[Cryptech-Commits] [user/sra/libhal] 01/02: First pass at RSA tests.
git at cryptech.is
git at cryptech.is
Thu May 28 07:46:41 UTC 2015
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sra at hactrn.net pushed a commit to branch master
in repository user/sra/libhal.
commit 2c81ecf429e266039a66d83742e22ea0eccfa327
Author: Rob Austein <sra at hactrn.net>
Date: Wed May 27 15:56:59 2015 +0200
First pass at RSA tests.
---
tests/Makefile.in | 2 +-
tests/test-rsa.c | 215 ++++++++++++++++++
tests/test-rsa.h | 644 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
tests/test-rsa.py | 86 ++++++++
4 files changed, 946 insertions(+), 1 deletion(-)
diff --git a/tests/Makefile.in b/tests/Makefile.in
index ba45a57..19c68c8 100644
--- a/tests/Makefile.in
+++ b/tests/Makefile.in
@@ -2,7 +2,7 @@
INC = ../cryptech.h
LIB = ../libcryptech.a
-BIN = test-aes-key-wrap test-hash
+BIN = test-aes-key-wrap test-hash test-rsa
CC = @CC@
CFLAGS = @CFLAGS@ -I..
diff --git a/tests/test-rsa.c b/tests/test-rsa.c
new file mode 100644
index 0000000..95b366a
--- /dev/null
+++ b/tests/test-rsa.c
@@ -0,0 +1,215 @@
+/*
+ * First stumblings towards a test harness for RSA using Cryptech
+ * ModExp core.
+ *
+ * For the moment this just does modular exponentiation tests using
+ * RSA keys and pre-formatted data-to-be-signed, without attempting
+ * CRT or any of the other clever stuff we should be doing. This is
+ * not usable for any sane purpose other than testing.
+ */
+
+#include <stdio.h>
+#include <stdint.h>
+#include <stdlib.h>
+#include <string.h>
+#include <assert.h>
+
+#include "cryptech.h"
+#include "test-rsa.h"
+
+/*
+ * Constant value to use with hal_io_write() when we don't want
+ * a read-back check thus aren't using set_register().
+ */
+
+static const uint8_t one[] = { 0, 0, 0, 1 };
+
+/*
+ * Debugging aid: check a result, report on failure.
+ */
+
+#define check(_expr_) \
+ do { \
+ if ((_expr_) != 0) \
+ return printf("%s failed\n", #_expr_), 1; \
+ } while (0)
+
+/*
+ * Set an ordinary register, with read-back check.
+ */
+
+static int _set_register(const off_t addr,
+ const char * const name,
+ uint32_t value)
+{
+ uint8_t w1[4], w2[4];
+ int i;
+ assert(name != NULL);
+ for (i = 3; i >= 0; i--) {
+ w1[i] = value & 0xFF;
+ value >>= 8;
+ }
+ printf("Setting register %#lx %s\n", (unsigned long) addr, name);
+ check(hal_io_write(addr, w1, sizeof(w1)));
+ check(hal_io_read(addr, w2, sizeof(w2)));
+ if (memcmp(w1, w2, sizeof(w1)) != 0)
+ printf("MISMATCH\n");
+ printf("\n");
+ return 0;
+}
+
+/*
+ * Get value of a block memory.
+ */
+
+static int _get_blockmem(const off_t reset_addr,
+ const char * const reset_name,
+ const off_t data_addr,
+ const char * const data_name,
+ uint8_t *value,
+ const size_t length)
+{
+ size_t i;
+ assert(reset_name != NULL && data_name != NULL && value != NULL && length % 4 == 0 && length <= sizeof(value));
+ printf("Setting register %#lx %s\n", (unsigned long) reset_addr, reset_name);
+ check(hal_io_write(reset_addr, one, sizeof(one)));
+ printf("\n");
+ printf("Getting blockmem %#lx %s\n", (unsigned long) data_addr, data_name);
+ for (i = 0; i < length; i += 4)
+ check(hal_io_read(data_addr, &value[i], 4));
+ return 0;
+}
+
+/*
+ * Set value of a block memory, with read-back check.
+ */
+
+static int _set_blockmem(const off_t reset_addr,
+ const char * const reset_name,
+ const off_t data_addr,
+ const char * const data_name,
+ const uint8_t * const value,
+ const size_t value_length,
+ uint8_t *buffer,
+ const size_t buffer_length)
+{
+ size_t i;
+ assert(reset_name != NULL && data_name != NULL && value != NULL && buffer_length >= value_length && value_length % 4 == 0);
+ printf("Setting register %#lx %s\n", (unsigned long) reset_addr, reset_name);
+ check(hal_io_write(reset_addr, one, sizeof(one)));
+ printf("\n");
+ printf("Setting blockmem %#lx %s\n", (unsigned long) data_addr, data_name);
+ for (i = 0; i < value_length; i += 4)
+ check(hal_io_write(data_addr, &value[i], 4));
+ printf("\n");
+ check(_get_blockmem(reset_addr, reset_name, data_addr, data_name, buffer, value_length));
+ if (memcmp(value, buffer, value_length))
+ printf("MISMATCH\n");
+ printf("\n");
+ return 0;
+}
+
+/*
+ * Syntactic sugar.
+ */
+
+#define set_register(_field_, _value_) \
+ _set_register(_field_, #_field_, _value_)
+
+#define get_blockmem(_field_, _value_) \
+ _get_blockmem(_field_##_PTR_RST, #_field_ "_PTR_RST", _field_##_DATA, #_field_ "_DATA", _value_, sizeof(_value_))
+
+#define set_blockmem(_field_, _value_, _buffer_) \
+ _set_blockmem(_field_##_PTR_RST, #_field_ "_PTR_RST", _field_##_DATA, #_field_ "_DATA", (_value_).val, (_value_).len, _buffer_, sizeof(_buffer_))
+
+/*
+ * Test driver.
+ */
+
+static int test(const rsa_tc_t * const tc)
+{
+ uint8_t b[4096];
+
+ printf("Signature test for %lu-bit RSA key\n", (unsigned long) tc->size);
+
+ check(set_blockmem(MODEXP_MODULUS, tc->n, b));
+ check(set_blockmem(MODEXP_MESSAGE, tc->m, b));
+ check(set_register(MODEXP_MODULUS_LENGTH, tc->n.len / 4));
+
+ check(set_blockmem(MODEXP_EXPONENT, tc->d, b));
+ check(set_register(MODEXP_EXPONENT_LENGTH, tc->d.len / 4));
+
+ printf("Checking ready status\n");
+ check(hal_io_wait_ready(MODEXP_ADDR_STATUS));
+ printf("\n");
+
+ check(set_register(MODEXP_ADDR_CTRL, 1));
+
+ printf("Waiting for ready\n");
+ check(hal_io_wait(MODEXP_ADDR_STATUS, STATUS_READY, NULL));
+ printf("\n");
+
+ check(get_blockmem(MODEXP_RESULT, b));
+
+ printf("Comparing results with known value...");
+ if (memcmp(b, tc->s.val, tc->s.len))
+ printf("MISMATCH\n");
+ else
+ printf("OK\n");
+
+ printf("Verification test for %lu-bit RSA key\n", (unsigned long) tc->size);
+
+ check(set_blockmem(MODEXP_MODULUS, tc->n, b));
+ check(set_blockmem(MODEXP_MESSAGE, tc->m, b));
+ check(set_register(MODEXP_MODULUS_LENGTH, tc->n.len / 4));
+
+ check(set_blockmem(MODEXP_EXPONENT, tc->e, b));
+ check(set_register(MODEXP_EXPONENT_LENGTH, tc->e.len / 4));
+
+ printf("Checking ready status\n");
+ check(hal_io_wait_ready(MODEXP_ADDR_STATUS));
+ printf("\n");
+
+ check(set_register(MODEXP_ADDR_CTRL, 1));
+
+ printf("Waiting for ready\n");
+ check(hal_io_wait(MODEXP_ADDR_STATUS, STATUS_READY, NULL));
+ printf("\n");
+
+ check(get_blockmem(MODEXP_RESULT, b));
+
+ printf("Comparing results with known value...");
+ if (memcmp(b, tc->m.val, tc->m.len))
+ printf("MISMATCH\n");
+ else
+ printf("OK\n");
+
+ return 0;
+}
+
+
+int main(int argc, char *argv[])
+{
+ uint8_t name[8], version[4];
+ int i;
+
+ /*
+ * Initialize EIM and report what core we're running.
+ */
+
+ check(hal_io_read(MODEXP_ADDR_NAME0, name, sizeof(name)));
+ check(hal_io_read(MODEXP_ADDR_VERSION, version, sizeof(version)));
+ printf("\"%8.8s\" \"%4.4s\"\n\n", name, version);
+
+ hal_io_set_debug(1);
+
+ /*
+ * Run all the test cases.
+ */
+
+ for (i = 0; i < sizeof(rsa_tc)/sizeof(*rsa_tc); i++)
+ if (test(&rsa_tc[i]))
+ return 1;
+
+ return 0;
+}
diff --git a/tests/test-rsa.h b/tests/test-rsa.h
new file mode 100644
index 0000000..b6e6ba6
--- /dev/null
+++ b/tests/test-rsa.h
@@ -0,0 +1,644 @@
+/*
+ * RSA signature test data for Cryptech project, automatically generated by
+ * test-rsa.py using PyCrypto version 2.6.1. Do not edit.
+ *
+ * Plaintext: "You can hack anything you want with TECO and DDT."
+ * SHA-256: 8e36fc9aa31724c32416263c0366a175fabbb92b741ca6496107074d0343b597
+ */
+
+/* 1024-bit RSA private key (PKCS #8)
+-----BEGIN PRIVATE KEY-----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+-----END PRIVATE KEY-----
+*/
+
+static const uint8_t n_1024[] = { /* key component n, 128 bytes */
+ 0xd0, 0x75, 0xec, 0x0a, 0x95, 0x04, 0x8e, 0xf8, 0xca, 0xa6, 0x90, 0x73,
+ 0x8d, 0x9d, 0x58, 0xe9, 0x17, 0x64, 0xb4, 0x37, 0x50, 0xb5, 0x8c, 0xad,
+ 0x8a, 0x6e, 0x31, 0x99, 0x13, 0x5f, 0x80, 0xee, 0x84, 0xeb, 0x2b, 0xde,
+ 0x58, 0xd3, 0x8e, 0xe3, 0x58, 0x25, 0xe9, 0x1e, 0xaf, 0xde, 0xb1, 0xba,
+ 0xa1, 0x5a, 0x16, 0x0b, 0x00, 0x57, 0xc4, 0x7c, 0xc7, 0x76, 0x5e, 0x31,
+ 0x86, 0x8a, 0x3e, 0x15, 0x5e, 0xe5, 0x7c, 0xef, 0xb0, 0x08, 0xc4, 0xdd,
+ 0x6a, 0x0a, 0x89, 0xee, 0x98, 0xa4, 0xee, 0x9c, 0x97, 0x1a, 0x07, 0xde,
+ 0x61, 0xe5, 0xb0, 0xd3, 0xcf, 0x70, 0xe1, 0xcd, 0xc6, 0xa0, 0xde, 0x5b,
+ 0x45, 0x1f, 0x2f, 0xb9, 0xdb, 0x99, 0x51, 0x96, 0x9f, 0x2f, 0x88, 0x4b,
+ 0x4b, 0x09, 0x74, 0x9a, 0xe6, 0xc4, 0xdd, 0xbe, 0x7e, 0xe6, 0x1f, 0x79,
+ 0x26, 0x5c, 0x6a, 0xdf, 0xb1, 0x6b, 0x30, 0x15
+};
+
+static const uint8_t e_1024[] = { /* key component e, 4 bytes */
+ 0x00, 0x01, 0x00, 0x01
+};
+
+static const uint8_t d_1024[] = { /* key component d, 128 bytes */
+ 0x3f, 0xf2, 0x6c, 0x9e, 0x32, 0x68, 0x5b, 0x93, 0x66, 0x57, 0x02, 0x28,
+ 0xf0, 0x60, 0x3c, 0x4e, 0x04, 0xa7, 0x17, 0xc1, 0x80, 0x38, 0xb1, 0x16,
+ 0xeb, 0x48, 0x32, 0x5e, 0xca, 0xda, 0x99, 0x2a, 0x92, 0x0b, 0xb2, 0x41,
+ 0x5a, 0xee, 0x4a, 0xfe, 0xe2, 0xa3, 0x7e, 0x87, 0xb3, 0x5b, 0x95, 0x19,
+ 0xb3, 0x35, 0x77, 0x5d, 0x98, 0x95, 0x53, 0xe9, 0x13, 0x26, 0xf4, 0x6e,
+ 0x2c, 0xdf, 0x6b, 0x7b, 0x84, 0xaa, 0xbf, 0xa9, 0xef, 0x24, 0xc6, 0x00,
+ 0xb5, 0x68, 0x72, 0xad, 0x5e, 0xdb, 0x90, 0x41, 0xe8, 0xec, 0xd7, 0xf8,
+ 0x53, 0x51, 0x33, 0xfb, 0xde, 0xfc, 0x92, 0xc7, 0x42, 0x38, 0x42, 0x26,
+ 0x7d, 0x40, 0xe5, 0xf5, 0xc9, 0x1b, 0xd7, 0x45, 0x95, 0x78, 0xe4, 0x60,
+ 0xfc, 0x85, 0x83, 0x74, 0x31, 0x72, 0xbe, 0xd3, 0x73, 0xb6, 0x95, 0x7c,
+ 0xc0, 0xd6, 0xa6, 0x8e, 0x33, 0x15, 0x6a, 0x61
+};
+
+static const uint8_t p_1024[] = { /* key component p, 64 bytes */
+ 0xd6, 0x91, 0x44, 0x30, 0xf6, 0xbf, 0xae, 0x10, 0x65, 0x8a, 0xed, 0x04,
+ 0xd8, 0xd1, 0x32, 0x2a, 0xf2, 0x0a, 0x19, 0x7c, 0xf9, 0x7d, 0x21, 0xc5,
+ 0xdd, 0xf7, 0x41, 0x75, 0xb8, 0x01, 0x1d, 0x40, 0x48, 0x29, 0x66, 0x2e,
+ 0x59, 0x89, 0x87, 0x94, 0x64, 0x9a, 0xc6, 0x68, 0xa6, 0x4b, 0x87, 0x10,
+ 0xc7, 0x6e, 0x26, 0x7d, 0xb2, 0xa9, 0x24, 0x2a, 0xf3, 0x07, 0x06, 0x9c,
+ 0xa4, 0xe2, 0x53, 0xe7
+};
+
+static const uint8_t q_1024[] = { /* key component q, 64 bytes */
+ 0xf8, 0xb6, 0xc6, 0xe5, 0x73, 0x1d, 0x03, 0xfc, 0xa6, 0x40, 0xf6, 0x2d,
+ 0xe1, 0x88, 0xc5, 0x56, 0xbc, 0x68, 0x09, 0x9d, 0xac, 0x56, 0x21, 0x12,
+ 0x63, 0x42, 0x2f, 0xba, 0x80, 0x85, 0x6a, 0x88, 0x19, 0x49, 0xaf, 0xfe,
+ 0x05, 0xa8, 0x48, 0xb7, 0x99, 0x71, 0x14, 0x46, 0x42, 0xdd, 0x19, 0xba,
+ 0xc1, 0x05, 0x37, 0x53, 0xb6, 0x9d, 0xa4, 0x29, 0xf4, 0xbd, 0xeb, 0x13,
+ 0x8e, 0x79, 0x9c, 0xa3
+};
+
+static const uint8_t u_1024[] = { /* key component u, 64 bytes */
+ 0x87, 0x5c, 0xc3, 0x4c, 0x33, 0xc7, 0x67, 0xfa, 0xc6, 0xf6, 0xcd, 0xf4,
+ 0x33, 0x85, 0x07, 0x78, 0x7f, 0x56, 0x80, 0x30, 0xee, 0x4c, 0x34, 0x03,
+ 0xa0, 0x5d, 0xa7, 0x34, 0x0d, 0xc9, 0x18, 0x8e, 0xd0, 0xd5, 0xe2, 0xb9,
+ 0x0b, 0x53, 0x4c, 0xb5, 0x00, 0x5b, 0x10, 0x9f, 0xba, 0xbf, 0x2f, 0x65,
+ 0x0a, 0x40, 0x58, 0x18, 0xb3, 0x83, 0xa0, 0x0c, 0x71, 0x01, 0xa4, 0x86,
+ 0xbe, 0xcc, 0x1b, 0x7b
+};
+
+static const uint8_t m_1024[] = { /* message to be signed, 128 bytes */
+ 0x00, 0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0x00, 0x30, 0x31, 0x30, 0x0d, 0x06, 0x09, 0x60,
+ 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x01, 0x05, 0x00, 0x04, 0x20,
+ 0x8e, 0x36, 0xfc, 0x9a, 0xa3, 0x17, 0x24, 0xc3, 0x24, 0x16, 0x26, 0x3c,
+ 0x03, 0x66, 0xa1, 0x75, 0xfa, 0xbb, 0xb9, 0x2b, 0x74, 0x1c, 0xa6, 0x49,
+ 0x61, 0x07, 0x07, 0x4d, 0x03, 0x43, 0xb5, 0x97
+};
+
+static const uint8_t s_1024[] = { /* signed message, 128 bytes */
+ 0x06, 0x33, 0x9a, 0x64, 0x36, 0x7d, 0xb0, 0x2a, 0xf4, 0x11, 0x58, 0xcc,
+ 0x95, 0xe7, 0x60, 0x49, 0x45, 0x19, 0xc1, 0x65, 0x11, 0x11, 0x84, 0xbe,
+ 0xe4, 0x1d, 0x8e, 0xe2, 0x2a, 0xe5, 0xf5, 0xd1, 0x1d, 0xa7, 0xf9, 0x62,
+ 0xac, 0x93, 0xac, 0x88, 0x91, 0x5e, 0xee, 0x13, 0xa3, 0x35, 0x0c, 0x22,
+ 0xf0, 0xdf, 0xa6, 0x2e, 0xfd, 0xfc, 0x2b, 0x62, 0x29, 0xf2, 0x6e, 0x27,
+ 0xbe, 0xbd, 0xc8, 0x4e, 0x47, 0x46, 0xdf, 0x79, 0x7b, 0x38, 0x7a, 0xd2,
+ 0x13, 0x42, 0x3c, 0x9f, 0x98, 0xe8, 0xa1, 0x46, 0xff, 0x48, 0x6b, 0x6c,
+ 0x1a, 0x85, 0x41, 0x4e, 0x73, 0x11, 0x71, 0x21, 0xb7, 0x00, 0xe5, 0x47,
+ 0xab, 0x4e, 0x07, 0xb2, 0x21, 0xb9, 0x88, 0xb8, 0x24, 0xdd, 0x77, 0xc2,
+ 0x04, 0x6b, 0x0a, 0x20, 0xcd, 0xdb, 0x98, 0x6a, 0xac, 0x75, 0xc2, 0xf2,
+ 0xb0, 0x44, 0xed, 0x59, 0xea, 0x56, 0x58, 0x79
+};
+
+/* 2048-bit RSA private key (PKCS #8)
+-----BEGIN PRIVATE KEY-----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+-----END PRIVATE KEY-----
+*/
+
+static const uint8_t n_2048[] = { /* key component n, 256 bytes */
+ 0xb9, 0xb4, 0x69, 0x69, 0xb0, 0x60, 0x43, 0xfe, 0xf1, 0x9f, 0x32, 0x23,
+ 0xcb, 0x51, 0x4a, 0x20, 0x81, 0xa1, 0x0d, 0x43, 0x8b, 0x68, 0xb6, 0x15,
+ 0x98, 0xa5, 0xcf, 0xaf, 0x7b, 0x7e, 0x6a, 0xe4, 0x08, 0x54, 0xab, 0x3c,
+ 0xf4, 0xe3, 0x26, 0x74, 0x82, 0x71, 0xde, 0xcb, 0x6a, 0xe4, 0x83, 0x9a,
+ 0x8d, 0x7f, 0x08, 0x9a, 0xba, 0x42, 0xfc, 0xaf, 0xa4, 0x03, 0x32, 0x0a,
+ 0xbf, 0xed, 0x68, 0x7a, 0x85, 0x6a, 0x13, 0xf0, 0xb0, 0x54, 0x58, 0x89,
+ 0x63, 0x37, 0xff, 0x73, 0xcd, 0xbe, 0x34, 0xed, 0xba, 0xc7, 0x64, 0x12,
+ 0x91, 0x44, 0xa9, 0x7f, 0x8f, 0x75, 0x97, 0x0b, 0x69, 0x09, 0xdf, 0x5f,
+ 0x92, 0x6c, 0x4e, 0xc1, 0x5d, 0x60, 0x83, 0xa8, 0xc9, 0x99, 0xe1, 0x7d,
+ 0xac, 0xa6, 0x1b, 0xd0, 0x2c, 0x8f, 0x66, 0xba, 0xf3, 0x77, 0x1e, 0xd8,
+ 0x19, 0xc5, 0x65, 0x69, 0xcc, 0x57, 0xcc, 0x5f, 0xe2, 0x38, 0x7a, 0xf7,
+ 0x9e, 0xa1, 0x56, 0x5c, 0x73, 0x9b, 0xd8, 0xad, 0x43, 0x6a, 0x4d, 0x2e,
+ 0x1a, 0xca, 0xca, 0xb6, 0x4c, 0xec, 0xed, 0xe3, 0x1e, 0x7a, 0xf3, 0x67,
+ 0x75, 0xb2, 0x91, 0x06, 0x58, 0x49, 0x1b, 0x5a, 0x03, 0x75, 0xae, 0x55,
+ 0x25, 0xc8, 0x24, 0x04, 0xdc, 0x8b, 0x5d, 0xa3, 0x51, 0x4f, 0x90, 0xf4,
+ 0xbb, 0x75, 0x54, 0xbb, 0xf7, 0xd6, 0xa3, 0x89, 0x06, 0x51, 0xc7, 0x57,
+ 0x47, 0x6e, 0x88, 0xe1, 0x0f, 0x14, 0xfe, 0xd2, 0xe4, 0xdd, 0x43, 0xd5,
+ 0x75, 0xe2, 0xa7, 0xa1, 0xca, 0x03, 0x86, 0x40, 0x60, 0x5f, 0xb7, 0xce,
+ 0xdd, 0x53, 0xbb, 0x7f, 0x05, 0x1d, 0x23, 0x6a, 0xdb, 0x7c, 0x5a, 0x51,
+ 0xfe, 0xe8, 0x4a, 0x97, 0x4d, 0xf6, 0x76, 0x10, 0xdc, 0xb0, 0x36, 0x30,
+ 0xd9, 0x0b, 0x59, 0x6b, 0xd5, 0x44, 0x8d, 0xf0, 0xab, 0x26, 0x08, 0x86,
+ 0x01, 0x21, 0xc8, 0x23
+};
+
+static const uint8_t e_2048[] = { /* key component e, 4 bytes */
+ 0x00, 0x01, 0x00, 0x01
+};
+
+static const uint8_t d_2048[] = { /* key component d, 256 bytes */
+ 0x0d, 0xf5, 0x4f, 0x8f, 0x10, 0x20, 0xcc, 0x3b, 0x97, 0x71, 0xbd, 0xd5,
+ 0x0e, 0xed, 0x37, 0x43, 0x26, 0x3b, 0x32, 0xc2, 0x06, 0xf2, 0x81, 0xed,
+ 0x31, 0xa2, 0x14, 0xf0, 0x3d, 0xba, 0x0c, 0xd2, 0xc3, 0x05, 0x8a, 0x31,
+ 0x74, 0xbe, 0xb6, 0x1f, 0x3f, 0xc6, 0xcb, 0x56, 0x42, 0xdc, 0x96, 0x3f,
+ 0xc1, 0xae, 0xf0, 0xb8, 0xa0, 0x93, 0x74, 0x66, 0xc7, 0x4f, 0x2e, 0x2d,
+ 0xbc, 0xab, 0x5d, 0x95, 0x07, 0xfe, 0x27, 0x2d, 0x8a, 0x33, 0x6c, 0xcc,
+ 0x36, 0xd6, 0xf8, 0xae, 0x7d, 0xa2, 0x74, 0x5c, 0x02, 0x14, 0x06, 0xa3,
+ 0x96, 0xa3, 0xb0, 0x91, 0xd3, 0xf8, 0xa4, 0xb7, 0xc8, 0xd7, 0x63, 0x20,
+ 0xcd, 0xe2, 0xb2, 0x30, 0xba, 0x92, 0x0c, 0x93, 0x5d, 0x43, 0xe1, 0xbd,
+ 0x0e, 0x83, 0x15, 0xc8, 0x19, 0xf1, 0x55, 0x69, 0x6b, 0xef, 0x62, 0x34,
+ 0x20, 0x0b, 0xc4, 0x49, 0xa5, 0x80, 0x5b, 0xee, 0x20, 0x22, 0xc4, 0x63,
+ 0x11, 0x81, 0x1f, 0x37, 0x11, 0x47, 0x93, 0x96, 0xcc, 0xd7, 0x5c, 0xc4,
+ 0xc3, 0xde, 0x3c, 0xed, 0xd5, 0x1e, 0x80, 0x35, 0x8d, 0x60, 0xea, 0x1d,
+ 0xe8, 0xf4, 0x3c, 0x6c, 0x78, 0x44, 0x94, 0x37, 0x0a, 0x2d, 0xc0, 0x06,
+ 0x23, 0xa4, 0x0d, 0x27, 0xba, 0x1b, 0xf4, 0x6a, 0xc2, 0xa8, 0xcc, 0x56,
+ 0x42, 0x96, 0x53, 0xa7, 0x5e, 0x3f, 0x0c, 0x0e, 0xb3, 0x69, 0xaa, 0xe6,
+ 0xeb, 0x1f, 0x19, 0x7e, 0x0a, 0x45, 0x14, 0x24, 0x9f, 0x5a, 0xd5, 0x4e,
+ 0xe2, 0x73, 0xd0, 0xc6, 0x6d, 0xe1, 0xeb, 0xfe, 0x1f, 0x52, 0x30, 0x3e,
+ 0xe2, 0x47, 0x76, 0x51, 0xa4, 0xad, 0x05, 0xdf, 0x75, 0x4b, 0x25, 0x05,
+ 0x83, 0xb3, 0xca, 0x4f, 0x69, 0xb3, 0x66, 0x50, 0x25, 0x3a, 0xc3, 0xd4,
+ 0xad, 0x62, 0x28, 0x66, 0xf4, 0xf4, 0x33, 0xa2, 0x57, 0x0c, 0x9d, 0x75,
+ 0x94, 0x14, 0x59, 0xa1
+};
+
+static const uint8_t p_2048[] = { /* key component p, 128 bytes */
+ 0xc5, 0x0a, 0xf2, 0x4f, 0xd1, 0xf2, 0x86, 0xca, 0x1e, 0x25, 0xbd, 0x65,
+ 0x2a, 0xf9, 0x75, 0xda, 0x3d, 0x98, 0x8a, 0xed, 0x0e, 0xfe, 0xc5, 0xa1,
+ 0x85, 0x8d, 0xb4, 0x95, 0x41, 0x4c, 0x6b, 0x5d, 0x64, 0x49, 0x39, 0x0f,
+ 0x0c, 0x21, 0x2b, 0x60, 0xce, 0x21, 0x04, 0xab, 0x32, 0x24, 0x8e, 0xb6,
+ 0xc6, 0x47, 0xc2, 0xed, 0xa0, 0x36, 0x99, 0xf6, 0xa1, 0x5c, 0x3a, 0x86,
+ 0x92, 0x41, 0x21, 0xe3, 0xe1, 0xc3, 0x4d, 0x8c, 0xa5, 0x6c, 0x9d, 0x04,
+ 0x7d, 0x04, 0x88, 0xa4, 0xe7, 0xce, 0xf6, 0x3f, 0xfe, 0xaa, 0xaf, 0xe4,
+ 0x8d, 0x87, 0x42, 0xbe, 0x31, 0x0d, 0x7c, 0xc0, 0xef, 0xfb, 0x27, 0x31,
+ 0x77, 0x0e, 0xe8, 0x1a, 0x88, 0x8d, 0xde, 0x6e, 0xa3, 0x1f, 0x73, 0x96,
+ 0x84, 0x8e, 0xc7, 0x43, 0x99, 0xb1, 0xa2, 0x9e, 0xb8, 0x61, 0x54, 0xa2,
+ 0x4d, 0x91, 0xfd, 0x87, 0x52, 0x6e, 0x2a, 0x7b
+};
+
+static const uint8_t q_2048[] = { /* key component q, 128 bytes */
+ 0xf1, 0x44, 0xff, 0x27, 0x56, 0x64, 0x25, 0x4f, 0x94, 0x6a, 0x1b, 0xc8,
+ 0x20, 0x05, 0x13, 0xd0, 0x24, 0x22, 0x4e, 0x20, 0x3c, 0x5a, 0x99, 0x8b,
+ 0xd4, 0xaa, 0xc0, 0x49, 0x0d, 0xef, 0x2b, 0x8c, 0x3a, 0xef, 0x55, 0x2a,
+ 0x19, 0xe6, 0x88, 0xc7, 0xdf, 0xcd, 0x54, 0x94, 0x03, 0x63, 0xa9, 0xad,
+ 0x4a, 0xec, 0x6a, 0xd0, 0xcd, 0x77, 0xfc, 0xae, 0xff, 0x0b, 0x63, 0x68,
+ 0xf6, 0xcc, 0xdc, 0xb7, 0x29, 0xe7, 0x46, 0xb4, 0x26, 0xf9, 0xa3, 0xed,
+ 0x32, 0x8d, 0xf7, 0x12, 0xa2, 0x19, 0xc2, 0xef, 0x52, 0xf7, 0xde, 0x91,
+ 0x48, 0x97, 0x6a, 0x18, 0x8b, 0x84, 0x0e, 0xaa, 0x62, 0xf2, 0xaa, 0x31,
+ 0x1e, 0xdc, 0x8a, 0x31, 0x30, 0x3b, 0x22, 0xec, 0x7c, 0x8b, 0x8c, 0xbd,
+ 0x4d, 0xe5, 0xb7, 0xb6, 0x68, 0xac, 0xaa, 0xff, 0x8e, 0x6e, 0x93, 0x14,
+ 0xa4, 0xef, 0x2b, 0x9f, 0x15, 0x4a, 0xdc, 0x79
+};
+
+static const uint8_t u_2048[] = { /* key component u, 128 bytes */
+ 0x5e, 0x42, 0x7f, 0x1d, 0x33, 0x81, 0x1e, 0xa4, 0x18, 0xdf, 0x86, 0xba,
+ 0xb0, 0x1b, 0x77, 0x56, 0xf4, 0x65, 0x91, 0x31, 0xd8, 0xac, 0xbc, 0x63,
+ 0x55, 0x55, 0x11, 0x5c, 0xc5, 0x31, 0x61, 0x08, 0xe0, 0xb3, 0x5c, 0xce,
+ 0x9e, 0x82, 0xbb, 0xc4, 0x7d, 0xd3, 0xc3, 0xc0, 0x95, 0x0b, 0xc0, 0xbf,
+ 0x7c, 0xaf, 0xcd, 0xa2, 0x1f, 0xbb, 0x8f, 0x7f, 0xce, 0xde, 0x42, 0x59,
+ 0xd5, 0x71, 0x49, 0xa2, 0x91, 0xe2, 0x24, 0xc2, 0xf7, 0x7f, 0xd2, 0xae,
+ 0x10, 0xbd, 0x34, 0xb6, 0xc4, 0xec, 0xa2, 0x17, 0xc8, 0x4f, 0x76, 0xf6,
+ 0x1d, 0x90, 0x72, 0x58, 0x55, 0x18, 0xbe, 0x44, 0xd4, 0xf1, 0x85, 0xf5,
+ 0x90, 0x65, 0x45, 0x4f, 0xf1, 0x3b, 0x65, 0xe7, 0x79, 0x3b, 0xe5, 0x4e,
+ 0x56, 0x28, 0x4b, 0x62, 0x4d, 0x8e, 0x1d, 0x25, 0x26, 0x37, 0x1a, 0xb5,
+ 0x5c, 0xd5, 0x14, 0x67, 0x73, 0x74, 0x70, 0x24
+};
+
+static const uint8_t m_2048[] = { /* message to be signed, 256 bytes */
+ 0x00, 0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0x00, 0x30, 0x31, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65,
+ 0x03, 0x04, 0x02, 0x01, 0x05, 0x00, 0x04, 0x20, 0x8e, 0x36, 0xfc, 0x9a,
+ 0xa3, 0x17, 0x24, 0xc3, 0x24, 0x16, 0x26, 0x3c, 0x03, 0x66, 0xa1, 0x75,
+ 0xfa, 0xbb, 0xb9, 0x2b, 0x74, 0x1c, 0xa6, 0x49, 0x61, 0x07, 0x07, 0x4d,
+ 0x03, 0x43, 0xb5, 0x97
+};
+
+static const uint8_t s_2048[] = { /* signed message, 256 bytes */
+ 0xa4, 0xcf, 0x2b, 0x55, 0x74, 0x6e, 0x9a, 0x97, 0x4e, 0x50, 0x7a, 0x8c,
+ 0xbb, 0x32, 0x3d, 0x42, 0x4a, 0x14, 0x0d, 0x50, 0x29, 0xc8, 0x76, 0x2c,
+ 0xd9, 0x25, 0x16, 0x62, 0xee, 0xc7, 0xd7, 0xf9, 0x7f, 0xc5, 0x0c, 0x4b,
+ 0xa4, 0x6e, 0xd3, 0xe5, 0x0d, 0x01, 0x7c, 0xd7, 0x9e, 0xe2, 0x9f, 0xa0,
+ 0xf0, 0x51, 0x57, 0x4f, 0x9b, 0xf2, 0x89, 0x03, 0x04, 0xe7, 0xda, 0x19,
+ 0x05, 0xe7, 0xcb, 0xea, 0xaf, 0x84, 0xae, 0x21, 0x44, 0x6f, 0x85, 0xc4,
+ 0x71, 0x9b, 0x35, 0xed, 0xd8, 0x55, 0xd7, 0x25, 0xaa, 0xdb, 0xd8, 0x0f,
+ 0x24, 0xac, 0x3e, 0x3d, 0xcd, 0xa5, 0x72, 0xd9, 0x96, 0x75, 0x4b, 0x93,
+ 0xc4, 0x37, 0xef, 0x25, 0xe4, 0xa0, 0xda, 0x66, 0x51, 0x5e, 0xc2, 0xa9,
+ 0xcb, 0x4b, 0xde, 0xca, 0x70, 0x68, 0xd0, 0x9a, 0x76, 0x79, 0x86, 0x5f,
+ 0xab, 0xc0, 0x5d, 0x35, 0x10, 0x59, 0xa5, 0x4b, 0x17, 0x56, 0x68, 0xe2,
+ 0x24, 0x53, 0x3c, 0x73, 0x0f, 0x9d, 0x74, 0xeb, 0xb8, 0x9e, 0xb3, 0x18,
+ 0x8c, 0x20, 0x32, 0xf6, 0x28, 0x98, 0xe8, 0x6e, 0x95, 0xf5, 0x62, 0x2f,
+ 0x72, 0x13, 0x38, 0xe6, 0xd7, 0xaa, 0x46, 0x69, 0x07, 0xe8, 0x1e, 0x14,
+ 0xe3, 0x45, 0x03, 0x34, 0xa7, 0xde, 0xaf, 0xca, 0x42, 0x08, 0x22, 0xea,
+ 0x27, 0xe8, 0xaa, 0x49, 0xaf, 0x2f, 0xbe, 0xa6, 0x1f, 0xdc, 0x28, 0x7f,
+ 0x75, 0x3c, 0xfc, 0xe0, 0x80, 0x63, 0xf0, 0xd2, 0xd2, 0x93, 0x6b, 0x91,
+ 0xe1, 0x3b, 0x97, 0x50, 0xf4, 0x0f, 0xce, 0x73, 0xa2, 0x01, 0x7d, 0x97,
+ 0x84, 0x97, 0x61, 0xf5, 0x50, 0x66, 0x23, 0x1b, 0x94, 0x91, 0x67, 0x21,
+ 0xdc, 0x1a, 0xe0, 0x2a, 0x83, 0x91, 0x29, 0x64, 0x73, 0xb7, 0x2a, 0x0c,
+ 0x44, 0x48, 0x11, 0x36, 0x5f, 0xb3, 0x73, 0x1d, 0x43, 0xb6, 0xc3, 0x5e,
+ 0x9c, 0x63, 0x3c, 0x93
+};
+
+/* 4096-bit RSA private key (PKCS #8)
+-----BEGIN PRIVATE KEY-----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+-----END PRIVATE KEY-----
+*/
+
+static const uint8_t n_4096[] = { /* key component n, 512 bytes */
+ 0x97, 0xa1, 0xe3, 0xe1, 0xe2, 0xae, 0x76, 0x00, 0x33, 0x36, 0x0f, 0x89,
+ 0x27, 0x00, 0x42, 0x31, 0x07, 0x9c, 0xf9, 0xb0, 0xdb, 0x22, 0x60, 0x2a,
+ 0xab, 0x0a, 0xd3, 0xcd, 0x47, 0x79, 0x13, 0xcd, 0x0d, 0x2f, 0x9e, 0xa8,
+ 0x32, 0xfa, 0x4e, 0xcb, 0x41, 0xe5, 0xe3, 0xfe, 0x4e, 0xdf, 0x5a, 0x7b,
+ 0x22, 0x83, 0x6e, 0x97, 0x46, 0xdf, 0x21, 0xa7, 0x81, 0x15, 0x3b, 0x7a,
+ 0xd2, 0x65, 0xae, 0x1a, 0xff, 0x59, 0x36, 0x27, 0xe7, 0x6e, 0x60, 0x81,
+ 0x53, 0x7b, 0x60, 0xeb, 0x04, 0x25, 0x8d, 0x04, 0x3f, 0x42, 0x0e, 0xe2,
+ 0x10, 0x3a, 0xad, 0x0f, 0xf0, 0x89, 0xb4, 0x39, 0xd6, 0x09, 0x4b, 0x89,
+ 0x8a, 0x9d, 0x7b, 0xcd, 0xf1, 0xb6, 0x1e, 0xb7, 0xbd, 0x5f, 0xcb, 0xbc,
+ 0x99, 0x43, 0x35, 0x3d, 0x0a, 0x48, 0xd1, 0xe1, 0xc0, 0x1a, 0x38, 0xaf,
+ 0xce, 0x4d, 0x95, 0x50, 0x40, 0xa3, 0x24, 0x8c, 0xca, 0x06, 0x6a, 0x66,
+ 0xda, 0xea, 0x7c, 0x4f, 0x0d, 0x5a, 0x65, 0xf7, 0x5d, 0xdf, 0xa1, 0x04,
+ 0xdc, 0xd1, 0xf1, 0xfb, 0x76, 0xd5, 0xce, 0x84, 0x1f, 0xcb, 0xfc, 0xc2,
+ 0xaf, 0xae, 0x86, 0x8b, 0x6f, 0x05, 0x73, 0xfe, 0x6c, 0xd2, 0xe2, 0xe8,
+ 0xec, 0x9b, 0x36, 0x0c, 0xfe, 0xb9, 0x7e, 0x1d, 0x6e, 0x14, 0xa8, 0x0e,
+ 0x20, 0xb2, 0x52, 0xd9, 0xfd, 0x51, 0x70, 0x4e, 0xcd, 0xf4, 0x87, 0x74,
+ 0xe0, 0xd3, 0x6a, 0xcb, 0xee, 0xe8, 0x04, 0x64, 0x2f, 0x34, 0xde, 0x71,
+ 0x61, 0xac, 0xc6, 0x7c, 0x65, 0x31, 0x6f, 0xd8, 0xdc, 0x4a, 0x49, 0x43,
+ 0xa7, 0xec, 0x19, 0xf3, 0x73, 0x2a, 0x77, 0x78, 0xe3, 0xc9, 0x0a, 0xc4,
+ 0xea, 0x6e, 0x36, 0x10, 0x8e, 0x50, 0x4d, 0xad, 0xea, 0x70, 0x6f, 0xc3,
+ 0xff, 0x68, 0x70, 0x0b, 0x0a, 0x9b, 0x38, 0x7b, 0x43, 0x0d, 0xc1, 0x99,
+ 0xac, 0x64, 0xc4, 0xb8, 0x53, 0xb5, 0xc5, 0x28, 0x87, 0x74, 0x88, 0x0e,
+ 0xcc, 0x06, 0x98, 0xd2, 0xf5, 0xb8, 0x86, 0xb7, 0x73, 0xc0, 0x23, 0x4f,
+ 0x32, 0x3b, 0x74, 0xef, 0xde, 0x14, 0xc7, 0xeb, 0x18, 0x94, 0x9b, 0xc3,
+ 0xcb, 0xef, 0x00, 0xf4, 0x9b, 0x2f, 0x07, 0x12, 0xfc, 0x5d, 0x69, 0x9f,
+ 0x45, 0x98, 0x3c, 0x6a, 0xee, 0x60, 0xfb, 0xee, 0x8c, 0xac, 0x98, 0xba,
+ 0x40, 0x25, 0xa4, 0x80, 0x39, 0xf7, 0x83, 0x23, 0xbc, 0x19, 0x1e, 0x17,
+ 0xb5, 0x0d, 0x90, 0xc3, 0xa4, 0xac, 0xe5, 0x76, 0xd3, 0x7f, 0x75, 0x6c,
+ 0x54, 0x27, 0x77, 0xf9, 0x75, 0x96, 0xa2, 0x84, 0x45, 0x24, 0xb2, 0x40,
+ 0x31, 0x42, 0x63, 0x16, 0x8c, 0x99, 0xdf, 0x90, 0xae, 0x6f, 0xa6, 0x04,
+ 0x62, 0x1f, 0xdf, 0x37, 0xc9, 0xd2, 0x9d, 0x68, 0xa3, 0x7f, 0x63, 0x3c,
+ 0xce, 0x39, 0x53, 0xc4, 0x66, 0x50, 0xba, 0x47, 0x50, 0x71, 0x47, 0xcf,
+ 0xbe, 0xf4, 0x4a, 0x02, 0xf7, 0xd2, 0xb2, 0x24, 0x98, 0xe8, 0x94, 0x99,
+ 0xb4, 0x3b, 0x3f, 0xc9, 0x4f, 0x52, 0x46, 0x4a, 0x12, 0x99, 0x61, 0x5d,
+ 0xfd, 0xaf, 0xba, 0x56, 0x7a, 0x3e, 0x85, 0xca, 0x06, 0xac, 0x8a, 0xf2,
+ 0x85, 0x36, 0xe3, 0x10, 0x32, 0x8f, 0xe7, 0x2b, 0x07, 0xc7, 0xe9, 0xdf,
+ 0x46, 0xfc, 0x03, 0xf1, 0xce, 0x97, 0x79, 0x87, 0x3f, 0xd1, 0xf3, 0x8a,
+ 0x38, 0x38, 0x2f, 0xc1, 0xb7, 0x99, 0x91, 0xc3, 0xa9, 0xc8, 0x78, 0x6f,
+ 0xbe, 0xf5, 0x9d, 0x91, 0x53, 0x1b, 0x52, 0xc5, 0xa4, 0x85, 0x9b, 0x18,
+ 0x12, 0xd1, 0x35, 0xf0, 0xe6, 0x5e, 0x04, 0x95, 0x48, 0x22, 0xb1, 0x3e,
+ 0xaf, 0xa2, 0x6d, 0xa9, 0xa2, 0xeb, 0xb8, 0xd9, 0xa5, 0x24, 0x02, 0x30,
+ 0x4d, 0x59, 0x69, 0xa7, 0xed, 0xfc, 0xe3, 0x60, 0xb8, 0xc6, 0xf9, 0x2b,
+ 0x52, 0x1d, 0x96, 0x15, 0x1d, 0xc4, 0xc9, 0xc3
+};
+
+static const uint8_t e_4096[] = { /* key component e, 4 bytes */
+ 0x00, 0x01, 0x00, 0x01
+};
+
+static const uint8_t d_4096[] = { /* key component d, 512 bytes */
+ 0x27, 0x8f, 0x3a, 0xee, 0xd1, 0xbf, 0x06, 0x56, 0x23, 0x06, 0x35, 0xa3,
+ 0x68, 0xa3, 0x6e, 0xa1, 0x70, 0x05, 0x0a, 0x37, 0x93, 0xd4, 0x32, 0x16,
+ 0xaf, 0xad, 0x11, 0x78, 0xfa, 0xee, 0xa1, 0xb5, 0xdb, 0x7c, 0xd2, 0xfd,
+ 0xba, 0xdf, 0x06, 0xf3, 0x8c, 0x6b, 0xb7, 0xc1, 0xbf, 0x3e, 0x12, 0x53,
+ 0x11, 0xbc, 0x0c, 0x7c, 0x37, 0x27, 0x3b, 0x96, 0x81, 0xdc, 0xd2, 0x39,
+ 0xc6, 0xee, 0x74, 0x2f, 0xe2, 0xf2, 0x99, 0x68, 0x6b, 0xbe, 0xa6, 0x3a,
+ 0xd7, 0x56, 0xd7, 0x00, 0x39, 0x82, 0xba, 0x79, 0xa3, 0x2f, 0x4e, 0xc6,
+ 0xb7, 0xc9, 0x37, 0x21, 0x73, 0x75, 0xd9, 0xa9, 0x45, 0x28, 0x03, 0xa7,
+ 0x0c, 0x9c, 0xed, 0x91, 0xdb, 0x3f, 0xd2, 0x5f, 0xc9, 0x6e, 0x56, 0xaf,
+ 0x0b, 0xa5, 0x37, 0x1c, 0x87, 0xb4, 0x5b, 0xdd, 0x73, 0xca, 0xe3, 0x83,
+ 0x2a, 0x65, 0x9f, 0x50, 0xe2, 0xac, 0x2d, 0x7a, 0xf5, 0xb2, 0x1a, 0xcc,
+ 0x5e, 0xcc, 0xd2, 0x45, 0xa5, 0x8c, 0x32, 0x12, 0x09, 0x51, 0xb0, 0xa6,
+ 0x9e, 0x1d, 0xbf, 0xee, 0x05, 0x20, 0xde, 0xd2, 0x25, 0xa1, 0x88, 0x7e,
+ 0x1a, 0x6b, 0x83, 0xfa, 0x98, 0xaa, 0x69, 0x8a, 0xb5, 0x45, 0x87, 0xa1,
+ 0x91, 0x29, 0x25, 0x3e, 0xda, 0xad, 0xf6, 0x33, 0x23, 0x67, 0x0c, 0x39,
+ 0x33, 0x5a, 0x92, 0xb7, 0x00, 0x99, 0xe0, 0x9d, 0x0e, 0xaa, 0x7f, 0x34,
+ 0x84, 0xfb, 0x63, 0x5f, 0x75, 0x22, 0xdf, 0x12, 0x6c, 0x26, 0x74, 0xea,
+ 0x4b, 0xbb, 0x51, 0xc5, 0x5e, 0x79, 0x39, 0x5e, 0xf0, 0x8a, 0x08, 0xf7,
+ 0x37, 0xb6, 0x27, 0x47, 0x16, 0x82, 0xbb, 0xcc, 0xb4, 0x50, 0xdd, 0x18,
+ 0x66, 0xb8, 0xfe, 0x2d, 0xef, 0x93, 0x0f, 0xd1, 0x11, 0xda, 0xe7, 0xad,
+ 0xd0, 0xd2, 0xa4, 0x78, 0x9c, 0xf9, 0xc6, 0x10, 0x92, 0x7b, 0xe2, 0x48,
+ 0x7f, 0x6b, 0x82, 0xce, 0xd5, 0x55, 0xb4, 0x8b, 0xb2, 0x75, 0x74, 0x53,
+ 0x89, 0xad, 0xd9, 0x24, 0x77, 0xea, 0x61, 0xf2, 0x21, 0x54, 0xa7, 0x41,
+ 0x33, 0x6d, 0xa8, 0xa3, 0x5b, 0xd1, 0xb7, 0xd8, 0xe8, 0x96, 0x1f, 0x46,
+ 0x65, 0x01, 0x4b, 0x8b, 0x1a, 0x50, 0x72, 0x96, 0x4f, 0x6c, 0x60, 0xe5,
+ 0x91, 0x74, 0x5c, 0xc8, 0x97, 0x8d, 0x49, 0x69, 0x0b, 0xbf, 0xa6, 0xd4,
+ 0xcc, 0xe0, 0x1f, 0x1a, 0x30, 0x32, 0x3a, 0x9f, 0xe1, 0xbe, 0x5c, 0x75,
+ 0xee, 0xae, 0xb3, 0xcc, 0x33, 0xdb, 0x99, 0xca, 0x6b, 0xef, 0xbf, 0x99,
+ 0xaf, 0x47, 0x78, 0x25, 0x3d, 0xf8, 0xbe, 0x49, 0xdb, 0x34, 0x36, 0x00,
+ 0x0c, 0xec, 0xb8, 0x7c, 0x04, 0x14, 0x9b, 0xea, 0x5f, 0x82, 0xaf, 0x83,
+ 0xf8, 0x6e, 0x85, 0xa5, 0x75, 0xf1, 0x60, 0x68, 0x21, 0xc3, 0x3a, 0xca,
+ 0x1e, 0xbd, 0x07, 0x4d, 0x2d, 0x83, 0x24, 0x9c, 0xa9, 0xdc, 0x4d, 0xaf,
+ 0x95, 0x7f, 0xef, 0x1d, 0x1e, 0x50, 0xea, 0x08, 0xef, 0xd5, 0xf9, 0xb2,
+ 0x9e, 0xb9, 0xed, 0x97, 0x1e, 0xfd, 0x1b, 0x56, 0xcd, 0x67, 0xa0, 0x57,
+ 0x54, 0x5f, 0x1d, 0x43, 0x2b, 0xde, 0x6b, 0xc7, 0x29, 0xe9, 0x9d, 0x0a,
+ 0x84, 0xd4, 0x25, 0xb4, 0xf3, 0xb3, 0xdb, 0x1c, 0x98, 0xdc, 0x91, 0x49,
+ 0x16, 0xec, 0xc8, 0xfa, 0xa1, 0xb2, 0x03, 0xb6, 0xe5, 0x7a, 0xb4, 0x56,
+ 0xb5, 0xf5, 0x70, 0x4b, 0x75, 0x68, 0xb9, 0x6e, 0xea, 0x66, 0xc9, 0xe2,
+ 0x25, 0xc2, 0x4d, 0xe3, 0x14, 0xcc, 0xc1, 0xf9, 0xa0, 0xe0, 0x8e, 0x71,
+ 0xa0, 0xbf, 0x53, 0xbb, 0x2f, 0x60, 0x37, 0x76, 0xca, 0xfb, 0x55, 0x57,
+ 0x65, 0xbd, 0xda, 0xef, 0xf4, 0x65, 0xb2, 0xe9, 0x3c, 0x17, 0xa3, 0x55,
+ 0x4f, 0x5e, 0x8f, 0xd5, 0xef, 0xce, 0x1e, 0x64, 0x92, 0x8f, 0x4b, 0xde,
+ 0x7c, 0x8b, 0x89, 0x62, 0xb1, 0x60, 0xe2, 0x81
+};
+
+static const uint8_t p_4096[] = { /* key component p, 256 bytes */
+ 0xbd, 0x67, 0x35, 0x89, 0x0c, 0xdd, 0x2d, 0xae, 0xfa, 0xf4, 0xc3, 0xac,
+ 0xa0, 0xe7, 0x01, 0xe0, 0x3b, 0xb5, 0x3c, 0x7f, 0xe0, 0xe1, 0x80, 0x18,
+ 0x96, 0xce, 0x0d, 0x5f, 0xaf, 0x83, 0x14, 0x9c, 0xda, 0x50, 0xdd, 0x86,
+ 0xf4, 0x5f, 0x22, 0xd1, 0x5d, 0xdc, 0xc2, 0x36, 0x49, 0x8a, 0x88, 0xc9,
+ 0x0d, 0xf4, 0xc7, 0x01, 0x03, 0x2e, 0xca, 0x6c, 0xd8, 0x5f, 0xd2, 0x5c,
+ 0x9b, 0xfb, 0xa5, 0x0d, 0x3f, 0x26, 0xb0, 0x04, 0x07, 0x3a, 0xf5, 0x12,
+ 0xd5, 0x58, 0xd5, 0xe4, 0x46, 0x42, 0x1d, 0x69, 0x09, 0x6d, 0x05, 0x7f,
+ 0x37, 0x4a, 0x00, 0x04, 0x08, 0xab, 0xa4, 0x2e, 0xf6, 0x18, 0xe0, 0x06,
+ 0x10, 0x89, 0xa4, 0x83, 0x1d, 0x6e, 0x6e, 0x5f, 0x7b, 0x40, 0x3f, 0x9a,
+ 0xcf, 0x64, 0x7a, 0xc6, 0x43, 0xb9, 0x76, 0xda, 0xb7, 0x24, 0x55, 0xe4,
+ 0xd4, 0x5e, 0xb5, 0xd3, 0xf7, 0xe0, 0xae, 0x85, 0x7d, 0x83, 0x29, 0xb3,
+ 0x93, 0x1b, 0x9a, 0x8e, 0x5e, 0x79, 0x5b, 0xc2, 0x3b, 0x32, 0x5f, 0x4c,
+ 0x06, 0x84, 0xaa, 0x9c, 0x13, 0x6f, 0xb6, 0xad, 0xf3, 0x1e, 0x81, 0xd8,
+ 0x4a, 0x7d, 0xea, 0x23, 0x54, 0xa5, 0x67, 0x70, 0x4b, 0x58, 0xe6, 0x24,
+ 0x14, 0x31, 0x29, 0x52, 0xc6, 0xd9, 0x71, 0x87, 0xfb, 0x52, 0x8f, 0x34,
+ 0xc9, 0x0d, 0xa1, 0x10, 0x38, 0xbe, 0xcd, 0xf8, 0x0c, 0xf4, 0x5e, 0x20,
+ 0x20, 0xa4, 0xc7, 0xfb, 0xee, 0x92, 0x3f, 0xeb, 0x9d, 0x6f, 0x21, 0xd9,
+ 0xfb, 0x53, 0x79, 0xed, 0x9a, 0x51, 0xb0, 0xab, 0xed, 0x3d, 0x79, 0x99,
+ 0x89, 0x39, 0xc7, 0x33, 0x4c, 0x7e, 0x57, 0xfa, 0x55, 0x82, 0x54, 0x8a,
+ 0xe8, 0xa1, 0xe8, 0x81, 0xb7, 0x4d, 0x9a, 0xde, 0x35, 0x47, 0x5e, 0xbd,
+ 0xae, 0xae, 0x96, 0xc2, 0xdb, 0x3d, 0x39, 0xde, 0x7e, 0xfc, 0xd8, 0xcc,
+ 0x3f, 0xea, 0x8b, 0x63
+};
+
+static const uint8_t q_4096[] = { /* key component q, 256 bytes */
+ 0xcc, 0xf2, 0xcf, 0xaf, 0x2f, 0x5a, 0x22, 0x36, 0x67, 0x12, 0xce, 0xf9,
+ 0xef, 0xdc, 0x6b, 0xc4, 0xdf, 0x9a, 0x6b, 0x59, 0x43, 0xa7, 0x55, 0x56,
+ 0xa8, 0x5f, 0x32, 0xe2, 0x5d, 0x41, 0x33, 0xd6, 0x5b, 0x89, 0xb5, 0x2a,
+ 0x30, 0x06, 0xe3, 0x1b, 0x68, 0xbd, 0xad, 0x57, 0x0a, 0xd1, 0x44, 0xe1,
+ 0x9f, 0xe4, 0x99, 0xed, 0x6e, 0x0d, 0x24, 0xdd, 0xdd, 0x52, 0xb6, 0x67,
+ 0xc8, 0x51, 0xe3, 0x25, 0x9a, 0xd4, 0x17, 0xb6, 0x06, 0x17, 0x53, 0x26,
+ 0x78, 0x12, 0x4e, 0x8b, 0xe8, 0x73, 0x1a, 0x1f, 0xfe, 0xfa, 0xe5, 0xc1,
+ 0x54, 0xc2, 0x22, 0x98, 0xc4, 0xcf, 0xc1, 0xf9, 0x1c, 0x8b, 0xfa, 0xe4,
+ 0xb2, 0x50, 0x7e, 0x25, 0x24, 0x49, 0xd9, 0x3f, 0x63, 0x96, 0x51, 0x20,
+ 0xa7, 0x14, 0xa7, 0x81, 0xf8, 0x97, 0x97, 0x14, 0x5c, 0x25, 0xe1, 0x4d,
+ 0x7c, 0x70, 0xa7, 0x2c, 0xba, 0x80, 0x22, 0xc4, 0xf3, 0xdc, 0x8f, 0x4c,
+ 0xf2, 0x4b, 0x76, 0xe7, 0x70, 0xeb, 0xb5, 0xe2, 0x18, 0xd0, 0x28, 0x03,
+ 0x28, 0xf0, 0x30, 0x91, 0x54, 0x05, 0x41, 0xe5, 0x4d, 0x84, 0x87, 0x8b,
+ 0x22, 0xc3, 0x28, 0x9b, 0xcc, 0xd1, 0x29, 0xda, 0xe5, 0x2c, 0x32, 0x44,
+ 0x95, 0xc7, 0x5b, 0x77, 0xf3, 0x6a, 0x97, 0x0a, 0x2f, 0x18, 0xa4, 0xb0,
+ 0x67, 0x99, 0x46, 0xad, 0xcf, 0x24, 0xba, 0x2a, 0xbc, 0x04, 0x54, 0xe5,
+ 0x91, 0xbe, 0x37, 0x3c, 0x11, 0xf7, 0x8a, 0xa4, 0x2d, 0x6f, 0xca, 0x4d,
+ 0x16, 0x71, 0x6a, 0x02, 0xf7, 0xdf, 0xa9, 0x1c, 0x0e, 0x53, 0x51, 0x19,
+ 0xb8, 0x6c, 0x46, 0x61, 0x8e, 0x9c, 0x3a, 0x8f, 0xfa, 0x1a, 0x56, 0xa8,
+ 0xef, 0x16, 0x2b, 0x45, 0xc4, 0x70, 0xbf, 0xb4, 0x45, 0xf2, 0xbb, 0x67,
+ 0x4d, 0x96, 0xbb, 0xbb, 0x77, 0x7c, 0xc6, 0x4f, 0x7b, 0xce, 0xcf, 0x93,
+ 0xde, 0x11, 0x86, 0x21
+};
+
+static const uint8_t u_4096[] = { /* key component u, 256 bytes */
+ 0x54, 0x31, 0x57, 0xff, 0x2c, 0xac, 0x38, 0xe7, 0xef, 0xa6, 0x8e, 0x0f,
+ 0xba, 0xcd, 0x7f, 0xcb, 0x8a, 0x30, 0x4a, 0x98, 0xd9, 0xf2, 0xb8, 0x61,
+ 0x5e, 0x93, 0x8f, 0x99, 0xf4, 0xe8, 0x3e, 0xd8, 0x23, 0x6f, 0xab, 0xc0,
+ 0x64, 0x7d, 0x1a, 0xf1, 0x10, 0x8c, 0xd3, 0x3f, 0x3d, 0x2e, 0x0d, 0xa1,
+ 0x6c, 0xb7, 0x27, 0x9f, 0x87, 0x0c, 0x73, 0x3a, 0xe4, 0xb3, 0x03, 0x14,
+ 0xfd, 0x1a, 0x5e, 0xe9, 0x98, 0xde, 0xb0, 0x93, 0xd7, 0x36, 0x42, 0x7a,
+ 0xc4, 0xc4, 0x78, 0x78, 0x8c, 0x4d, 0x88, 0xc1, 0x5f, 0x6c, 0x6e, 0x05,
+ 0x65, 0xe9, 0x88, 0x04, 0xc4, 0x42, 0x3f, 0x02, 0x29, 0x79, 0xfe, 0x80,
+ 0xaa, 0x60, 0x5f, 0x7a, 0x20, 0xb5, 0x63, 0x71, 0x58, 0x0f, 0x37, 0xdf,
+ 0x0e, 0x94, 0x1b, 0xbb, 0x27, 0xb7, 0xcd, 0x03, 0xb6, 0x74, 0xd4, 0x2d,
+ 0xe4, 0xe1, 0xa3, 0x7a, 0xdc, 0x98, 0xeb, 0x31, 0x85, 0x6b, 0x0b, 0x0e,
+ 0x69, 0x1a, 0x5e, 0xfb, 0x45, 0x88, 0x23, 0x88, 0x83, 0x08, 0x1f, 0xe2,
+ 0xd2, 0x91, 0xfd, 0x12, 0xbc, 0x5d, 0x55, 0x9e, 0x4b, 0x1d, 0x7f, 0xb3,
+ 0xd3, 0xe9, 0x1b, 0x66, 0xdd, 0x37, 0x0d, 0x74, 0x0c, 0x42, 0xf2, 0xb3,
+ 0xd0, 0x04, 0xa9, 0x68, 0x41, 0x20, 0xe8, 0x4f, 0xfd, 0x92, 0xd3, 0xc0,
+ 0x24, 0xe7, 0x6d, 0x69, 0xd2, 0xe8, 0xc8, 0x08, 0x52, 0xd9, 0xfe, 0xcb,
+ 0x4b, 0x0c, 0x72, 0x56, 0x0a, 0x2a, 0xa3, 0x63, 0x00, 0xe6, 0xc5, 0xe1,
+ 0x91, 0x93, 0x21, 0x76, 0x2c, 0x14, 0xa4, 0xe3, 0xff, 0xf4, 0x45, 0xc0,
+ 0x1a, 0x0e, 0x94, 0xb3, 0x6d, 0x52, 0xe3, 0x88, 0x22, 0xaf, 0xa2, 0x85,
+ 0xa0, 0xfe, 0xdb, 0x2a, 0xfe, 0xa0, 0x4e, 0x9a, 0x2d, 0x1c, 0xbc, 0xe0,
+ 0xbe, 0x15, 0xaf, 0xec, 0xa8, 0xc9, 0x2d, 0x7a, 0x69, 0xd3, 0x3d, 0xac,
+ 0xa3, 0x92, 0x36, 0x0b
+};
+
+static const uint8_t m_4096[] = { /* message to be signed, 512 bytes */
+ 0x00, 0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0x00, 0x30, 0x31, 0x30, 0x0d, 0x06, 0x09, 0x60,
+ 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x01, 0x05, 0x00, 0x04, 0x20,
+ 0x8e, 0x36, 0xfc, 0x9a, 0xa3, 0x17, 0x24, 0xc3, 0x24, 0x16, 0x26, 0x3c,
+ 0x03, 0x66, 0xa1, 0x75, 0xfa, 0xbb, 0xb9, 0x2b, 0x74, 0x1c, 0xa6, 0x49,
+ 0x61, 0x07, 0x07, 0x4d, 0x03, 0x43, 0xb5, 0x97
+};
+
+static const uint8_t s_4096[] = { /* signed message, 512 bytes */
+ 0x57, 0x1c, 0xea, 0xc6, 0xef, 0x58, 0x63, 0x7f, 0x9f, 0x61, 0xd7, 0x28,
+ 0x33, 0xb2, 0x06, 0x55, 0xf6, 0x19, 0x30, 0x04, 0x40, 0xbd, 0x8a, 0x1b,
+ 0x61, 0x21, 0x5f, 0xc2, 0x97, 0x38, 0xd4, 0x3e, 0x20, 0x92, 0x12, 0x58,
+ 0x40, 0xd9, 0x60, 0x6f, 0x52, 0x82, 0x00, 0x00, 0x44, 0x68, 0x29, 0xf5,
+ 0xcb, 0x00, 0xf2, 0xde, 0xc8, 0x49, 0xba, 0x47, 0xf3, 0x5c, 0xb7, 0x8d,
+ 0xfd, 0x5f, 0x67, 0x12, 0xb9, 0x76, 0xed, 0x24, 0x1f, 0x25, 0x04, 0x17,
+ 0x08, 0x45, 0xaa, 0x55, 0x0a, 0x9b, 0x5e, 0x88, 0x03, 0x95, 0x1a, 0x77,
+ 0x7b, 0xe0, 0xe2, 0xd8, 0xc2, 0xef, 0x53, 0x22, 0x66, 0x92, 0x73, 0x19,
+ 0xcf, 0x1a, 0x26, 0x98, 0x57, 0x2e, 0xbc, 0x04, 0x36, 0xab, 0x26, 0xe9,
+ 0x57, 0x1b, 0x5d, 0x3f, 0x49, 0x13, 0xf8, 0x53, 0x3d, 0x4f, 0xbe, 0x41,
+ 0x59, 0x68, 0xa2, 0x34, 0x4e, 0xc7, 0x9d, 0x14, 0x0d, 0xaf, 0xdf, 0x91,
+ 0xba, 0xf7, 0xe4, 0xce, 0x04, 0x12, 0x9b, 0x47, 0x17, 0x3d, 0xb4, 0xd3,
+ 0x76, 0x74, 0xdb, 0x34, 0x80, 0x91, 0x26, 0x56, 0x7f, 0x55, 0x30, 0x64,
+ 0x15, 0xa4, 0xc2, 0x20, 0x1a, 0x34, 0xde, 0x0a, 0x6b, 0x99, 0x6a, 0x92,
+ 0xf0, 0x40, 0x26, 0xe4, 0x77, 0x73, 0x60, 0x98, 0xa9, 0xb8, 0xbf, 0xc6,
+ 0xda, 0x68, 0xa4, 0xcb, 0xee, 0xae, 0x58, 0xf9, 0xa4, 0xb1, 0xfd, 0xb9,
+ 0xaa, 0xfd, 0xea, 0xd2, 0x29, 0xec, 0x30, 0xb0, 0x30, 0xc7, 0x8e, 0xdb,
+ 0x4b, 0x65, 0x59, 0x65, 0x11, 0xe5, 0xc2, 0xe8, 0xca, 0x43, 0x33, 0x32,
+ 0x14, 0x5c, 0x97, 0xf4, 0xc2, 0xe9, 0xde, 0xc9, 0xa9, 0x9e, 0x55, 0x51,
+ 0x0e, 0xf7, 0x93, 0xda, 0x95, 0xbb, 0xe5, 0xd0, 0xf6, 0xd9, 0x1b, 0x54,
+ 0x34, 0x26, 0x25, 0x3a, 0xeb, 0xbf, 0x80, 0x0a, 0x8d, 0x94, 0x9f, 0x42,
+ 0x82, 0xfe, 0x46, 0x33, 0xe8, 0x33, 0x2b, 0xe2, 0xf3, 0xb3, 0x62, 0x1f,
+ 0x95, 0xbf, 0x80, 0xf1, 0x55, 0xc1, 0x10, 0xaf, 0xe4, 0x9f, 0x45, 0x97,
+ 0xa7, 0x2e, 0xdc, 0xaf, 0xba, 0xe9, 0x0a, 0x35, 0x15, 0x53, 0xbb, 0x23,
+ 0xad, 0xa4, 0x1a, 0xc5, 0x3b, 0x70, 0xb0, 0xe8, 0xad, 0x55, 0xb8, 0xd7,
+ 0x92, 0x82, 0xf5, 0xb9, 0xbb, 0x4c, 0x86, 0xe3, 0x7e, 0xe4, 0x56, 0xde,
+ 0x32, 0xa2, 0xd7, 0x9d, 0x2e, 0x78, 0x02, 0x32, 0x1e, 0x3e, 0x2c, 0x8e,
+ 0x2c, 0xa3, 0xad, 0x67, 0x46, 0x68, 0xe7, 0x9e, 0x4b, 0x9b, 0x39, 0xa2,
+ 0xdc, 0x41, 0x15, 0x77, 0xb2, 0xf7, 0xb6, 0xbe, 0xd0, 0xac, 0x6d, 0x30,
+ 0xda, 0x2e, 0xa0, 0x2d, 0xac, 0x1f, 0x25, 0xd3, 0xf1, 0xaf, 0xed, 0x42,
+ 0xd2, 0x8f, 0x3c, 0x34, 0xda, 0xb0, 0xab, 0xbe, 0xf6, 0xbc, 0xb2, 0xd2,
+ 0x8c, 0x1c, 0x8b, 0x8e, 0x65, 0x4c, 0xbf, 0x35, 0x67, 0xe0, 0x4f, 0x14,
+ 0xf1, 0x43, 0xea, 0x41, 0xce, 0x45, 0xc0, 0xbd, 0x56, 0xe1, 0xd7, 0x39,
+ 0x82, 0x40, 0x68, 0xbc, 0x5e, 0x36, 0xed, 0x5a, 0x29, 0x1e, 0x97, 0x50,
+ 0x3a, 0x73, 0x16, 0x75, 0x30, 0x7b, 0xb1, 0x90, 0x68, 0x3d, 0xba, 0xb1,
+ 0x09, 0x90, 0x27, 0x7a, 0x0c, 0x7b, 0x25, 0x2d, 0xac, 0x66, 0xf5, 0x1e,
+ 0xca, 0xdb, 0xf1, 0x96, 0x39, 0xb2, 0xf3, 0xa4, 0x3d, 0x26, 0xa2, 0x27,
+ 0xa5, 0xab, 0xb2, 0x24, 0x34, 0xb0, 0xb5, 0xbf, 0xb7, 0xd1, 0x18, 0x4e,
+ 0x74, 0x7b, 0x85, 0xe8, 0xfb, 0x1e, 0x54, 0x36, 0xf9, 0x85, 0xd5, 0x74,
+ 0x47, 0xe9, 0xf7, 0x6a, 0x29, 0x65, 0xb4, 0x53, 0x9b, 0x5c, 0xd3, 0xae,
+ 0xbc, 0x9f, 0x06, 0x27, 0xce, 0xa5, 0xf5, 0x7b, 0xd3, 0x93, 0xda, 0x09,
+ 0x2d, 0xad, 0xa0, 0xca, 0xb7, 0xe8, 0xba, 0xf9, 0xa9, 0x6a, 0xe3, 0x2e,
+ 0xd6, 0xc6, 0x3d, 0xae, 0x07, 0x24, 0x5a, 0xd7
+};
+
+typedef struct { const uint8_t *val; size_t len; } rsa_tc_bn_t;
+typedef struct { size_t size; rsa_tc_bn_t n, e, d, p, q, u, m, s; } rsa_tc_t;
+
+static const rsa_tc_t rsa_tc[] = {
+ { 1024,
+ { n_1024, sizeof(n_1024) },
+ { e_1024, sizeof(e_1024) },
+ { d_1024, sizeof(d_1024) },
+ { p_1024, sizeof(p_1024) },
+ { q_1024, sizeof(q_1024) },
+ { u_1024, sizeof(u_1024) },
+ { m_1024, sizeof(m_1024) },
+ { s_1024, sizeof(s_1024) }
+ },
+ { 2048,
+ { n_2048, sizeof(n_2048) },
+ { e_2048, sizeof(e_2048) },
+ { d_2048, sizeof(d_2048) },
+ { p_2048, sizeof(p_2048) },
+ { q_2048, sizeof(q_2048) },
+ { u_2048, sizeof(u_2048) },
+ { m_2048, sizeof(m_2048) },
+ { s_2048, sizeof(s_2048) }
+ },
+ { 4096,
+ { n_4096, sizeof(n_4096) },
+ { e_4096, sizeof(e_4096) },
+ { d_4096, sizeof(d_4096) },
+ { p_4096, sizeof(p_4096) },
+ { q_4096, sizeof(q_4096) },
+ { u_4096, sizeof(u_4096) },
+ { m_4096, sizeof(m_4096) },
+ { s_4096, sizeof(s_4096) }
+ }
+};
diff --git a/tests/test-rsa.py b/tests/test-rsa.py
new file mode 100644
index 0000000..759d5a3
--- /dev/null
+++ b/tests/test-rsa.py
@@ -0,0 +1,86 @@
+# Use PyCrypto to generate test data for Cryptech ModExp core.
+#
+# Funnily enough, PyCrypto and Cryptlib use exactly the same names for
+# RSA key components, see Cryptlib documentation pages 186-187 & 339.
+
+key_lengths = (1024, 2048, 4096) # Lengths in bits of keys to generate
+pkcs_encoding = 8 # PKCS encoding for PEM comment (1 or 8)
+
+plaintext = "You can hack anything you want with TECO and DDT."
+
+from Crypto import __version__ as PyCryptoVersion
+from Crypto.PublicKey import RSA
+from Crypto.Hash import SHA256
+from Crypto.Util.number import long_to_bytes
+from Crypto.Signature.PKCS1_v1_5 import EMSA_PKCS1_V1_5_ENCODE, PKCS115_SigScheme
+from textwrap import TextWrapper
+import sys, os.path
+
+assert all(key_length % 8 == 0 for key_length in key_lengths)
+
+scriptname = os.path.basename(sys.argv[0])
+
+wrapper = TextWrapper(width = 78, initial_indent = " " * 2, subsequent_indent = " " * 2)
+
+def printlines(*lines, **kwargs):
+ for line in lines:
+ sys.stdout.write(line % kwargs + "\n")
+
+def trailing_comma(item, sequence):
+ return "" if item == sequence[-1] else ","
+
+def print_hex(name, value, comment):
+ printlines("static const uint8_t %(name)s[] = { /* %(comment)s, %(length)d bytes */",
+ wrapper.fill(", ".join("0x%02x" % ord(v) for v in value)),
+ "};", "",
+ name = name, comment = comment, length = len(value))
+
+h = SHA256.new(plaintext)
+
+printlines("/*",
+ " * RSA signature test data for Cryptech project, automatically generated by",
+ " * %(scriptname)s using PyCrypto version %(version)s. Do not edit.",
+ " *",
+ " * Plaintext: \"%(plaintext)s\"",
+ " * SHA-256: %(digest)s",
+ " */", "",
+ scriptname = scriptname,
+ version = PyCryptoVersion,
+ plaintext = plaintext,
+ digest = h.hexdigest())
+
+for k_len in key_lengths:
+
+ k = RSA.generate(k_len) # Cryptlib insists u < p, probably with good reason,
+ while k.u >= k.p: # and I'm sure not going to argue the math with Peter,
+ k = RSA.generate(k_len) # so keep trying until we pass this test
+
+ m = EMSA_PKCS1_V1_5_ENCODE(h, k_len/8)
+ s = PKCS115_SigScheme(k).sign(h)
+ assert len(m) == len(s)
+
+ printlines("/* %(k_len)d-bit RSA private key (PKCS #%(pkcs)d)",
+ k.exportKey(format = "PEM", pkcs = pkcs_encoding),
+ "*/", "",
+ k_len = k_len, pkcs = pkcs_encoding)
+
+ for component in k.keydata:
+ print_hex("%s_%d" % (component, k_len),
+ long_to_bytes(getattr(k, component), blocksize = 4),
+ "key component %s" % component)
+ print_hex("m_%d" % k_len, m, "message to be signed")
+ print_hex("s_%d" % k_len, s, "signed message")
+
+fields = "nedpqums"
+printlines("typedef struct { const uint8_t *val; size_t len; } rsa_tc_bn_t;",
+ "typedef struct { size_t size; rsa_tc_bn_t %(fields)s; } rsa_tc_t;",
+ "",
+ "static const rsa_tc_t rsa_tc[] = {",
+ fields = ", ".join(fields))
+for k_len in key_lengths:
+ printlines(" { %(k_len)d,", k_len = k_len)
+ for field in fields:
+ printlines(" { %(field)s_%(k_len)d, sizeof(%(field)s_%(k_len)d) }%(comma)s",
+ field = field, k_len = k_len, comma = trailing_comma(field, fields))
+ printlines(" }%(comma)s", comma = trailing_comma(k_len, key_lengths))
+printlines("};")
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