CBMC: Add spec + proof for gen_matrix

All loops in gen_matrix() are unrolled by CBMC. The loop
handling residual polynomials after x4-batched entry
generation is replaced by conditional generation of a
single polynomial: For K=2 and K=4, batching gives the
full matrix, while for K=3, only one polynomial remains.

Signed-off-by: Hanno Becker <[email protected]>

cbmc/proofs/gen_matrix/Makefile

@@ -0,0 +1,54 @@
+# SPDX-License-Identifier: Apache-2.0
+
+include ../Makefile_params.common
+
+HARNESS_ENTRY = harness
+HARNESS_FILE = gen_matrix_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 = gen_matrix
+
+DEFINES +=
+INCLUDES +=
+
+REMOVE_FUNCTION_BODY +=
+UNWINDSET += $(MLKEM_NAMESPACE)gen_matrix.0:4 $(MLKEM_NAMESPACE)gen_matrix.1:4 $(MLKEM_NAMESPACE)gen_matrix.2:4
+
+PROOF_SOURCES += $(PROOFDIR)/$(HARNESS_FILE).c
+PROJECT_SOURCES += $(SRCDIR)/mlkem/indcpa.c
+
+CHECK_FUNCTION_CONTRACTS=$(MLKEM_NAMESPACE)gen_matrix
+USE_FUNCTION_CONTRACTS=gen_matrix_entry gen_matrix_entry_x4
+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 = $(MLKEM_NAMESPACE)gen_matrix
+
+# 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/gen_matrix/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/gen_matrix/gen_matrix_harness.c

@@ -0,0 +1,30 @@
+// Copyright Amazon.com, Inc. or its affiliates. All Rights Reserved.
+// SPDX-License-Identifier: MIT-0
+
+/*
+ * Insert copyright notice
+ */
+
+/**
+ * @file gen_matrix_harness.c
+ * @brief Implements the proof harness for gen_matrix function.
+ */
+
+/*
+ * Insert project header files that
+ *   - include the declaration of the function
+ *   - include the types needed to declare function arguments
+ */
+#include <stdint.h>
+#include "indcpa.h"
+
+/**
+ * @brief Starting point for formal analysis
+ *
+ */
+void harness(void) {
+  polyvec *a;
+  uint8_t *seed;
+  int transposed;
+  gen_matrix(a, seed, transposed);
+}

mlkem/indcpa.c

@@ -304,8 +304,8 @@ void gen_matrix(polyvec *a, const uint8_t seed[MLKEM_SYMBYTES],
     gen_matrix_entry_x4(&a[0].vec[0] + i, seedxy);
   }
 
-  // For left over vector, we use single keccak.
-  for (; i < MLKEM_K * MLKEM_K; i++) {
+  // For left over polynomial, we use single keccak.
+  if (i < MLKEM_K * MLKEM_K) {
     uint8_t x, y;
     x = i / MLKEM_K;
     y = i % MLKEM_K;
@@ -319,8 +319,11 @@ void gen_matrix(polyvec *a, const uint8_t seed[MLKEM_SYMBYTES],
     }
 
     gen_matrix_entry(&a[0].vec[0] + i, seed0);
+    i++;
   }
 
+  ASSERT(i == MLKEM_K * MLKEM_K, "gen_matrix: failed to generate whole matrix");
+
 #if defined(MLKEM_USE_NATIVE_NTT_CUSTOM_ORDER)
   // The public matrix is generated in NTT domain. If the native backend
   // uses a custom order in NTT domain, permute A accordingly.

mlkem/indcpa.h

@@ -3,11 +3,20 @@
 #define INDCPA_H
 
 #include <stdint.h>
+#include "cbmc.h"
 #include "params.h"
 #include "polyvec.h"
 
+// clang-format off
 #define gen_matrix MLKEM_NAMESPACE(gen_matrix)
-void gen_matrix(polyvec *a, const uint8_t seed[MLKEM_SYMBYTES], int transposed);
+void gen_matrix(polyvec *a, const uint8_t seed[MLKEM_SYMBYTES], int transposed)
+REQUIRES(IS_FRESH(a, sizeof(polyvec) * MLKEM_K))
+REQUIRES(IS_FRESH(seed, MLKEM_SYMBYTES))
+REQUIRES(transposed == 0 || transposed == 1)
+ASSIGNS(OBJECT_UPTO(a, sizeof(polyvec) * MLKEM_K))
+ENSURES(FORALL(int, x, 0, MLKEM_K - 1, FORALL(int, y, 0, MLKEM_K - 1,
+  ARRAY_IN_BOUNDS(int, i, 0, MLKEM_N - 1, a[x].vec[y].coeffs, 0, (MLKEM_Q - 1)))))
+;  // clang-format on
 
 #define indcpa_keypair_derand MLKEM_NAMESPACE(indcpa_keypair_derand)
 void indcpa_keypair_derand(uint8_t pk[MLKEM_INDCPA_PUBLICKEYBYTES],