void polyvec_reduce(polyvec *r) {
  *            - const polyvec *a: pointer to first input vector of polynomials
  *            - const polyvec *b: pointer to second input vector of polynomials
  **************************************************/
-void polyvec_add(polyvec *r, const polyvec *a, const polyvec *b) {
+void polyvec_add(polyvec *r, const polyvec *b) {
   unsigned int i;
   for (i = 0; i < MLKEM_K; i++) {
-    poly_add(&r->vec[i], &a->vec[i], &b->vec[i]);
+    poly_add(&r->vec[i], &b->vec[i]);
   }
 }

mlkem/polyvec.h

@@ -40,9 +40,37 @@ void polyvec_basemul_acc_montgomery(poly *r, const polyvec *a,
 // REF-CHANGE: This function does not exist in the reference implementation
 #define polyvec_basemul_acc_montgomery_cached \
   MLKEM_NAMESPACE(polyvec_basemul_acc_montgomery_cached)
+/*************************************************
+ * Name:        polyvec_basemul_acc_montgomery_cached
+ *
+ * Description: Scalar product of two vectors of polynomials in NTT domain,
+ *              using mulcache for second operand.
+ *
+ *              Bounds:
+ *              - a is assumed to be coefficient-wise < q in absolute value.
+ *              - No bounds guarantees for the coefficients in the result.
+ *
+ * Arguments:   - poly *r: pointer to output polynomial
+ *              - const polyvec *a: pointer to first input polynomial vector
+ *              - const polyvec *b: pointer to second input polynomial vector
+ *              - const polyvec_mulcache *b_cache: pointer to mulcache
+ *                  for second input polynomial vector. Can be computed
+ *                  via polyvec_mulcache_compute().
+ **************************************************/
 void polyvec_basemul_acc_montgomery_cached(poly *r, const polyvec *a,
                                            const polyvec *b,
-                                           const polyvec_mulcache *b_cache);
+                                           const polyvec_mulcache *b_cache)
+    // clang-format off
+REQUIRES(IS_FRESH(r, sizeof(poly)))
+REQUIRES(IS_FRESH(a, sizeof(polyvec)))
+REQUIRES(IS_FRESH(b, sizeof(polyvec)))
+REQUIRES(IS_FRESH(b_cache, sizeof(polyvec_mulcache)))
+// Input is coefficient-wise < q in absolute value
+REQUIRES(FORALL(int, k1, 0, MLKEM_K - 1,
+ ARRAY_IN_BOUNDS(int, k2, 0, MLKEM_N - 1,
+   a->vec[k1].coeffs, -(MLKEM_Q - 1), (MLKEM_Q - 1))))
+ASSIGNS(OBJECT_WHOLE(r));
+// clang-format on
 
 // REF-CHANGE: This function does not exist in the reference implementation
 #define polyvec_mulcache_compute MLKEM_NAMESPACE(polyvec_mulcache_compute)
@@ -80,6 +108,6 @@ ASSIGNS(OBJECT_WHOLE(x));
 void polyvec_reduce(polyvec *r);
 
 #define polyvec_add MLKEM_NAMESPACE(polyvec_add)
-void polyvec_add(polyvec *r, const polyvec *a, const polyvec *b);
+void polyvec_add(polyvec *r, const polyvec *b);
 
 #endif