Does psa_asymmetric_encrypt work for nrf52840 ?

[JY wu]

Hello~

I am developing nrf52840 with zephyr ncs tool chain v2.7.0 and SDK v2.6.1.

Our project needs RSA to exchange secure data.

I use example "samples/crypto/rsa", modified it, tring to encrypt message. be failed.

I add this function to the example :

int rsa_encrypt_msg(const uint8_t * planttext,size_t plantlen, uint8_t * encrypttext,size_t * encryptlen)
{
      psa_status_t status =  psa_asymmetric_encrypt(pub_key_handle, PSA_ALG_RSA_PKCS1V15_SIGN(PSA_ALG_SHA_256), \
                                        planttext, plantlen, NULL, 0, encrypttext, 1024, encryptlen);
 
      if (status != PSA_SUCCESS) 
      {
          printk("encrypt_msg failed! (Error: %d )\n", status);
          switch(status)
          {
              case PSA_ERROR_INVALID_HANDLE:  LOG_INF("PSA_ERROR_INVALID_HANDLE"); break;
              case PSA_ERROR_NOT_PERMITTED:  LOG_INF("PSA_ERROR_NOT_PERMITTED"); break;
              case PSA_ERROR_BUFFER_TOO_SMALL:  LOG_INF("PSA_ERROR_BUFFER_TOO_SMALL"); break;
              case PSA_ERROR_NOT_SUPPORTED:  LOG_INF("PSA_ERROR_NOT_SUPPORTED"); break;
              case PSA_ERROR_INVALID_ARGUMENT:  LOG_INF("PSA_ERROR_INVALID_ARGUMENT"); break;
              case PSA_ERROR_INSUFFICIENT_MEMORY:  LOG_INF("PSA_ERROR_INSUFFICIENT_MEMORY"); break;
              case PSA_ERROR_COMMUNICATION_FAILURE:  LOG_INF("PSA_ERROR_COMMUNICATION_FAILURE"); break;
              case PSA_ERROR_HARDWARE_FAILURE:  LOG_INF("PSA_ERROR_HARDWARE_FAILURE"); break;
              case PSA_ERROR_CORRUPTION_DETECTED:  LOG_INF("PSA_ERROR_CORRUPTION_DETECTED"); break;
              case PSA_ERROR_STORAGE_FAILURE:  LOG_INF("PSA_ERROR_STORAGE_FAILURE"); break;
              case PSA_ERROR_INSUFFICIENT_ENTROPY:  LOG_INF("PSA_ERROR_INSUFFICIENT_ENTROPY"); break;
              case PSA_ERROR_BAD_STATE:  LOG_INF("PSA_ERROR_BAD_STATE"); break;
          }
          return APP_ERROR;
      }
 
      printk("Encrypttext");
      return status;
}

and then call this function in main(), just after 

status = import_rsa_pub_key();

    uint8_t buffer_in[10] = {1,2,3,4,5,6,7,8,9,0};
	uint8_t bufferOut[1024] = {0};
	int outputlen = 0;
    rsa_encrypt_msg(buffer_in,sizeof(buffer_in), bufferOut,&outputlen);

But I always get error:

encrypt_msg failed! (Error: -134 )
[00:00:00.314,178] <inf> rsa: PSA_ERROR_NOT_SUPPORTED

Would you please show me the correct way to use psa_asymmetric_encrypt / psa_asymmetric_decrypt ?

[Vidar Berg]

Hello,

Have you tried adding CONFIG_PSA_WANT_ALG_RSA_PKCS1V15_CRYPT=y to your prj.conf file? It does not look like this is enabled by default in the RSA sample.

Best regards,

Vidar

[JY wu]

Hi!

Thanks for your suggestion.

I add CONFIG_PSA_WANT_ALG_RSA_PKCS1V15_CRYPT=y to my prj.conf , rebuild, flash, then get this error message:

encrypt_msg failed! (Error: -135 )
[00:00:00.315,979] <inf> rsa: PSA_ERROR_INVALID_ARGUMENT

Still not work.

[Vidar Berg]

Hi,

Can you upload the modified version of your project so I can debug it on my end?

Thanks,

Vidar

[JY wu]

Thanks for your support, please check our code below,

main.c

/*
 * Copyright (c) 2021 Nordic Semiconductor ASA
 *
 * SPDX-License-Identifier: LicenseRef-Nordic-5-Clause
 */

#include <zephyr/kernel.h>
#include <zephyr/sys/printk.h>
#include <zephyr/logging/log.h>
#include <stdio.h>
#include <stdlib.h>
#include <psa/crypto.h>
#include <psa/crypto_extra.h>

#include "key.h"

#ifdef CONFIG_BUILD_WITH_TFM
#include <tfm_ns_interface.h>
#endif

#define APP_SUCCESS	    (0)
#define APP_ERROR	    (-1)
#define APP_SUCCESS_MESSAGE "Example finished successfully!"
#define APP_ERROR_MESSAGE   "Example exited with error!"

#define PRINT_HEX(p_label, p_text, len)                                                            \
	({                                                                                         \
		LOG_INF("---- %s (len: %u): ----", p_label, len);                                  \
		LOG_HEXDUMP_INF(p_text, len, "Content:");                                          \
		LOG_INF("---- %s end  ----", p_label);                                             \
	})

LOG_MODULE_REGISTER(rsa, LOG_LEVEL_DBG);

/* ====================================================================== */
/*				Global variables/defines for the RSA example			  */

#ifndef CONFIG_PSA_WANT_RSA_KEY_SIZE_4096
#error "This sample needs a key size of 4096"
#endif

#define NRF_CRYPTO_EXAMPLE_RSA_TEXT_SIZE       (100)
#define NRF_CRYPTO_EXAMPLE_RSA_PUBLIC_KEY_SIZE (PSA_KEY_EXPORT_RSA_PUBLIC_KEY_MAX_SIZE(4096))
#define NRF_CRYPTO_EXAMPLE_RSA_SIGNATURE_SIZE  (PSA_BITS_TO_BYTES(4096))

/* Below text is used as plaintext for signing using RSA . */
static char m_plain_text[NRF_CRYPTO_EXAMPLE_RSA_TEXT_SIZE] = {
	"Example string to demonstrate basic usage of RSA."};

static char m_signature[NRF_CRYPTO_EXAMPLE_RSA_SIGNATURE_SIZE];
static char m_hash[32];

static psa_key_id_t keypair_handle;
static psa_key_id_t pub_key_handle;
/* ====================================================================== */

int crypto_init(void)
{
	psa_status_t status;

	/* Initialize PSA Crypto */
	status = psa_crypto_init();
	if (status != PSA_SUCCESS) {
		return APP_ERROR;
	}

	return APP_SUCCESS;
}

int crypto_finish(void)
{
	psa_status_t status;

	/* Destroy the key handle */
	status = psa_destroy_key(keypair_handle);
	if (status != PSA_SUCCESS) {
		LOG_INF("psa_destroy_key failed! (Error: %d)", status);
		return APP_ERROR;
	}

	status = psa_destroy_key(pub_key_handle);
	if (status != PSA_SUCCESS) {
		LOG_INF("psa_destroy_key failed! (Error: %d)", status);
		return APP_ERROR;
	}

	return APP_SUCCESS;
}

int import_rsa_keypair(void)
{
	psa_status_t status;

	LOG_INF("Importing RSA keypair...");

	/* Configure the key attributes */
	psa_key_attributes_t key_attributes = PSA_KEY_ATTRIBUTES_INIT;

	/* Configure the key attributes */
	psa_set_key_usage_flags(&key_attributes, PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_ENCRYPT );
	psa_set_key_lifetime(&key_attributes, PSA_KEY_LIFETIME_VOLATILE);
	psa_set_key_algorithm(&key_attributes, PSA_ALG_RSA_PKCS1V15_CRYPT);
	psa_set_key_type(&key_attributes, PSA_KEY_TYPE_RSA_KEY_PAIR);
	psa_set_key_bits(&key_attributes, 4096);

	/* Generate a random keypair. The keypair is not exposed to the application,
	 * we can use it to signing/verification the key handle.
	 */
	status = psa_import_key(&key_attributes, private_key_der, sizeof(private_key_der),
				&keypair_handle);
	if (status != PSA_SUCCESS) {
		LOG_INF("psa_import_key failed! (Error: %d)", status);
		return APP_ERROR;
	}

	/* After the key handle is acquired the attributes are not needed */
	psa_reset_key_attributes(&key_attributes);

	LOG_INF("RSA generated successfully!");

	return APP_SUCCESS;
}

int import_rsa_pub_key(void)
{
	/* Configure the key attributes */
	psa_key_attributes_t key_attributes = PSA_KEY_ATTRIBUTES_INIT;
	psa_status_t status;

	/* Configure the key attributes */
	psa_set_key_usage_flags(&key_attributes, PSA_KEY_USAGE_VERIFY_HASH | PSA_KEY_USAGE_ENCRYPT  );
	psa_set_key_lifetime(&key_attributes, PSA_KEY_LIFETIME_VOLATILE);
	psa_set_key_algorithm(&key_attributes, PSA_ALG_RSA_PKCS1V15_CRYPT);
	psa_set_key_type(&key_attributes, PSA_KEY_TYPE_RSA_PUBLIC_KEY);
	psa_set_key_bits(&key_attributes, 4096);

	status = psa_import_key(&key_attributes, public_key_der, sizeof(public_key_der),
				&pub_key_handle);
	if (status != PSA_SUCCESS) {
		LOG_INF("psa_import_key failed! (Error: %d)", status);
		return APP_ERROR;
	}

	/* After the key handle is acquired the attributes are not needed */
	psa_reset_key_attributes(&key_attributes);

	return APP_SUCCESS;
}

int sign_message_rsa(void)
{
	uint32_t olen;
	psa_status_t status;

	LOG_INF("Signing a message using RSA...");

	/* Compute the SHA256 hash */
	status = psa_hash_compute(PSA_ALG_SHA_256, m_plain_text, sizeof(m_plain_text), m_hash,
				  sizeof(m_hash), &olen);
	if (status != PSA_SUCCESS) {
		LOG_INF("psa_hash_compute failed! (Error: %d)", status);
		return APP_ERROR;
	}

	/* Sign the hash using RSA */
	status = psa_sign_hash(keypair_handle, PSA_ALG_RSA_PKCS1V15_SIGN(PSA_ALG_SHA_256), m_hash,
			       sizeof(m_hash), m_signature, sizeof(m_signature), &olen);
	if (status != PSA_SUCCESS) {
		LOG_INF("psa_sign_hash failed! (Error: %d)", status);
		return APP_ERROR;
	}

	LOG_INF("Signing was successful!");
	PRINT_HEX("Plaintext", m_plain_text, sizeof(m_plain_text));
	PRINT_HEX("SHA256 hash", m_hash, sizeof(m_hash));
	PRINT_HEX("Signature", m_signature, sizeof(m_signature));

	return APP_SUCCESS;
}

int verify_message_rsa(void)
{
	psa_status_t status;

	LOG_INF("Verifying RSA signature...");

	/* Verify the hash */
	status = psa_verify_hash(pub_key_handle, PSA_ALG_RSA_PKCS1V15_SIGN(PSA_ALG_SHA_256), m_hash,
				 sizeof(m_hash), m_signature, sizeof(m_signature));
	if (status != PSA_SUCCESS) {
		LOG_INF("psa_verify_hash failed! (Error: %d)", status);
		return APP_ERROR;
	}

	LOG_INF("Signature verification was successful!");

	return APP_SUCCESS;
}


int rsa_encrypt_msg(const uint8_t * planttext,size_t plantlen, uint8_t * encrypttext,size_t * encryptlen)
{
      psa_status_t status =  psa_asymmetric_encrypt(pub_key_handle, PSA_ALG_RSA_PKCS1V15_CRYPT, \
                                        planttext, plantlen, NULL, 0, encrypttext, 1024, encryptlen);
 
      if (status != PSA_SUCCESS) 
      {
          printk("encrypt_msg failed! (Error: %d )\n", status);
          switch(status)
          {
              case PSA_ERROR_INVALID_HANDLE:  LOG_INF("PSA_ERROR_INVALID_HANDLE"); break;
              case PSA_ERROR_NOT_PERMITTED:  LOG_INF("PSA_ERROR_NOT_PERMITTED"); break;
              case PSA_ERROR_BUFFER_TOO_SMALL:  LOG_INF("PSA_ERROR_BUFFER_TOO_SMALL"); break;
              case PSA_ERROR_NOT_SUPPORTED:  LOG_INF("PSA_ERROR_NOT_SUPPORTED"); break;
              case PSA_ERROR_INVALID_ARGUMENT:  LOG_INF("PSA_ERROR_INVALID_ARGUMENT"); break;
              case PSA_ERROR_INSUFFICIENT_MEMORY:  LOG_INF("PSA_ERROR_INSUFFICIENT_MEMORY"); break;
              case PSA_ERROR_COMMUNICATION_FAILURE:  LOG_INF("PSA_ERROR_COMMUNICATION_FAILURE"); break;
              case PSA_ERROR_HARDWARE_FAILURE:  LOG_INF("PSA_ERROR_HARDWARE_FAILURE"); break;
              case PSA_ERROR_CORRUPTION_DETECTED:  LOG_INF("PSA_ERROR_CORRUPTION_DETECTED"); break;
              case PSA_ERROR_STORAGE_FAILURE:  LOG_INF("PSA_ERROR_STORAGE_FAILURE"); break;
              case PSA_ERROR_INSUFFICIENT_ENTROPY:  LOG_INF("PSA_ERROR_INSUFFICIENT_ENTROPY"); break;
              case PSA_ERROR_BAD_STATE:  LOG_INF("PSA_ERROR_BAD_STATE"); break;
          }
          return APP_ERROR;
      }
 
      printk("Encrypttext");
      return status;
}



int main(void)
{
	int status;

	LOG_INF("Starting the RSA example...");

	status = crypto_init();
	if (status != APP_SUCCESS) {
		LOG_INF(APP_ERROR_MESSAGE);
		return APP_ERROR;
	}

	status = import_rsa_keypair();
	if (status != APP_SUCCESS) {
		LOG_INF(APP_ERROR_MESSAGE);
		return APP_ERROR;
	}

	status = import_rsa_pub_key();
	if (status != APP_SUCCESS) {
		LOG_INF(APP_ERROR_MESSAGE);
		return APP_ERROR;
	}

	uint8_t buffer_in[10] = {1,2,3,4,5,6,7,8,9,0};
	uint8_t bufferOut[1024] = {0};
	int outputlen = 0;
    rsa_encrypt_msg(buffer_in,sizeof(buffer_in), bufferOut,&outputlen);

	k_msleep(10000);
	/*
	status = sign_message_rsa();
	if (status != APP_SUCCESS) {
		LOG_INF(APP_ERROR_MESSAGE);
		return APP_ERROR;
	}

	status = verify_message_rsa();
	if (status != APP_SUCCESS) {
		LOG_INF(APP_ERROR_MESSAGE);
		return APP_ERROR;
	}
	*/

	status = crypto_finish();
	if (status != APP_SUCCESS) {
		LOG_INF(APP_ERROR_MESSAGE);
		return APP_ERROR;
	}

	LOG_INF(APP_SUCCESS_MESSAGE);

	return APP_SUCCESS;
}

Key.h

/*
 * Copyright (c) 2024 Nordic Semiconductor ASA
 *
 * SPDX-License-Identifier: LicenseRef-Nordic-5-Clause
 */

/*
 * $ openssl genpkey -algorithm RSA -outform DER -out private_key.der -pkeyopt rsa_keygen_bits:4096
 * $ openssl rsa -in private_key.der -inform DER -pubout -outform DER -out public_key.der
 */
const unsigned char private_key_der[] = {
	0x30, 0x82, 0x09, 0x28, 0x02, 0x01, 0x00, 0x02, 0x82, 0x02, 0x01, 0x00, 0xb7, 0xe5, 0xa6,
	0x58, 0x69, 0x16, 0xda, 0x73, 0xa1, 0x2c, 0x8f, 0x71, 0x91, 0x67, 0x41, 0x02, 0xfa, 0x5d,
	0x58, 0x95, 0x08, 0x2b, 0xdd, 0xc3, 0xd0, 0xbd, 0x6c, 0x41, 0xc9, 0x17, 0x97, 0xf1, 0xf4,
	0x34, 0xcb, 0x37, 0xdc, 0xc5, 0xb9, 0x57, 0x63, 0x16, 0xf7, 0xce, 0x6c, 0xf6, 0x89, 0xda,
	0xf4, 0xa8, 0x0f, 0x37, 0x8f, 0x1a, 0x66, 0x7c, 0x1e, 0x93, 0x5e, 0x0e, 0x63, 0xa7, 0x5f,
	0x1b, 0x90, 0x48, 0x21, 0xac, 0x02, 0x13, 0xf9, 0x36, 0x44, 0x53, 0x07, 0x77, 0x45, 0x9c,
	0xdc, 0xc1, 0x08, 0x51, 0xb7, 0xa6, 0x73, 0x26, 0x32, 0x93, 0xb2, 0x9c, 0x7e, 0xba, 0x39,
	0x67, 0x59, 0xf1, 0x01, 0xdb, 0xc6, 0xfa, 0x4c, 0x2a, 0xac, 0x43, 0x44, 0xb7, 0x6b, 0x42,
	0xe6, 0xb1, 0x20, 0xf4, 0x5a, 0xc0, 0x6d, 0x22, 0x1f, 0x64, 0x8d, 0x1d, 0xb5, 0x04, 0x10,
	0x57, 0x51, 0x12, 0x8d, 0xcd, 0x5d, 0xd9, 0xb1, 0x06, 0xd7, 0x47, 0x8b, 0x18, 0x5f, 0x1e,
	0x96, 0xd2, 0x0d, 0xa9, 0x8e, 0xf5, 0x5c, 0x80, 0xdb, 0xc5, 0xaf, 0xe2, 0x2a, 0x23, 0x2e,
	0xfd, 0x43, 0x6e, 0x66, 0x0d, 0x2d, 0x45, 0x12, 0xa4, 0xcb, 0x47, 0x12, 0xc2, 0xe8, 0xba,
	0xfb, 0x99, 0xec, 0x05, 0x57, 0x6d, 0xd6, 0xa0, 0x66, 0x3a, 0x9a, 0x63, 0x6f, 0x58, 0x9f,
	0x72, 0xf6, 0x0a, 0x47, 0xb7, 0xea, 0x8e, 0xae, 0xb1, 0x52, 0x28, 0xfd, 0xe9, 0x16, 0x14,
	0x46, 0x8b, 0x1b, 0x2e, 0x85, 0xc6, 0x7e, 0x99, 0x85, 0x22, 0x16, 0x23, 0x14, 0x49, 0x22,
	0x53, 0x1e, 0x7b, 0x04, 0x6c, 0xb9, 0x75, 0xe8, 0xdb, 0xba, 0x96, 0x8a, 0x63, 0x38, 0xcc,
	0x9f, 0x59, 0xeb, 0xcf, 0x27, 0x3b, 0x66, 0x21, 0xfe, 0x4b, 0xa3, 0x76, 0x5c, 0xb0, 0x64,
	0x40, 0xfb, 0x93, 0x25, 0x68, 0xb9, 0xa1, 0xc4, 0x9b, 0x80, 0x5e, 0x25, 0xee, 0xc6, 0xa8,
	0xd3, 0x9c, 0x3a, 0xfe, 0x71, 0xef, 0x56, 0xaa, 0xef, 0x4a, 0x33, 0x47, 0xd6, 0xbe, 0x7b,
	0x77, 0x9b, 0x66, 0x49, 0xaa, 0x58, 0x67, 0xef, 0xb8, 0xe8, 0x5b, 0x84, 0xa0, 0x9f, 0xdc,
	0xcf, 0x38, 0x62, 0x05, 0x6d, 0x5b, 0x88, 0xd5, 0x1b, 0xc7, 0x3a, 0xd0, 0x3a, 0xd3, 0x58,
	0x04, 0xa0, 0x5b, 0x8b, 0x60, 0x82, 0x28, 0x44, 0xbf, 0x89, 0xbf, 0xe1, 0xbc, 0x0e, 0x6e,
	0xf7, 0x98, 0x38, 0xd4, 0x90, 0x38, 0xa1, 0xd6, 0x5a, 0x52, 0x95, 0x4a, 0xdf, 0xf1, 0x06,
	0x94, 0x81, 0x95, 0x53, 0xe8, 0xb7, 0x4b, 0xa4, 0x3f, 0x0a, 0x0e, 0xbd, 0x53, 0x38, 0x67,
	0x64, 0x3c, 0x86, 0x1e, 0xa5, 0x5d, 0xb7, 0x9d, 0xc8, 0x9b, 0x76, 0xea, 0xde, 0x3a, 0x45,
	0x95, 0x7f, 0xb0, 0xb6, 0x6b, 0xc3, 0x25, 0x32, 0x0a, 0xbd, 0x6a, 0x05, 0x23, 0x76, 0x1d,
	0x9f, 0xb9, 0xe1, 0xe8, 0x47, 0xbf, 0xb4, 0x0f, 0x67, 0xeb, 0x64, 0xfc, 0xdd, 0x8c, 0xda,
	0x14, 0xf5, 0x55, 0x7b, 0xce, 0x8d, 0x7d, 0xb2, 0x6f, 0xab, 0x51, 0xbf, 0x62, 0xa1, 0x99,
	0x52, 0x92, 0x99, 0xca, 0xdf, 0x2f, 0x18, 0x9e, 0x29, 0x94, 0x42, 0xe4, 0x77, 0x3c, 0x59,
	0x04, 0x03, 0x1f, 0xc7, 0x82, 0x13, 0x93, 0x01, 0xbc, 0xf7, 0x2b, 0x0f, 0xf9, 0x46, 0xbc,
	0x44, 0xcf, 0xb7, 0x2f, 0xa1, 0x91, 0x68, 0x25, 0xa7, 0x1d, 0x7e, 0x8a, 0x98, 0x88, 0x63,
	0x8a, 0xba, 0xef, 0xed, 0x90, 0x7b, 0xc0, 0x91, 0x79, 0x72, 0x41, 0xf3, 0x15, 0x8e, 0xc7,
	0x12, 0x5c, 0xdd, 0xf9, 0x20, 0x92, 0x2d, 0x7c, 0x4e, 0x01, 0x67, 0xce, 0x97, 0x61, 0xf4,
	0xff, 0x64, 0x4a, 0xf0, 0x1a, 0xf7, 0x14, 0xf9, 0x71, 0x97, 0xc6, 0x07, 0x91, 0xe9, 0xbd,
	0xf0, 0xa0, 0x3c, 0xc3, 0x7b, 0x91, 0xb0, 0x36, 0x10, 0x3a, 0xc9, 0x65, 0x97, 0x17, 0x02,
	0x03, 0x01, 0x00, 0x01, 0x02, 0x82, 0x01, 0xff, 0x71, 0x3b, 0xdd, 0xa0, 0xa3, 0xe1, 0xbb,
	0x5d, 0x44, 0x83, 0x45, 0x47, 0xb1, 0x5a, 0x51, 0xd8, 0x58, 0xeb, 0x10, 0x75, 0xc5, 0x01,
	0x3d, 0xc8, 0x08, 0x73, 0x89, 0xd7, 0x80, 0xae, 0x86, 0x72, 0x28, 0xc2, 0x37, 0x2c, 0x8c,
	0x77, 0xbb, 0xf5, 0x0a, 0x9f, 0xde, 0x29, 0xdf, 0x87, 0xef, 0x27, 0x74, 0xa0, 0xb1, 0xcf,
	0x15, 0x35, 0x23, 0xd4, 0xd2, 0x0f, 0xfd, 0x05, 0x12, 0x68, 0xc1, 0x2f, 0xea, 0xf4, 0x7f,
	0x60, 0xea, 0xd5, 0x94, 0xda, 0x44, 0x5a, 0x0f, 0x03, 0x15, 0x6b, 0x45, 0x93, 0xfd, 0x2d,
	0x87, 0x67, 0xdd, 0x08, 0x06, 0x0b, 0x85, 0xa2, 0xc6, 0x21, 0x6d, 0x8c, 0xa4, 0xff, 0xca,
	0x4f, 0xd6, 0xb5, 0xae, 0xec, 0x75, 0x9d, 0x5c, 0x87, 0xfa, 0xd0, 0xc8, 0x19, 0xd1, 0xd3,
	0x0a, 0xfd, 0x60, 0xbe, 0x33, 0x2f, 0xf2, 0xc5, 0xb5, 0xec, 0x28, 0x8a, 0x24, 0x03, 0xb7,
	0xa2, 0x5f, 0x1f, 0x0a, 0x2f, 0x12, 0x93, 0x58, 0xe8, 0x06, 0xbb, 0x0a, 0xdf, 0x08, 0x46,
	0x57, 0x40, 0xac, 0xce, 0x89, 0x73, 0xd2, 0xbf, 0xac, 0x10, 0x75, 0x80, 0xc1, 0x84, 0xa7,
	0xeb, 0xa8, 0x63, 0x4e, 0xb9, 0xb2, 0xd8, 0x08, 0x24, 0x51, 0x5c, 0xf3, 0x7e, 0xba, 0x22,
	0xd4, 0x21, 0xd6, 0x97, 0x87, 0x4a, 0x17, 0x0a, 0xf0, 0x04, 0xee, 0xb2, 0x16, 0xbc, 0xf9,
	0x7d, 0x4e, 0x5f, 0xaf, 0x42, 0xc4, 0xb2, 0x45, 0xc8, 0x9e, 0x3e, 0xbb, 0xb9, 0xc9, 0xe9,
	0x5b, 0x98, 0x3b, 0xa0, 0x5d, 0x51, 0x53, 0x0b, 0xf1, 0x47, 0x17, 0x17, 0x5b, 0x82, 0xb9,
	0x72, 0x7d, 0x6a, 0xf2, 0x66, 0x38, 0x0f, 0x58, 0x05, 0x04, 0xeb, 0xe9, 0x55, 0x4a, 0x91,
	0x4c, 0x39, 0x1c, 0x5d, 0x9e, 0xeb, 0x05, 0x4d, 0x29, 0x4e, 0x40, 0xb1, 0x5c, 0x59, 0x58,
	0x62, 0xc5, 0xeb, 0x00, 0xc7, 0x03, 0xb2, 0xf5, 0x2f, 0xfd, 0xa7, 0xd5, 0x04, 0x6f, 0xff,
	0xeb, 0xca, 0x78, 0x96, 0x09, 0xd7, 0x52, 0x48, 0xb3, 0xa8, 0x33, 0xab, 0x99, 0x1c, 0x87,
	0x99, 0x9d, 0x9b, 0x9f, 0xa5, 0x32, 0x58, 0xcd, 0xd1, 0x97, 0x5d, 0xa5, 0x12, 0x18, 0xe8,
	0x3f, 0x7b, 0x17, 0x92, 0x74, 0x98, 0xd4, 0xc0, 0x6c, 0x65, 0x98, 0x9b, 0xec, 0x23, 0xd4,
	0xb4, 0x86, 0x4c, 0x2c, 0x61, 0x22, 0x50, 0xf9, 0x4f, 0x8e, 0xf3, 0x5d, 0x61, 0x34, 0x0e,
	0x41, 0x50, 0xfb, 0x67, 0x5e, 0xdd, 0x4e, 0x29, 0x57, 0x4a, 0xe5, 0xbf, 0x1e, 0x92, 0xaf,
	0x1d, 0x37, 0x97, 0x84, 0xc7, 0xc5, 0xa8, 0x01, 0x7c, 0x90, 0x92, 0x37, 0xd4, 0x5b, 0x86,
	0x30, 0xdd, 0x59, 0x53, 0x32, 0xd5, 0x90, 0xff, 0xe3, 0xb9, 0x87, 0x0f, 0x41, 0x29, 0x6a,
	0xd3, 0x91, 0xf5, 0x2b, 0xd3, 0x33, 0xaa, 0x26, 0xd9, 0xf6, 0x22, 0xe8, 0x73, 0xdf, 0x45,
	0x83, 0x3b, 0xa4, 0x25, 0xb7, 0x61, 0x2c, 0x30, 0x43, 0x25, 0xbb, 0xb6, 0xb5, 0xf6, 0x0b,
	0x89, 0xda, 0x7d, 0x63, 0x86, 0x47, 0x25, 0xf4, 0x58, 0xa5, 0x82, 0xba, 0x68, 0xda, 0xc7,
	0xb9, 0x22, 0xd6, 0x08, 0xf3, 0x13, 0x49, 0x23, 0x29, 0x7e, 0x96, 0xca, 0x27, 0xb7, 0x5f,
	0x51, 0x6a, 0x31, 0xcb, 0xde, 0xbc, 0xe5, 0x9e, 0x4e, 0x47, 0xf9, 0x74, 0x2b, 0x50, 0xff,
	0x24, 0x20, 0x0f, 0x10, 0x85, 0xce, 0x7c, 0x9c, 0xd1, 0x7f, 0xa8, 0x5a, 0x5b, 0xfe, 0x19,
	0x18, 0x58, 0xaf, 0xcf, 0xd9, 0xa9, 0xc1, 0xe0, 0xd9, 0xe0, 0x68, 0x67, 0x1a, 0x01, 0x36,
	0x2b, 0x4d, 0x8c, 0xc2, 0xa4, 0x16, 0x6d, 0x32, 0xf1, 0xa2, 0x02, 0xa2, 0x4b, 0x3e, 0xf6,
	0x21, 0x05, 0xca, 0xbf, 0xe7, 0x53, 0x01, 0x6d, 0x48, 0xb0, 0xfa, 0x27, 0x9a, 0x07, 0xa9,
	0x64, 0xbb, 0x43, 0xc8, 0x75, 0xfb, 0x57, 0x9d, 0x59, 0x02, 0x82, 0x01, 0x01, 0x00, 0xcc,
	0x64, 0x0c, 0x1f, 0x0f, 0xa4, 0xa4, 0xcb, 0x02, 0x41, 0xd0, 0x86, 0x45, 0x18, 0xe6, 0xc9,
	0x4b, 0xe0, 0xcf, 0x89, 0xcb, 0x91, 0x93, 0x1d, 0x4c, 0x75, 0x13, 0x6f, 0x96, 0x0c, 0x71,
	0x0a, 0x0c, 0x9c, 0x0e, 0xb9, 0x3f, 0x3c, 0x65, 0x68, 0xd0, 0xaa, 0x3a, 0x74, 0xa7, 0xbc,
	0x5d, 0x98, 0x81, 0xb2, 0x4d, 0x74, 0x85, 0x68, 0xbd, 0xe6, 0xb8, 0xc3, 0x8a, 0xdc, 0x57,
	0xb1, 0x96, 0x50, 0x13, 0xae, 0x25, 0x90, 0x43, 0x91, 0xc2, 0x3e, 0x85, 0x36, 0x45, 0x0e,
	0xcf, 0x68, 0x97, 0x25, 0x91, 0x51, 0xc2, 0x8a, 0x1e, 0xea, 0xae, 0xd4, 0x8b, 0xf7, 0x4d,
	0xf1, 0x20, 0x36, 0xd8, 0x53, 0xd6, 0x36, 0xba, 0xa9, 0x38, 0x7e, 0x53, 0x96, 0x73, 0x1b,
	0x12, 0xe7, 0x90, 0x35, 0x38, 0xfb, 0x55, 0xc0, 0x54, 0x25, 0x7a, 0xbe, 0x01, 0xbc, 0x1e,
	0x46, 0x66, 0x03, 0x3a, 0xa3, 0xa1, 0x70, 0x06, 0x3d, 0x9a, 0xb2, 0xd2, 0x96, 0x0f, 0x4e,
	0x12, 0x33, 0x23, 0x9b, 0x17, 0x85, 0x18, 0x4a, 0xf1, 0xac, 0xbd, 0x35, 0x51, 0x75, 0x08,
	0x83, 0x32, 0x51, 0xd7, 0x45, 0x82, 0x30, 0xb7, 0xef, 0x17, 0xea, 0x24, 0x44, 0x71, 0xc0,
	0x7e, 0xc1, 0xc0, 0x7e, 0xfa, 0x5d, 0x7f, 0xb5, 0x3c, 0xc9, 0x6f, 0x11, 0x42, 0x77, 0x14,
	0xa2, 0xc6, 0xdf, 0xda, 0xea, 0x7b, 0x12, 0xee, 0xee, 0x52, 0x17, 0x22, 0xd2, 0xa0, 0x5d,
	0x2d, 0x81, 0x68, 0x49, 0xf4, 0xfe, 0x17, 0x5a, 0xd3, 0x63, 0x4e, 0x77, 0x0c, 0xe6, 0xdd,
	0x33, 0x6f, 0x8d, 0xa7, 0x57, 0x23, 0x84, 0x94, 0x56, 0xc9, 0xaa, 0x5c, 0xfa, 0x2b, 0xd7,
	0x30, 0xe5, 0x67, 0x4a, 0x9c, 0xbf, 0xf1, 0x56, 0x06, 0x01, 0x46, 0x88, 0x48, 0x7c, 0x2f,
	0x25, 0x0a, 0x6f, 0xd5, 0x04, 0x3e, 0x71, 0x3f, 0x73, 0x2e, 0xd7, 0x65, 0xde, 0xf0, 0x6f,
	0x02, 0x82, 0x01, 0x01, 0x00, 0xe6, 0x54, 0xdf, 0xbb, 0x18, 0x0d, 0x29, 0x21, 0x87, 0x10,
	0x37, 0x75, 0xe1, 0x50, 0x15, 0x75, 0xcd, 0x74, 0x26, 0x90, 0xc4, 0x9d, 0x61, 0x2f, 0x4a,
	0x58, 0x35, 0x13, 0x8e, 0x99, 0xd2, 0x10, 0x09, 0x16, 0x8b, 0xbd, 0xbb, 0xeb, 0x0c, 0xec,
	0xf2, 0x70, 0x10, 0xa0, 0x8f, 0xa7, 0x97, 0xb9, 0xef, 0x36, 0xd2, 0xfc, 0xe5, 0x32, 0x06,
	0x0b, 0x95, 0x03, 0x17, 0xdf, 0x3a, 0x74, 0xdb, 0x5b, 0xe6, 0xd6, 0xa2, 0xe4, 0xf0, 0x20,
	0x66, 0xb4, 0x9c, 0x07, 0x6d, 0xeb, 0x31, 0x88, 0x3d, 0xb7, 0x97, 0x24, 0x14, 0xe6, 0xde,
	0x88, 0x8e, 0x7c, 0xa6, 0xb4, 0xcc, 0x37, 0x2c, 0x5d, 0x4e, 0xb3, 0x20, 0xcd, 0xfb, 0x2f,
	0x8b, 0xcb, 0x8f, 0x8b, 0x00, 0xc3, 0x5b, 0xd8, 0xc8, 0xd9, 0x9e, 0xe9, 0xc3, 0x1d, 0x2e,
	0x26, 0x7b, 0x50, 0x1d, 0x6a, 0x83, 0xfa, 0xd7, 0x50, 0xce, 0x26, 0xbc, 0xfc, 0x71, 0x0f,
	0x18, 0xa3, 0xe2, 0x31, 0x5f, 0x6d, 0xb8, 0xe5, 0x5f, 0xec, 0xce, 0xe0, 0xa8, 0x17, 0xab,
	0xe5, 0x85, 0x91, 0x78, 0x01, 0x84, 0x88, 0x02, 0xd3, 0x46, 0x4c, 0xc6, 0x6b, 0xa1, 0xda,
	0xab, 0x9a, 0xe7, 0xa8, 0x8d, 0x17, 0x91, 0x41, 0xf8, 0xd5, 0x6d, 0xdd, 0x85, 0x3a, 0xce,
	0xc0, 0xc0, 0x9d, 0xbe, 0x90, 0x29, 0xbd, 0xad, 0x8e, 0xe6, 0x8e, 0x92, 0x2f, 0x70, 0x15,
	0x87, 0x41, 0x06, 0x35, 0xb6, 0xeb, 0x43, 0x7c, 0x70, 0x3d, 0x66, 0x28, 0xc2, 0x2f, 0xe4,
	0x84, 0x04, 0xb5, 0x11, 0xe8, 0xb7, 0xa6, 0xfe, 0xd2, 0x73, 0x06, 0x65, 0x3c, 0xd3, 0x90,
	0x11, 0x55, 0xe7, 0x72, 0xa5, 0xd8, 0xcb, 0x23, 0x82, 0x4f, 0xdd, 0xec, 0xe2, 0xaf, 0xe4,
	0x81, 0x3f, 0xe7, 0x43, 0xf2, 0x67, 0x66, 0xf7, 0x8b, 0xdc, 0xd8, 0x28, 0x14, 0x61, 0xd9,
	0xca, 0xa7, 0xa5, 0x93, 0x47, 0xd9, 0x02, 0x82, 0x01, 0x00, 0x1e, 0xc2, 0x83, 0xcc, 0x7c,
	0xe7, 0x33, 0x61, 0xd6, 0x02, 0x1f, 0xa6, 0xc5, 0x69, 0x5c, 0xfa, 0x38, 0x70, 0x29, 0xeb,
	0xbb, 0xf6, 0x39, 0xa4, 0xb4, 0x27, 0xfe, 0x77, 0xd1, 0xa6, 0x27, 0xb0, 0xf2, 0x7a, 0xde,
	0x00, 0x65, 0x12, 0xea, 0xd4, 0x1e, 0x6b, 0x30, 0x06, 0xf4, 0x63, 0x75, 0xd6, 0x88, 0xd6,
	0x53, 0xaf, 0xd0, 0x90, 0x15, 0xdc, 0x4e, 0x3c, 0x27, 0x7e, 0xc7, 0xb7, 0xd3, 0x3e, 0x53,
	0xe7, 0xe6, 0x81, 0x52, 0x99, 0xf2, 0x18, 0xc4, 0xa5, 0x89, 0x39, 0x14, 0x5f, 0xd2, 0x37,
	0x76, 0x2a, 0x4e, 0xd3, 0xc8, 0x99, 0x5b, 0x1c, 0x63, 0xc0, 0x21, 0x3b, 0xc3, 0xb4, 0x5d,
	0x54, 0x28, 0xad, 0xed, 0xe3, 0x9f, 0xbb, 0xeb, 0x4a, 0x7e, 0x22, 0x39, 0xf3, 0x1d, 0x91,
	0xd4, 0xf4, 0x86, 0x50, 0x3e, 0x99, 0xb1, 0x62, 0x3d, 0x12, 0x99, 0x9f, 0xd0, 0xa4, 0x75,
	0xc3, 0xc0, 0x7d, 0x02, 0x83, 0x6c, 0xef, 0xb2, 0x9f, 0xa0, 0xc8, 0x08, 0x17, 0x28, 0x29,
	0xa4, 0x1d, 0x84, 0xad, 0x6a, 0xb7, 0xab, 0x76, 0x05, 0xbf, 0x4e, 0x3b, 0xa8, 0x6c, 0x06,
	0xb0, 0xd0, 0x4a, 0x12, 0xb4, 0x69, 0xed, 0xf3, 0xed, 0x55, 0x0d, 0x3a, 0x46, 0x60, 0x78,
	0xfb, 0xa6, 0xec, 0x9c, 0x52, 0xfc, 0xa1, 0xb9, 0x80, 0x3e, 0x39, 0x9d, 0xd1, 0xbe, 0x48,
	0xcc, 0xf7, 0x1e, 0xbf, 0x54, 0xa0, 0x88, 0x18, 0xd6, 0x88, 0x09, 0xdd, 0xda, 0x56, 0xde,
	0xa2, 0x7f, 0x46, 0xf6, 0x85, 0x4f, 0xb1, 0xb4, 0x5a, 0xfd, 0xb7, 0x96, 0x91, 0x18, 0x49,
	0x71, 0xe4, 0xc7, 0x84, 0x27, 0x97, 0x8c, 0x0b, 0x18, 0x1f, 0x56, 0xf0, 0x65, 0xe5, 0xe8,
	0xa5, 0xb4, 0x81, 0x56, 0x87, 0xea, 0xd3, 0x39, 0x99, 0x67, 0x0f, 0x15, 0x4c, 0xff, 0xcd,
	0x98, 0x28, 0xe9, 0x94, 0x39, 0xfa, 0x77, 0xb2, 0x3e, 0x1e, 0x03, 0x02, 0x82, 0x01, 0x01,
	0x00, 0x95, 0xde, 0xb5, 0xf1, 0x14, 0x16, 0x44, 0x24, 0x17, 0xb0, 0xfa, 0x95, 0x4e, 0x35,
	0x00, 0xb1, 0xb5, 0x2c, 0x95, 0x87, 0x6f, 0x17, 0x84, 0x4b, 0xf4, 0x10, 0xef, 0x00, 0x39,
	0xb2, 0x66, 0xd7, 0x9e, 0x42, 0x38, 0x4d, 0x0d, 0x80, 0x44, 0xd9, 0xcc, 0x6a, 0x14, 0xb7,
	0x94, 0xa1, 0x94, 0xfd, 0x1b, 0xe4, 0xcd, 0x66, 0x56, 0x6f, 0xb5, 0x35, 0x46, 0x11, 0x4c,
	0x30, 0x28, 0xe6, 0x2e, 0x71, 0x5f, 0x03, 0x5b, 0xdc, 0xa1, 0x4e, 0x43, 0xe5, 0xd2, 0xfc,
	0x96, 0x8e, 0x09, 0x9d, 0xbf, 0xa2, 0xbc, 0xca, 0x72, 0x7b, 0x42, 0x63, 0x12, 0x6b, 0x93,
	0x41, 0x62, 0xfb, 0xa7, 0x77, 0x53, 0x25, 0x04, 0xfc, 0x62, 0x2b, 0xae, 0xc7, 0x96, 0x2f,
	0xf9, 0x20, 0x24, 0x9c, 0x2b, 0x1c, 0x46, 0xe5, 0x8d, 0xda, 0x67, 0xd4, 0x0c, 0x3a, 0xb5,
	0xd9, 0x3f, 0xe5, 0x30, 0xc2, 0xd8, 0x50, 0xa6, 0x79, 0x8f, 0xcb, 0x25, 0xda, 0x44, 0xec,
	0xa1, 0x4e, 0x50, 0x97, 0x97, 0x52, 0x0b, 0xce, 0x6c, 0x31, 0x72, 0xdd, 0x16, 0x8a, 0xef,
	0xcd, 0xf5, 0x01, 0x56, 0xed, 0x47, 0xf9, 0xde, 0xc5, 0xdb, 0xfb, 0xdf, 0xdb, 0x1c, 0x4f,
	0x34, 0xf7, 0x17, 0xc2, 0x18, 0x7a, 0x2f, 0x51, 0x8b, 0x46, 0x17, 0x8f, 0x9e, 0x05, 0x46,
	0x20, 0xa1, 0xb8, 0x54, 0xbc, 0xfd, 0xd1, 0xd8, 0xd6, 0xdb, 0x14, 0x76, 0xfc, 0x5d, 0x61,
	0x08, 0x13, 0x8e, 0xc6, 0xe2, 0x75, 0x61, 0x0a, 0xb6, 0x47, 0xd9, 0x65, 0xf9, 0x76, 0x24,
	0x20, 0x0b, 0x97, 0xb2, 0x89, 0x16, 0xe5, 0x1b, 0x6c, 0x77, 0xb0, 0x6f, 0x47, 0x39, 0x21,
	0x05, 0x3e, 0xc9, 0xf6, 0xe1, 0xec, 0xbb, 0xd7, 0x4e, 0x2c, 0xea, 0xff, 0x1a, 0xa8, 0x8d,
	0x32, 0xa6, 0x0b, 0x7e, 0x99, 0x57, 0xea, 0xa2, 0x31, 0x98, 0xf5, 0xd0, 0x82, 0x43, 0x1f,
	0x51, 0x09, 0x02, 0x82, 0x01, 0x01, 0x00, 0xbc, 0x01, 0x10, 0x53, 0x17, 0x77, 0xd7, 0xad,
	0x24, 0xff, 0xe4, 0xe8, 0x89, 0x0a, 0x25, 0x61, 0x8c, 0x0e, 0xaf, 0xa8, 0xa1, 0xbd, 0x95,
	0x2d, 0x9b, 0xe9, 0xdc, 0xbc, 0xe5, 0x15, 0xe8, 0x9e, 0xd2, 0xa5, 0x8b, 0x9e, 0xce, 0x35,
	0xa2, 0x15, 0x2d, 0x36, 0xc5, 0x93, 0x8d, 0xfe, 0x0d, 0xb1, 0x44, 0xb4, 0xd4, 0x0a, 0x44,
	0x65, 0x0f, 0x27, 0x63, 0xe8, 0xdd, 0x17, 0x80, 0x8f, 0x72, 0xae, 0xc7, 0x5a, 0x35, 0x9d,
	0x74, 0xee, 0x61, 0xc6, 0x26, 0xc3, 0x45, 0x55, 0x66, 0xe7, 0x76, 0x75, 0x47, 0x68, 0x69,
	0x33, 0xcb, 0xe9, 0x39, 0x68, 0x04, 0x89, 0xfc, 0x9a, 0xe0, 0xeb, 0xee, 0x41, 0x80, 0xe2,
	0xf6, 0x98, 0x59, 0x6d, 0xab, 0xcb, 0x22, 0xaf, 0x12, 0xb7, 0xf4, 0x48, 0x75, 0x52, 0x94,
	0xcd, 0x94, 0xd6, 0xf7, 0x78, 0xeb, 0x8b, 0x97, 0xbe, 0x79, 0xec, 0x62, 0xe2, 0xbf, 0x3a,
	0x3e, 0xe4, 0xad, 0x04, 0xb0, 0x53, 0x4a, 0xc3, 0xe1, 0x27, 0xb6, 0xc0, 0xa9, 0xa7, 0x43,
	0x55, 0xc9, 0xcc, 0xc3, 0x26, 0xed, 0xdd, 0x23, 0xfb, 0x4b, 0xa4, 0x2c, 0xd8, 0x2e, 0xf9,
	0x3c, 0xbc, 0x9a, 0xb3, 0xdd, 0x8a, 0xb2, 0xda, 0xfc, 0x61, 0x6e, 0xa2, 0x41, 0x34, 0x1b,
	0x16, 0x2f, 0xbe, 0xfb, 0x3b, 0xcb, 0x51, 0x45, 0xdc, 0x12, 0x57, 0x09, 0xf8, 0xe1, 0x33,
	0x5a, 0x1e, 0x5e, 0x06, 0x86, 0x01, 0xdd, 0x82, 0x54, 0x4a, 0xf0, 0x9b, 0x92, 0x7e, 0xbe,
	0x63, 0x55, 0x6e, 0xd5, 0x5c, 0xaf, 0xbb, 0x36, 0x5a, 0x50, 0x7d, 0x1e, 0xbf, 0xd9, 0x69,
	0xc5, 0xef, 0x9d, 0xe5, 0x7d, 0x40, 0xef, 0xe0, 0xe9, 0x07, 0x6c, 0x6f, 0xf6, 0xe9, 0x23,
	0xb5, 0xf1, 0x85, 0x87, 0x5e, 0x9e, 0x5b, 0xae, 0x8d, 0x29, 0x8d, 0xf6, 0x17, 0x83, 0x91,
	0x16, 0x12, 0xcb, 0x6b, 0x6c, 0x13, 0x12, 0xda};

const unsigned char public_key_der[] = {
	0x30, 0x82, 0x02, 0x22, 0x30, 0x0d, 0x06, 0x09, 0x2a, 0x86, 0x48, 0x86, 0xf7, 0x0d, 0x01,
	0x01, 0x01, 0x05, 0x00, 0x03, 0x82, 0x02, 0x0f, 0x00, 0x30, 0x82, 0x02, 0x0a, 0x02, 0x82,
	0x02, 0x01, 0x00, 0xb7, 0xe5, 0xa6, 0x58, 0x69, 0x16, 0xda, 0x73, 0xa1, 0x2c, 0x8f, 0x71,
	0x91, 0x67, 0x41, 0x02, 0xfa, 0x5d, 0x58, 0x95, 0x08, 0x2b, 0xdd, 0xc3, 0xd0, 0xbd, 0x6c,
	0x41, 0xc9, 0x17, 0x97, 0xf1, 0xf4, 0x34, 0xcb, 0x37, 0xdc, 0xc5, 0xb9, 0x57, 0x63, 0x16,
	0xf7, 0xce, 0x6c, 0xf6, 0x89, 0xda, 0xf4, 0xa8, 0x0f, 0x37, 0x8f, 0x1a, 0x66, 0x7c, 0x1e,
	0x93, 0x5e, 0x0e, 0x63, 0xa7, 0x5f, 0x1b, 0x90, 0x48, 0x21, 0xac, 0x02, 0x13, 0xf9, 0x36,
	0x44, 0x53, 0x07, 0x77, 0x45, 0x9c, 0xdc, 0xc1, 0x08, 0x51, 0xb7, 0xa6, 0x73, 0x26, 0x32,
	0x93, 0xb2, 0x9c, 0x7e, 0xba, 0x39, 0x67, 0x59, 0xf1, 0x01, 0xdb, 0xc6, 0xfa, 0x4c, 0x2a,
	0xac, 0x43, 0x44, 0xb7, 0x6b, 0x42, 0xe6, 0xb1, 0x20, 0xf4, 0x5a, 0xc0, 0x6d, 0x22, 0x1f,
	0x64, 0x8d, 0x1d, 0xb5, 0x04, 0x10, 0x57, 0x51, 0x12, 0x8d, 0xcd, 0x5d, 0xd9, 0xb1, 0x06,
	0xd7, 0x47, 0x8b, 0x18, 0x5f, 0x1e, 0x96, 0xd2, 0x0d, 0xa9, 0x8e, 0xf5, 0x5c, 0x80, 0xdb,
	0xc5, 0xaf, 0xe2, 0x2a, 0x23, 0x2e, 0xfd, 0x43, 0x6e, 0x66, 0x0d, 0x2d, 0x45, 0x12, 0xa4,
	0xcb, 0x47, 0x12, 0xc2, 0xe8, 0xba, 0xfb, 0x99, 0xec, 0x05, 0x57, 0x6d, 0xd6, 0xa0, 0x66,
	0x3a, 0x9a, 0x63, 0x6f, 0x58, 0x9f, 0x72, 0xf6, 0x0a, 0x47, 0xb7, 0xea, 0x8e, 0xae, 0xb1,
	0x52, 0x28, 0xfd, 0xe9, 0x16, 0x14, 0x46, 0x8b, 0x1b, 0x2e, 0x85, 0xc6, 0x7e, 0x99, 0x85,
	0x22, 0x16, 0x23, 0x14, 0x49, 0x22, 0x53, 0x1e, 0x7b, 0x04, 0x6c, 0xb9, 0x75, 0xe8, 0xdb,
	0xba, 0x96, 0x8a, 0x63, 0x38, 0xcc, 0x9f, 0x59, 0xeb, 0xcf, 0x27, 0x3b, 0x66, 0x21, 0xfe,
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proj.conf

CONFIG_MAIN_STACK_SIZE=16384
CONFIG_HEAP_MEM_POOL_SIZE=16384

# Enable logging
CONFIG_CONSOLE=y
CONFIG_LOG=y

# Enable nordic security backend and PSA APIs
CONFIG_NRF_SECURITY=y
CONFIG_MBEDTLS_PSA_CRYPTO_C=y

# Mbedtls configuration
CONFIG_MBEDTLS_ENABLE_HEAP=y
CONFIG_MBEDTLS_HEAP_SIZE=16384

CONFIG_PSA_WANT_ALG_RSA_PKCS1V15_SIGN=y
CONFIG_PSA_WANT_KEY_TYPE_RSA_KEY_PAIR=y
CONFIG_PSA_WANT_ALG_SHA_256=y

# This samples source code explicitly uses an RSA key size of 4096
CONFIG_PSA_WANT_RSA_KEY_SIZE_4096=y
CONFIG_PSA_WANT_ALG_RSA_PKCS1V15_CRYPT=y 

My development board is PCA10056.

If anything missed, please let me know.

[Vidar Berg]

I ran your code and got -ENOTSUP ('-134') when the algorithm tried to request random numbers. Fixed this by adding CONFIG_PSA_WANT_GENERATE_RANDOM=y to the project configuration.

 

[JY wu]

It works, thank you very much!

[heroizen]

Hi Vidar,

Im very glad for your help now it works that i was facing the same error on rsa. But can i ask how i can get detailed information about this errors? Its only print (Error: -134) on terminal with rtt. How did you see -ENOTSUP information? And how did you understood this was due to the CONFIG_PSA_WANT_GENERATE_RANDOM=y ?. If you can give a little more insight i will be very happy and learn how to catch fish. Thanks! 

[Vidar Berg]

Hi,

I'm glad to hear that it works. I found the problem in this case by single-stepping through the functions with the debugger to find the line where -ENOTSUP was returned. Once you know where the error is returned, it is usually easy to determine the problem. Unfortunately, I have forgotten where it got returned now.