Progress on Mr. Solver SHA512 example

heapster-saw/examples/Makefile

@@ -34,7 +34,7 @@ rust_lifetimes.bc: rust_lifetimes.rs
 	rustc --crate-type=lib --emit=llvm-bc rust_lifetimes.rs
 
 # Lists all the Mr Solver tests, without their ".saw" suffix
-MR_SOLVER_TESTS = arrays_mr_solver linked_list_mr_solver
+MR_SOLVER_TESTS = arrays_mr_solver linked_list_mr_solver sha512_mr_solver
 
 .PHONY: mr-solver-tests $(MR_SOLVER_TESTS)
 mr-solver-tests: $(MR_SOLVER_TESTS)

heapster-saw/examples/sha512.c

@@ -1,7 +1,17 @@
+// ============================================================================
+// The code in this file is based off of that in:
+// https://github.com/awslabs/aws-lc/
+// (commit: d84d2f329dccbc7f3866eab54951bd012e317041)
+// ============================================================================
+
 #include <stdlib.h>
 #include <stdint.h>
 #include <string.h>
 
+// ============================================================================
+// Helper functions from crypto/internal.h
+// ============================================================================
+
 static inline void *OPENSSL_memcpy(void *dst, const void *src, size_t n) {
   if (n == 0) {
     return dst;
@@ -26,6 +36,14 @@ static inline uint64_t CRYPTO_load_u64_be(const void *ptr) {
   return CRYPTO_bswap8(ret);
 }
 
+// ============================================================================
+// The defintion of sha512_block_data_order from crypto/fipsmodule/sha/sha512.c
+// with only one addition (return_state), needed for Heapster typechecking 
+// ============================================================================
+
+// Used in sha512_block_data_order below, needed for Heapster typechecking
+void return_state(uint64_t *state) { }
+
 static const uint64_t K512[80] = {
     UINT64_C(0x428a2f98d728ae22), UINT64_C(0x7137449123ef65cd),
     UINT64_C(0xb5c0fbcfec4d3b2f), UINT64_C(0xe9b5dba58189dbbc),
@@ -69,9 +87,7 @@ static const uint64_t K512[80] = {
     UINT64_C(0x5fcb6fab3ad6faec), UINT64_C(0x6c44198c4a475817),
 };
 
-#ifndef ROTR
 #define ROTR(x, s) (((x) >> s) | (x) << (64 - s))
-#endif
 
 #define Sigma0(x) (ROTR((x), 28) ^ ROTR((x), 34) ^ ROTR((x), 39))
 #define Sigma1(x) (ROTR((x), 14) ^ ROTR((x), 18) ^ ROTR((x), 41))
@@ -99,8 +115,6 @@ static const uint64_t K512[80] = {
     ROUND_00_15(i + j, a, b, c, d, e, f, g, h);        \
   } while (0)
 
-void return_state(uint64_t *state) { }
-
 static void sha512_block_data_order(uint64_t *state, const uint8_t *in,
                                     size_t num) {
   uint64_t a, b, c, d, e, f, g, h, s0, s1, T1;
@@ -184,7 +198,132 @@ static void sha512_block_data_order(uint64_t *state, const uint8_t *in,
   }
 }
 
-// needed for Heapster to be able to see the static function above
+
+// ============================================================================
+// A definition equivalent to sha512_block_data_order which uses multiple
+// functions, for use with Mr. Solver
+// ============================================================================
+
+static void round_00_15(uint64_t i,
+                        uint64_t *a, uint64_t *b, uint64_t *c, uint64_t *d,
+                        uint64_t *e, uint64_t *f, uint64_t *g, uint64_t *h,
+                        uint64_t *T1) {
+  *T1 += *h + Sigma1(*e) + Ch(*e, *f, *g) + K512[i];
+  *h = Sigma0(*a) + Maj(*a, *b, *c);
+  *d += *T1;
+  *h += *T1;
+}
+
+static void round_16_80(uint64_t i, uint64_t j,
+                        uint64_t *a, uint64_t *b, uint64_t *c, uint64_t *d,
+                        uint64_t *e, uint64_t *f, uint64_t *g, uint64_t *h,
+                        uint64_t *X,
+                        uint64_t* s0, uint64_t *s1, uint64_t *T1) {
+  *s0 = X[(j + 1) & 0x0f];
+  *s0 = sigma0(*s0);
+  *s1 = X[(j + 14) & 0x0f];
+  *s1 = sigma1(*s1);
+  *T1 = X[(j) & 0x0f] += *s0 + *s1 + X[(j + 9) & 0x0f];
+  round_00_15(i + j, a, b, c, d, e, f, g, h, T1);
+}
+
+// Used in processBlock below, needed for Heapster typechecking
+void return_X(uint64_t *X) { }
+
+static void processBlock(uint64_t *a, uint64_t *b, uint64_t *c, uint64_t *d,
+                         uint64_t *e, uint64_t *f, uint64_t *g, uint64_t *h,
+                         const uint8_t *in) {
+  uint64_t s0, s1, T1;
+  uint64_t X[16];
+  int i;
+
+  T1 = X[0] = CRYPTO_load_u64_be(in);
+  round_00_15(0, a, b, c, d, e, f, g, h, &T1);
+  T1 = X[1] = CRYPTO_load_u64_be(in + 8);
+  round_00_15(1, h, a, b, c, d, e, f, g, &T1);
+  T1 = X[2] = CRYPTO_load_u64_be(in + 2 * 8);
+  round_00_15(2, g, h, a, b, c, d, e, f, &T1);
+  T1 = X[3] = CRYPTO_load_u64_be(in + 3 * 8);
+  round_00_15(3, f, g, h, a, b, c, d, e, &T1);
+  T1 = X[4] = CRYPTO_load_u64_be(in + 4 * 8);
+  round_00_15(4, e, f, g, h, a, b, c, d, &T1);
+  T1 = X[5] = CRYPTO_load_u64_be(in + 5 * 8);
+  round_00_15(5, d, e, f, g, h, a, b, c, &T1);
+  T1 = X[6] = CRYPTO_load_u64_be(in + 6 * 8);
+  round_00_15(6, c, d, e, f, g, h, a, b, &T1);
+  T1 = X[7] = CRYPTO_load_u64_be(in + 7 * 8);
+  round_00_15(7, b, c, d, e, f, g, h, a, &T1);
+  T1 = X[8] = CRYPTO_load_u64_be(in + 8 * 8);
+  round_00_15(8, a, b, c, d, e, f, g, h, &T1);
+  T1 = X[9] = CRYPTO_load_u64_be(in + 9 * 8);
+  round_00_15(9, h, a, b, c, d, e, f, g, &T1);
+  T1 = X[10] = CRYPTO_load_u64_be(in + 10 * 8);
+  round_00_15(10, g, h, a, b, c, d, e, f, &T1);
+  T1 = X[11] = CRYPTO_load_u64_be(in + 11 * 8);
+  round_00_15(11, f, g, h, a, b, c, d, e, &T1);
+  T1 = X[12] = CRYPTO_load_u64_be(in + 12 * 8);
+  round_00_15(12, e, f, g, h, a, b, c, d, &T1);
+  T1 = X[13] = CRYPTO_load_u64_be(in + 13 * 8);
+  round_00_15(13, d, e, f, g, h, a, b, c, &T1);
+  T1 = X[14] = CRYPTO_load_u64_be(in + 14 * 8);
+  round_00_15(14, c, d, e, f, g, h, a, b, &T1);
+  T1 = X[15] = CRYPTO_load_u64_be(in + 15 * 8);
+  round_00_15(15, b, c, d, e, f, g, h, a, &T1);
+
+  return_X(X); // for Heapster
+
+  for (i = 16; i < 80; i += 16) {
+    round_16_80(i, 0, a, b, c, d, e, f, g, h, X, &s0, &s1, &T1);
+    round_16_80(i, 1, h, a, b, c, d, e, f, g, X, &s0, &s1, &T1);
+    round_16_80(i, 2, g, h, a, b, c, d, e, f, X, &s0, &s1, &T1);
+    round_16_80(i, 3, f, g, h, a, b, c, d, e, X, &s0, &s1, &T1);
+    round_16_80(i, 4, e, f, g, h, a, b, c, d, X, &s0, &s1, &T1);
+    round_16_80(i, 5, d, e, f, g, h, a, b, c, X, &s0, &s1, &T1);
+    round_16_80(i, 6, c, d, e, f, g, h, a, b, X, &s0, &s1, &T1);
+    round_16_80(i, 7, b, c, d, e, f, g, h, a, X, &s0, &s1, &T1);
+    round_16_80(i, 8, a, b, c, d, e, f, g, h, X, &s0, &s1, &T1);
+    round_16_80(i, 9, h, a, b, c, d, e, f, g, X, &s0, &s1, &T1);
+    round_16_80(i, 10, g, h, a, b, c, d, e, f, X, &s0, &s1, &T1);
+    round_16_80(i, 11, f, g, h, a, b, c, d, e, X, &s0, &s1, &T1);
+    round_16_80(i, 12, e, f, g, h, a, b, c, d, X, &s0, &s1, &T1);
+    round_16_80(i, 13, d, e, f, g, h, a, b, c, X, &s0, &s1, &T1);
+    round_16_80(i, 14, c, d, e, f, g, h, a, b, X, &s0, &s1, &T1);
+    round_16_80(i, 15, b, c, d, e, f, g, h, a, X, &s0, &s1, &T1);
+  }
+}
+
+static void processBlocks(uint64_t *state, const uint8_t *in, size_t num) {
+  uint64_t a, b, c, d, e, f, g, h;
+
+  while (num--) {
+
+    a = state[0];
+    b = state[1];
+    c = state[2];
+    d = state[3];
+    e = state[4];
+    f = state[5];
+    g = state[6];
+    h = state[7];
+
+    processBlock(&a, &b, &c, &d, &e, &f, &g, &h, in);
+
+    state[0] += a;
+    state[1] += b;
+    state[2] += c;
+    state[3] += d;
+    state[4] += e;
+    state[5] += f;
+    state[6] += g;
+    state[7] += h;
+
+    in += 16 * 8;
+  }
+}
+
+
+// Needed for Heapster to be able to see the static functions above
 void dummy(uint64_t *state, const uint8_t *in, size_t num) {
   sha512_block_data_order(state, in, num);
+  processBlocks(state, in, num);
 }

heapster-saw/examples/sha512.cry

@@ -0,0 +1,86 @@
+
+module SHA512 where
+
+// ============================================================================
+// Definitions from cryptol-specs/Primitive/Keyless/Hash/SHA512.cry, with some
+// type annotations added to SIGMA_0, SIGMA_1, sigma_0, and sigma_1 to get
+// monadification to go through
+// ============================================================================
+
+type w = 64
+
+type j = 80
+
+K : [j][w]
+K = [ 0x428a2f98d728ae22, 0x7137449123ef65cd, 0xb5c0fbcfec4d3b2f, 0xe9b5dba58189dbbc,
+      0x3956c25bf348b538, 0x59f111f1b605d019, 0x923f82a4af194f9b, 0xab1c5ed5da6d8118,
+      0xd807aa98a3030242, 0x12835b0145706fbe, 0x243185be4ee4b28c, 0x550c7dc3d5ffb4e2,
+      0x72be5d74f27b896f, 0x80deb1fe3b1696b1, 0x9bdc06a725c71235, 0xc19bf174cf692694,
+      0xe49b69c19ef14ad2, 0xefbe4786384f25e3, 0x0fc19dc68b8cd5b5, 0x240ca1cc77ac9c65,
+      0x2de92c6f592b0275, 0x4a7484aa6ea6e483, 0x5cb0a9dcbd41fbd4, 0x76f988da831153b5,
+      0x983e5152ee66dfab, 0xa831c66d2db43210, 0xb00327c898fb213f, 0xbf597fc7beef0ee4,
+      0xc6e00bf33da88fc2, 0xd5a79147930aa725, 0x06ca6351e003826f, 0x142929670a0e6e70,
+      0x27b70a8546d22ffc, 0x2e1b21385c26c926, 0x4d2c6dfc5ac42aed, 0x53380d139d95b3df,
+      0x650a73548baf63de, 0x766a0abb3c77b2a8, 0x81c2c92e47edaee6, 0x92722c851482353b,
+      0xa2bfe8a14cf10364, 0xa81a664bbc423001, 0xc24b8b70d0f89791, 0xc76c51a30654be30,
+      0xd192e819d6ef5218, 0xd69906245565a910, 0xf40e35855771202a, 0x106aa07032bbd1b8,
+      0x19a4c116b8d2d0c8, 0x1e376c085141ab53, 0x2748774cdf8eeb99, 0x34b0bcb5e19b48a8,
+      0x391c0cb3c5c95a63, 0x4ed8aa4ae3418acb, 0x5b9cca4f7763e373, 0x682e6ff3d6b2b8a3,
+      0x748f82ee5defb2fc, 0x78a5636f43172f60, 0x84c87814a1f0ab72, 0x8cc702081a6439ec,
+      0x90befffa23631e28, 0xa4506cebde82bde9, 0xbef9a3f7b2c67915, 0xc67178f2e372532b,
+      0xca273eceea26619c, 0xd186b8c721c0c207, 0xeada7dd6cde0eb1e, 0xf57d4f7fee6ed178,
+      0x06f067aa72176fba, 0x0a637dc5a2c898a6, 0x113f9804bef90dae, 0x1b710b35131c471b,
+      0x28db77f523047d84, 0x32caab7b40c72493, 0x3c9ebe0a15c9bebc, 0x431d67c49c100d4c,
+      0x4cc5d4becb3e42b6, 0x597f299cfc657e2a, 0x5fcb6fab3ad6faec, 0x6c44198c4a475817]
+
+SIGMA_0 : [w] -> [w]
+SIGMA_0 x = (x >>> (28 : [w])) ^ (x >>> (34 : [w])) ^ (x >>> (39 : [w]))
+
+SIGMA_1 : [w] -> [w]
+SIGMA_1 x = (x >>> (14 : [w])) ^ (x >>> (18 : [w])) ^ (x >>> (41 : [w]))
+
+sigma_0 : [w] -> [w]
+sigma_0 x = (x >>> (1 : [w])) ^ (x >>> (8 : [w])) ^ (x >> (7 : [w]))
+
+sigma_1 : [w] -> [w]
+sigma_1 x = (x >>> (19 : [w])) ^ (x >>> (61 : [w])) ^ (x >> (6 : [w]))
+
+
+// ============================================================================
+// Definitions from cryptol-specs/Primitive/Keyless/Hash/SHA.cry
+// ============================================================================
+
+Ch : [w] -> [w] -> [w] -> [w]
+Ch x y z = (x && y) ^ (~x && z)
+
+Maj : [w] -> [w] -> [w] -> [w]
+Maj x y z = (x && y) ^ (x && z) ^ (y && z)
+
+
+// ============================================================================
+// Cryptol functions which closely match the definitions in sha512.c
+// ============================================================================
+
+round_00_15_spec : [w] ->
+                   [w] -> [w] -> [w] -> [w] -> [w] -> [w] -> [w] -> [w] ->
+                   [w] ->
+                   ([w], [w], [w], [w], [w], [w], [w], [w], [w])
+round_00_15_spec i a b c d e f g h T1 =
+  (a, b, c, d', e, f, g, h', T1')
+  where T1' = T1 + h + SIGMA_1 e + Ch e f g + K @ i
+        d' = d + T1'
+        h' = SIGMA_0 a + Maj a b c + T1'
+
+round_16_80_spec : [w] -> [w] ->
+                   [w] -> [w] -> [w] -> [w] -> [w] -> [w] -> [w] -> [w] ->
+                   [16][w] ->
+                   [w] -> [w] -> [w] ->
+                   ([w], [w], [w], [w], [w], [w], [w], [w], [16][w], [w], [w], [w])
+round_16_80_spec i j a b c d e f g h X s0 s1 T1 =
+  (a', b', c', d', e', f', g', h', X', s0', s1', T1'')
+  where s0' = sigma_0 (X @ ((j + 1) && 15))
+        s1' = sigma_1 (X @ ((j +  4) && 15))
+        T1' = X @ (j && 15) + s0' + s1' + X @ ((j + 9) && 15)
+        X' = update X (j && 15) T1'
+        (a', b', c', d', e', f', g', h', T1'') =
+          round_00_15_spec (i + j) a b c d e f g h T1'

heapster-saw/examples/sha512_mr_solver.saw

@@ -0,0 +1,108 @@
+enable_experimental;
+env <- heapster_init_env "SHA512" "sha512.bc";
+
+// Heapster
+
+heapster_define_perm env "int64" " " "llvmptr 64" "exists x:bv 64.eq(llvmword(x))";
+heapster_define_perm env "int32" " " "llvmptr 32" "exists x:bv 32.eq(llvmword(x))";
+heapster_define_perm env "int8" " " "llvmptr 8" "exists x:bv 8.eq(llvmword(x))";
+
+heapster_define_perm env "int64_ptr" " " "llvmptr 64" "ptr((W,0) |-> int64<>)";
+
+heapster_assume_fun env "CRYPTO_load_u64_be"
+  "(). arg0:ptr((R,0) |-> int64<>) -o \
+     \ arg0:ptr((R,0) |-> int64<>), ret:int64<>"
+  "\\ (x:Vec 64 Bool) -> returnM (Vec 64 Bool * Vec 64 Bool) (x, x)";
+
+heapster_typecheck_fun env "round_00_15"
+ "(). arg0:int64<>, \
+    \ arg1:int64_ptr<>, arg2:int64_ptr<>, arg3:int64_ptr<>, arg4:int64_ptr<>, \
+    \ arg5:int64_ptr<>, arg6:int64_ptr<>, arg7:int64_ptr<>, arg8:int64_ptr<>, \
+    \ arg9:int64_ptr<> -o \
+    \ arg1:int64_ptr<>, arg2:int64_ptr<>, arg3:int64_ptr<>, arg4:int64_ptr<>, \
+    \ arg5:int64_ptr<>, arg6:int64_ptr<>, arg7:int64_ptr<>, arg8:int64_ptr<>, \
+    \ arg9:int64_ptr<>, ret:true";
+
+heapster_typecheck_fun env "round_16_80"
+ "(). arg0:int64<>, arg1:int64<>, \
+    \ arg2:int64_ptr<>, arg3:int64_ptr<>, arg4:int64_ptr<>, arg5:int64_ptr<>, \
+    \ arg6:int64_ptr<>, arg7:int64_ptr<>, arg8:int64_ptr<>, arg9:int64_ptr<>, \
+    \ arg10:array(W,0,<16,*8,fieldsh(int64<>)), \
+    \ arg11:ptr((W,0) |-> true), arg12:ptr((W,0) |-> true), arg13:int64_ptr<> -o \
+    \ arg2:int64_ptr<>, arg3:int64_ptr<>, arg4:int64_ptr<>, arg5:int64_ptr<>, \
+    \ arg6:int64_ptr<>, arg7:int64_ptr<>, arg8:int64_ptr<>, arg9:int64_ptr<>, \
+    \ arg10:array(W,0,<16,*8,fieldsh(int64<>)), \
+    \ arg11:int64_ptr<>, arg12:int64_ptr<>, arg13:int64_ptr<>, ret:true";
+
+heapster_typecheck_fun env "return_X"
+  "(). arg0:array(W,0,<16,*8,fieldsh(int64<>)) -o \
+     \ arg0:array(W,0,<16,*8,fieldsh(int64<>))";
+
+heapster_set_translation_checks env false;
+heapster_typecheck_fun env "processBlock"
+  "(). arg0:int64_ptr<>, arg1:int64_ptr<>, arg2:int64_ptr<>, \
+     \ arg3:int64_ptr<>, arg4:int64_ptr<>, arg5:int64_ptr<>, \
+     \ arg6:int64_ptr<>, arg7:int64_ptr<>, \
+     \ arg8:array(R,0,<16,*8,fieldsh(int64<>)) -o \
+     \ arg0:int64_ptr<>, arg1:int64_ptr<>, arg2:int64_ptr<>, \
+     \ arg3:int64_ptr<>, arg4:int64_ptr<>, arg5:int64_ptr<>, \
+     \ arg6:int64_ptr<>, arg7:int64_ptr<>, \
+     \ arg8:array(R,0,<16,*8,fieldsh(int64<>)), ret:true";
+
+// FIXME: This translation contains errors
+heapster_set_translation_checks env false;
+heapster_typecheck_fun env "processBlocks"
+  "(num:bv 64). arg0:array(W,0,<8,*8,fieldsh(int64<>)), \
+              \ arg1:array(R,0,<16*num,*8,fieldsh(int64<>)), \
+              \ arg2:eq(llvmword(num)) -o \
+              \ arg0:array(W,0,<8,*8,fieldsh(int64<>)), \
+              \ arg1:array(R,0,<16*num,*8,fieldsh(int64<>)), \
+              \ arg2:true, ret:true";
+
+heapster_export_coq env "sha512_mr_solver_gen.v";
+
+// Mr. Solver
+
+let eq_bool b1 b2 =
+  if b1 then
+    if b2 then true else false
+  else
+    if b2 then false else true;
+
+let fail = do { print "Test failed"; exit 1; };
+let run_test name test expected =
+  do { if expected then print (str_concat "Test: " name) else
+         print (str_concat (str_concat "Test: " name) " (expecting failure)");
+       actual <- test;
+       if eq_bool actual expected then print "Success\n" else
+         do { print "Test failed\n"; exit 1; }; };
+
+round_00_15 <- parse_core_mod "SHA512" "round_00_15";
+round_16_80 <- parse_core_mod "SHA512" "round_16_80";
+processBlock <- parse_core_mod "SHA512" "processBlock";
+processBlocks <- parse_core_mod "SHA512" "processBlocks";
+
+// Test that every function refines itself
+// run_test "processBlocks |= processBlocks" (mr_solver processBlocks processBlocks) true;
+// run_test "processBlock |= processBlock" (mr_solver processBlock processBlock) true;
+// run_test "round_16_80 |= round_16_80" (mr_solver round_16_80 round_16_80) true;
+// run_test "round_00_15 |= round_00_15" (mr_solver round_00_15 round_00_15) true;
+
+import "sha512.cry";
+// FIXME: Why aren't we monadifying these automatically when they're used?
+monadify_term {{ K }};
+monadify_term {{ SIGMA_0 }};
+monadify_term {{ SIGMA_1 }};
+monadify_term {{ sigma_0 }};
+monadify_term {{ sigma_1 }};
+monadify_term {{ Ch }};
+monadify_term {{ Maj }};
+
+// FIXME: Why does monadification fail without this line while running
+// "round_16_80 |= round_16_80_spec"?
+monadify_term {{ round_00_15_spec }};
+
+run_test "round_00_15 |= round_00_15_spec" (mr_solver round_00_15 {{ round_00_15_spec }}) true;
+
+// FIXME: Need to add heterogenous equality on output types for this to work
+// run_test "round_16_80 |= round_16_80_spec" (mr_solver_debug 0 round_16_80 {{ round_16_80_spec }}) true;