Merge pull request #7351 from gabor-mezei-arm/7109_ecp_fast_reduction_testing
Test unlikely cases of ECC modular reduction
diff --git a/library/ecp_curves.c b/library/ecp_curves.c
index c23ff2c..30ae79e 100644
--- a/library/ecp_curves.c
+++ b/library/ecp_curves.c
@@ -4897,7 +4897,7 @@
#define A(i) Np + (i) * WIDTH
#define ADD(i) add64(p, A(i), &c)
#define NEXT p += WIDTH; carry64(p, &c)
-#define LAST p += WIDTH; *p = c; while (++p < end) *p = 0
+#define LAST p += WIDTH; do *p = 0; while (++p < end)
#define RESET last_carry[0] = c; c = 0; p = Np
#define ADD_LAST add64(p, last_carry, &c)
@@ -4936,11 +4936,21 @@
/* Use the reduction for the carry as well:
* 2^192 * last_carry = 2^64 * last_carry + last_carry mod P192
+ * It can generate a carry. */
+ ADD_LAST; NEXT; // A0 += last_carry
+ ADD_LAST; NEXT; // A1 += last_carry
+ // A2 += carry
+
+ RESET;
+
+ /* Use the reduction for the carry as well:
+ * 2^192 * last_carry = 2^64 * last_carry + last_carry mod P192
*/
ADD_LAST; NEXT; // A0 += last_carry
ADD_LAST; NEXT; // A1 += last_carry
+ // A2 += carry
- LAST; // A2 += carry
+ LAST;
return 0;
}
diff --git a/scripts/mbedtls_dev/ecp.py b/scripts/mbedtls_dev/ecp.py
index aee8718..1c03205 100644
--- a/scripts/mbedtls_dev/ecp.py
+++ b/scripts/mbedtls_dev/ecp.py
@@ -28,7 +28,7 @@
class EcpP192R1Raw(bignum_common.ModOperationCommon,
EcpTarget):
- """Test cases for ecp quasi_reduction()."""
+ """Test cases for ECP P192 fast reduction."""
symbol = "-"
test_function = "ecp_mod_p192_raw"
test_name = "ecp_mod_p192_raw"
@@ -43,6 +43,24 @@
# Modulus - 1
"fffffffffffffffffffffffffffffffefffffffffffffffe",
+ # Modulus + 1
+ "ffffffffffffffffffffffffffffffff0000000000000000",
+
+ # 2^192 - 1
+ "ffffffffffffffffffffffffffffffffffffffffffffffff",
+
+ # Maximum canonical P192 multiplication result
+ ("fffffffffffffffffffffffffffffffdfffffffffffffffc"
+ "000000000000000100000000000000040000000000000004"),
+
+ # Generate an overflow during reduction
+ ("00000000000000000000000000000001ffffffffffffffff"
+ "ffffffffffffffffffffffffffffffff0000000000000000"),
+
+ # Generate an overflow during carry reduction
+ ("ffffffffffffffff00000000000000010000000000000000"
+ "fffffffffffffffeffffffffffffffff0000000000000000"),
+
# First 8 number generated by random.getrandbits(384) - seed(2,2)
("cf1822ffbc6887782b491044d5e341245c6e433715ba2bdd"
"177219d30e7a269fd95bafc8f2a4d27bdcf4bb99f4bea973"),
@@ -81,7 +99,7 @@
class EcpP224R1Raw(bignum_common.ModOperationCommon,
EcpTarget):
- """Test cases for ecp quasi_reduction()."""
+ """Test cases for ECP P224 fast reduction."""
symbol = "-"
test_function = "ecp_mod_p224_raw"
test_name = "ecp_mod_p224_raw"
@@ -96,6 +114,12 @@
# Modulus - 1
"ffffffffffffffffffffffffffffffff000000000000000000000000",
+ # Modulus + 1
+ "ffffffffffffffffffffffffffffffff000000000000000000000002",
+
+ # 2^224 - 1
+ "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
+
# Maximum canonical P224 multiplication result
("fffffffffffffffffffffffffffffffe000000000000000000000000"
"00000001000000000000000000000000000000000000000000000000"),
@@ -145,100 +169,6 @@
return True
-class EcpP384R1Raw(bignum_common.ModOperationCommon,
- EcpTarget):
- """Test cases for ecp quasi_reduction modulo p384."""
- test_function = "ecp_mod_p384_raw"
- test_name = "ecp_mod_p384_raw"
- input_style = "fixed"
- arity = 1
-
- moduli = [("ffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
- "fffffeffffffff0000000000000000ffffffff")
- ] # type: List[str]
-
- input_values = [
- "0", "1",
-
- # Modulus - 1
- ("fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffef"
- "fffffff0000000000000000fffffffe"),
-
- # Maximum canonical P384 multiplication result
- ("ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
- "fdfffffffe0000000000000001fffffffc0000000000000000000000000000000"
- "10000000200000000fffffffe000000020000000400000000fffffffc00000004"),
-
- # Testing with overflow in A(12) + A(21) + A(20);
- ("497811378624857a2c2af60d70583376545484cfae5c812fe2999fc1abb51d18b"
- "559e8ca3b50aaf263fdf8f24bdfb98fffffffff20e65bf9099e4e73a5e8b517cf"
- "4fbeb8fd1750fdae6d43f2e53f82d5ffffffffffffffffcc6f1e06111c62e0"),
-
- # Testing with underflow in A(13) + A(22) + A(23) - A(12) - A(20);
- ("dfdd25e96777406b3c04b8c7b406f5fcf287e1e576003a092852a6fbe517f2712"
- "b68abef41dbd35183a0614fb7222606ffffffff84396eee542f18a9189d94396c"
- "784059c17a9f18f807214ef32f2f10ffffffff8a77fac20000000000000000"),
-
- # Testing with overflow in A(23) + A(20) + A(19) - A(22);
- ("783753f8a5afba6c1862eead1deb2fcdd907272be3ffd18542b24a71ee8b26ca"
- "b0aa33513610ff973042bbe1637cc9fc99ad36c7f703514572cf4f5c3044469a"
- "8f5be6312c19e5d3f8fc1ac6ffffffffffffffff8c86252400000000ffffffff"),
-
- # Testing with underflow in A(23) + A(20) + A(19) - A(22);
- ("65e1d2362fce922663b7fd517586e88842a9b4bd092e93e6251c9c69f278cbf8"
- "285d99ae3b53da5ba36e56701e2b17c225f1239556c5f00117fa140218b46ebd8"
- "e34f50d0018701fa8a0a5cc00000000000000004410bcb4ffffffff00000000"),
-
- # Testing the second round of carry reduction
- ("000000000000000000000000ffffffffffffffffffffffffffffffffffffffff"
- "ffffffffffffffff00000000000000000000000000000000ffffffff00000000"
- "000000000000000100000000000000000000000000000000ffffffff00000001"),
-
- # First 8 number generated by random.getrandbits(768) - seed(2,2)
- ("ffed9235288bc781ae66267594c9c9500925e4749b575bd13653f8dd9b1f282e"
- "4067c3584ee207f8da94e3e8ab73738fcf1822ffbc6887782b491044d5e34124"
- "5c6e433715ba2bdd177219d30e7a269fd95bafc8f2a4d27bdcf4bb99f4bea973"),
- ("e8624fab5186ee32ee8d7ee9770348a05d300cb90706a045defc044a09325626"
- "e6b58de744ab6cce80877b6f71e1f6d2ef8acd128b4f2fc15f3f57ebf30b94fa"
- "82523e86feac7eb7dc38f519b91751dacdbd47d364be8049a372db8f6e405d93"),
- ("fec3f6b32e8d4b8a8f54f8ceacaab39e83844b40ffa9b9f15c14bc4a829e07b0"
- "829a48d422fe99a22c70501e533c91352d3d854e061b90303b08c6e33c729578"
- "2d6c797f8f7d9b782a1be9cd8697bbd0e2520e33e44c50556c71c4a66148a86f"),
- ("bd143fa9b714210c665d7435c1066932f4767f26294365b2721dea3bf63f23d0"
- "dbe53fcafb2147df5ca495fa5a91c89b97eeab64ca2ce6bc5d3fd983c34c769f"
- "e89204e2e8168561867e5e15bc01bfce6a27e0dfcbf8754472154e76e4c11ab2"),
- ("8ebdbfe3eb9ac688b9d39cca91551e8259cc60b17604e4b4e73695c3e652c71a"
- "74667bffe202849da9643a295a9ac6decbd4d3e2d4dec9ef83f0be4e80371eb9"
- "7f81375eecc1cb6347733e847d718d733ff98ff387c56473a7a83ee0761ebfd2"),
- ("d4c0dca8b4c9e755cc9c3adcf515a8234da4daeb4f3f87777ad1f45ae9500ec9"
- "c5e2486c44a4a8f69dc8db48e86ec9c6e06f291b2a838af8d5c44a4eb3172062"
- "d08f1bb2531d6460f0caeef038c89b38a8acb5137c9260dc74e088a9b9492f25"),
- ("227eeb7b9d7d01f5769da05d205bbfcc8c69069134bccd3e1cf4f589f8e4ce0a"
- "f29d115ef24bd625dd961e6830b54fa7d28f93435339774bb1e386c4fd5079e6"
- "81b8f5896838b769da59b74a6c3181c81e220df848b1df78feb994a81167346"),
- ("d322a7353ead4efe440e2b4fda9c025a22f1a83185b98f5fc11e60de1b343f52"
- "ea748db9e020307aaeb6db2c3a038a709779ac1f45e9dd320c855fdfa7251af0"
- "930cdbd30f0ad2a81b2d19a2beaa14a7ff3fe32a30ffc4eed0a7bd04e85bfcdd"),
-
- # Next 2 number generated by random.getrandbits(384)
- ("5c3747465cc36c270e8a35b10828d569c268a20eb78ac332e5e138e26c4454b9"
- "0f756132e16dce72f18e859835e1f291"),
- ("eb2b5693babb7fbb0a76c196067cfdcb11457d9cf45e2fa01d7f427515392480"
- "0600571fac3a5b263fdf57cd2c006497")
- ]
-
- @property
- def arg_a(self) -> str:
- return super().format_arg('{:x}'.format(self.int_a)).zfill(2 * self.hex_digits)
-
- def result(self) -> List[str]:
- result = self.int_a % self.int_n
- return [self.format_result(result)]
-
- @property
- def is_valid(self) -> bool:
- return True
-
class EcpP256R1Raw(bignum_common.ModOperationCommon,
EcpTarget):
"""Test cases for ECP P256 fast reduction."""
@@ -256,6 +186,12 @@
# Modulus - 1
"ffffffff00000001000000000000000000000000fffffffffffffffffffffffe",
+ # Modulus + 1
+ "ffffffff00000001000000000000000000000001000000000000000000000000",
+
+ # 2^256 - 1
+ "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
+
# Maximum canonical P256 multiplication result
("fffffffe00000002fffffffe0000000100000001fffffffe00000001fffffffc"
"00000003fffffffcfffffffffffffffffffffffc000000000000000000000004"),
@@ -312,9 +248,125 @@
return True
+class EcpP384R1Raw(bignum_common.ModOperationCommon,
+ EcpTarget):
+ """Test cases for ECP P384 fast reduction."""
+ test_function = "ecp_mod_p384_raw"
+ test_name = "ecp_mod_p384_raw"
+ input_style = "fixed"
+ arity = 1
+
+ moduli = [("ffffffffffffffffffffffffffffffffffffffffffffffff"
+ "fffffffffffffffeffffffff0000000000000000ffffffff")
+ ] # type: List[str]
+
+ input_values = [
+ "0", "1",
+
+ # Modulus - 1
+ ("ffffffffffffffffffffffffffffffffffffffffffffffff"
+ "fffffffffffffffeffffffff0000000000000000fffffffe"),
+
+ # Modulus + 1
+ ("ffffffffffffffffffffffffffffffffffffffffffffffff"
+ "fffffffffffffffeffffffff000000000000000100000000"),
+
+ # 2^384 - 1
+ ("ffffffffffffffffffffffffffffffffffffffffffffffff"
+ "ffffffffffffffffffffffffffffffffffffffffffffffff"),
+
+ # Maximum canonical P384 multiplication result
+ ("ffffffffffffffffffffffffffffffffffffffffffffffff"
+ "fffffffffffffffdfffffffe0000000000000001fffffffc"
+ "000000000000000000000000000000010000000200000000"
+ "fffffffe000000020000000400000000fffffffc00000004"),
+
+ # Testing with overflow in A(12) + A(21) + A(20);
+ ("497811378624857a2c2af60d70583376545484cfae5c812f"
+ "e2999fc1abb51d18b559e8ca3b50aaf263fdf8f24bdfb98f"
+ "ffffffff20e65bf9099e4e73a5e8b517cf4fbeb8fd1750fd"
+ "ae6d43f2e53f82d5ffffffffffffffffcc6f1e06111c62e0"),
+
+ # Testing with underflow in A(13) + A(22) + A(23) - A(12) - A(20);
+ ("dfdd25e96777406b3c04b8c7b406f5fcf287e1e576003a09"
+ "2852a6fbe517f2712b68abef41dbd35183a0614fb7222606"
+ "ffffffff84396eee542f18a9189d94396c784059c17a9f18"
+ "f807214ef32f2f10ffffffff8a77fac20000000000000000"),
+
+ # Testing with overflow in A(23) + A(20) + A(19) - A(22);
+ ("783753f8a5afba6c1862eead1deb2fcdd907272be3ffd185"
+ "42b24a71ee8b26cab0aa33513610ff973042bbe1637cc9fc"
+ "99ad36c7f703514572cf4f5c3044469a8f5be6312c19e5d3"
+ "f8fc1ac6ffffffffffffffff8c86252400000000ffffffff"),
+
+ # Testing with underflow in A(23) + A(20) + A(19) - A(22);
+ ("65e1d2362fce922663b7fd517586e88842a9b4bd092e93e6"
+ "251c9c69f278cbf8285d99ae3b53da5ba36e56701e2b17c2"
+ "25f1239556c5f00117fa140218b46ebd8e34f50d0018701f"
+ "a8a0a5cc00000000000000004410bcb4ffffffff00000000"),
+
+ # Testing the second round of carry reduction
+ ("000000000000000000000000ffffffffffffffffffffffff"
+ "ffffffffffffffffffffffffffffffff0000000000000000"
+ "0000000000000000ffffffff000000000000000000000001"
+ "00000000000000000000000000000000ffffffff00000001"),
+
+ # First 8 number generated by random.getrandbits(768) - seed(2,2)
+ ("ffed9235288bc781ae66267594c9c9500925e4749b575bd1"
+ "3653f8dd9b1f282e4067c3584ee207f8da94e3e8ab73738f"
+ "cf1822ffbc6887782b491044d5e341245c6e433715ba2bdd"
+ "177219d30e7a269fd95bafc8f2a4d27bdcf4bb99f4bea973"),
+ ("e8624fab5186ee32ee8d7ee9770348a05d300cb90706a045"
+ "defc044a09325626e6b58de744ab6cce80877b6f71e1f6d2"
+ "ef8acd128b4f2fc15f3f57ebf30b94fa82523e86feac7eb7"
+ "dc38f519b91751dacdbd47d364be8049a372db8f6e405d93"),
+ ("fec3f6b32e8d4b8a8f54f8ceacaab39e83844b40ffa9b9f1"
+ "5c14bc4a829e07b0829a48d422fe99a22c70501e533c9135"
+ "2d3d854e061b90303b08c6e33c7295782d6c797f8f7d9b78"
+ "2a1be9cd8697bbd0e2520e33e44c50556c71c4a66148a86f"),
+ ("bd143fa9b714210c665d7435c1066932f4767f26294365b2"
+ "721dea3bf63f23d0dbe53fcafb2147df5ca495fa5a91c89b"
+ "97eeab64ca2ce6bc5d3fd983c34c769fe89204e2e8168561"
+ "867e5e15bc01bfce6a27e0dfcbf8754472154e76e4c11ab2"),
+ ("8ebdbfe3eb9ac688b9d39cca91551e8259cc60b17604e4b4"
+ "e73695c3e652c71a74667bffe202849da9643a295a9ac6de"
+ "cbd4d3e2d4dec9ef83f0be4e80371eb97f81375eecc1cb63"
+ "47733e847d718d733ff98ff387c56473a7a83ee0761ebfd2"),
+ ("d4c0dca8b4c9e755cc9c3adcf515a8234da4daeb4f3f8777"
+ "7ad1f45ae9500ec9c5e2486c44a4a8f69dc8db48e86ec9c6"
+ "e06f291b2a838af8d5c44a4eb3172062d08f1bb2531d6460"
+ "f0caeef038c89b38a8acb5137c9260dc74e088a9b9492f25"),
+ ("0227eeb7b9d7d01f5769da05d205bbfcc8c69069134bccd3"
+ "e1cf4f589f8e4ce0af29d115ef24bd625dd961e6830b54fa"
+ "7d28f93435339774bb1e386c4fd5079e681b8f5896838b76"
+ "9da59b74a6c3181c81e220df848b1df78feb994a81167346"),
+ ("d322a7353ead4efe440e2b4fda9c025a22f1a83185b98f5f"
+ "c11e60de1b343f52ea748db9e020307aaeb6db2c3a038a70"
+ "9779ac1f45e9dd320c855fdfa7251af0930cdbd30f0ad2a8"
+ "1b2d19a2beaa14a7ff3fe32a30ffc4eed0a7bd04e85bfcdd"),
+
+ # Next 2 number generated by random.getrandbits(384)
+ ("5c3747465cc36c270e8a35b10828d569c268a20eb78ac332"
+ "e5e138e26c4454b90f756132e16dce72f18e859835e1f291"),
+ ("eb2b5693babb7fbb0a76c196067cfdcb11457d9cf45e2fa0"
+ "1d7f4275153924800600571fac3a5b263fdf57cd2c006497")
+ ]
+
+ @property
+ def arg_a(self) -> str:
+ return super().format_arg('{:x}'.format(self.int_a)).zfill(2 * self.hex_digits)
+
+ def result(self) -> List[str]:
+ result = self.int_a % self.int_n
+ return [self.format_result(result)]
+
+ @property
+ def is_valid(self) -> bool:
+ return True
+
class EcpP521R1Raw(bignum_common.ModOperationCommon,
EcpTarget):
- """Test cases for ecp quasi_reduction()."""
+ """Test cases for ECP P521 fast reduction."""
test_function = "ecp_mod_p521_raw"
test_name = "ecp_mod_p521_raw"
input_style = "arch_split"
@@ -327,7 +379,15 @@
input_values = [
"0", "1",
- # Corner case: maximum canonical P521 multiplication result
+ # Modulus - 1
+ ("01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
+ "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe"),
+
+ # Modulus + 1
+ ("020000000000000000000000000000000000000000000000000000000000000000"
+ "000000000000000000000000000000000000000000000000000000000000000000"),
+
+ # Maximum canonical P521 multiplication result
("0003ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
"ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
"fffff800"