diff mbox series

crypto: testmgr - populate RSA CRT parameters in RSA test vectors

Message ID 20220630140506.904-1-ignat@cloudflare.com (mailing list archive)
State Superseded
Delegated to: Herbert Xu
Headers show
Series crypto: testmgr - populate RSA CRT parameters in RSA test vectors | expand

Commit Message

Ignat Korchagin June 30, 2022, 2:05 p.m. UTC 
In f145d411a67e ("crypto: rsa - implement Chinese Remainder Theorem for faster
private key operations") we have started to use the additional primes and
coefficients for RSA private key operations. However, these additional
parameters are not present (defined as 0 integers) in the RSA test vectors.

Some parameters were borrowed from OpenSSL, so I was able to find the source.
I could not find the public source for 1 vector though, so had to recover the
parameters by implementing Appendix C from [1].

[1]: https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-56Br1.pdf

Fixes: f145d411a67e ("crypto: rsa - implement Chinese Remainder Theorem for faster private key operations")
Reported-by: Tasmiya Nalatwad <tasmiya@linux.vnet.ibm.com>
Signed-off-by: Ignat Korchagin <ignat@cloudflare.com>
---
 crypto/testmgr.h | 121 +++++++++++++++++++++++++++++++++++++++--------
 1 file changed, 100 insertions(+), 21 deletions(-)

--
2.36.1

Comments

Cabiddu, Giovanni July 2, 2022, 8:37 a.m. UTC | #1 
On Thu, Jun 30, 2022 at 03:05:06PM +0100, Ignat Korchagin wrote:
> In f145d411a67e ("crypto: rsa - implement Chinese Remainder Theorem for faster
> private key operations") we have started to use the additional primes and
> coefficients for RSA private key operations. However, these additional
> parameters are not present (defined as 0 integers) in the RSA test vectors.
> 
> Some parameters were borrowed from OpenSSL, so I was able to find the source.
> I could not find the public source for 1 vector though, so had to recover the
> parameters by implementing Appendix C from [1].
> 
> [1]: https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-56Br1.pdf
> 
> Fixes: f145d411a67e ("crypto: rsa - implement Chinese Remainder Theorem for faster private key operations")
> Reported-by: Tasmiya Nalatwad <tasmiya@linux.vnet.ibm.com>
> Signed-off-by: Ignat Korchagin <ignat@cloudflare.com>
> ---
>  crypto/testmgr.h | 121 +++++++++++++++++++++++++++++++++++++++--------
>  1 file changed, 100 insertions(+), 21 deletions(-)
> 
> diff --git a/crypto/testmgr.h b/crypto/testmgr.h
> index 8e2dce86dd48..7d503b4e1e41 100644
> --- a/crypto/testmgr.h
> +++ b/crypto/testmgr.h
> @@ -185,7 +185,7 @@ static const struct akcipher_testvec rsa_tv_template[] = {
>  	{
>  #ifndef CONFIG_CRYPTO_FIPS
>  	.key =
> -	"\x30\x81\x9A" /* sequence of 154 bytes */
> +	"\x30\x82\x01\x38" /* sequence of 312 bytes */
>  	"\x02\x01\x00" /* version - integer of 1 byte */
>  	"\x02\x41" /* modulus - integer of 65 bytes */
>  	"\x00\xAA\x36\xAB\xCE\x88\xAC\xFD\xFF\x55\x52\x3C\x7F\xC4\x52\x3F"
> @@ -199,23 +199,36 @@ static const struct akcipher_testvec rsa_tv_template[] = {
>  	"\xC2\xCD\x2D\xFF\x43\x40\x98\xCD\x20\xD8\xA1\x38\xD0\x90\xBF\x64"
>  	"\x79\x7C\x3F\xA7\xA2\xCD\xCB\x3C\xD1\xE0\xBD\xBA\x26\x54\xB4\xF9"
>  	"\xDF\x8E\x8A\xE5\x9D\x73\x3D\x9F\x33\xB3\x01\x62\x4A\xFD\x1D\x51"
> -	"\x02\x01\x00" /* prime1 - integer of 1 byte */
> -	"\x02\x01\x00" /* prime2 - integer of 1 byte */
> -	"\x02\x01\x00" /* exponent1 - integer of 1 byte */
> -	"\x02\x01\x00" /* exponent2 - integer of 1 byte */
> -	"\x02\x01\x00", /* coefficient - integer of 1 byte */
> +	"\x02\x21" /* prime1 - integer of 33 bytes */
> +	"\x00\xD8\x40\xB4\x16\x66\xB4\x2E\x92\xEA\x0D\xA3\xB4\x32\x04\xB5"
> +    "\xCF\xCE\x33\x52\x52\x4D\x04\x16\xA5\xA4\x41\xE7\x00\xAF\x46\x12"
> +    "\x0D"
Spaces should be replaced with tabs.
Checkpatch reports 1 error and 27 warnings.

Regards,
Ignat Korchagin July 4, 2022, 10:40 a.m. UTC | #2 
On Sat, Jul 2, 2022 at 9:38 AM Giovanni Cabiddu
<giovanni.cabiddu@intel.com> wrote:
>
> On Thu, Jun 30, 2022 at 03:05:06PM +0100, Ignat Korchagin wrote:
> > In f145d411a67e ("crypto: rsa - implement Chinese Remainder Theorem for faster
> > private key operations") we have started to use the additional primes and
> > coefficients for RSA private key operations. However, these additional
> > parameters are not present (defined as 0 integers) in the RSA test vectors.
> >
> > Some parameters were borrowed from OpenSSL, so I was able to find the source.
> > I could not find the public source for 1 vector though, so had to recover the
> > parameters by implementing Appendix C from [1].
> >
> > [1]: https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-56Br1.pdf
> >
> > Fixes: f145d411a67e ("crypto: rsa - implement Chinese Remainder Theorem for faster private key operations")
> > Reported-by: Tasmiya Nalatwad <tasmiya@linux.vnet.ibm.com>
> > Signed-off-by: Ignat Korchagin <ignat@cloudflare.com>
> > ---
> >  crypto/testmgr.h | 121 +++++++++++++++++++++++++++++++++++++++--------
> >  1 file changed, 100 insertions(+), 21 deletions(-)
> >
> > diff --git a/crypto/testmgr.h b/crypto/testmgr.h
> > index 8e2dce86dd48..7d503b4e1e41 100644
> > --- a/crypto/testmgr.h
> > +++ b/crypto/testmgr.h
> > @@ -185,7 +185,7 @@ static const struct akcipher_testvec rsa_tv_template[] = {
> >       {
> >  #ifndef CONFIG_CRYPTO_FIPS
> >       .key =
> > -     "\x30\x81\x9A" /* sequence of 154 bytes */
> > +     "\x30\x82\x01\x38" /* sequence of 312 bytes */
> >       "\x02\x01\x00" /* version - integer of 1 byte */
> >       "\x02\x41" /* modulus - integer of 65 bytes */
> >       "\x00\xAA\x36\xAB\xCE\x88\xAC\xFD\xFF\x55\x52\x3C\x7F\xC4\x52\x3F"
> > @@ -199,23 +199,36 @@ static const struct akcipher_testvec rsa_tv_template[] = {
> >       "\xC2\xCD\x2D\xFF\x43\x40\x98\xCD\x20\xD8\xA1\x38\xD0\x90\xBF\x64"
> >       "\x79\x7C\x3F\xA7\xA2\xCD\xCB\x3C\xD1\xE0\xBD\xBA\x26\x54\xB4\xF9"
> >       "\xDF\x8E\x8A\xE5\x9D\x73\x3D\x9F\x33\xB3\x01\x62\x4A\xFD\x1D\x51"
> > -     "\x02\x01\x00" /* prime1 - integer of 1 byte */
> > -     "\x02\x01\x00" /* prime2 - integer of 1 byte */
> > -     "\x02\x01\x00" /* exponent1 - integer of 1 byte */
> > -     "\x02\x01\x00" /* exponent2 - integer of 1 byte */
> > -     "\x02\x01\x00", /* coefficient - integer of 1 byte */
> > +     "\x02\x21" /* prime1 - integer of 33 bytes */
> > +     "\x00\xD8\x40\xB4\x16\x66\xB4\x2E\x92\xEA\x0D\xA3\xB4\x32\x04\xB5"
> > +    "\xCF\xCE\x33\x52\x52\x4D\x04\x16\xA5\xA4\x41\xE7\x00\xAF\x46\x12"
> > +    "\x0D"
> Spaces should be replaced with tabs.
> Checkpatch reports 1 error and 27 warnings.
Indeed! Not sure how they got there. Sent a v2.

Ignat
> Regards,
>
> --
> Giovanni
diff mbox series

Patch

diff --git a/crypto/testmgr.h b/crypto/testmgr.h
index 8e2dce86dd48..7d503b4e1e41 100644
--- a/crypto/testmgr.h
+++ b/crypto/testmgr.h
@@ -185,7 +185,7 @@  static const struct akcipher_testvec rsa_tv_template[] = {
 	{
 #ifndef CONFIG_CRYPTO_FIPS
 	.key =
-	"\x30\x81\x9A" /* sequence of 154 bytes */
+	"\x30\x82\x01\x38" /* sequence of 312 bytes */
 	"\x02\x01\x00" /* version - integer of 1 byte */
 	"\x02\x41" /* modulus - integer of 65 bytes */
 	"\x00\xAA\x36\xAB\xCE\x88\xAC\xFD\xFF\x55\x52\x3C\x7F\xC4\x52\x3F"
@@ -199,23 +199,36 @@  static const struct akcipher_testvec rsa_tv_template[] = {
 	"\xC2\xCD\x2D\xFF\x43\x40\x98\xCD\x20\xD8\xA1\x38\xD0\x90\xBF\x64"
 	"\x79\x7C\x3F\xA7\xA2\xCD\xCB\x3C\xD1\xE0\xBD\xBA\x26\x54\xB4\xF9"
 	"\xDF\x8E\x8A\xE5\x9D\x73\x3D\x9F\x33\xB3\x01\x62\x4A\xFD\x1D\x51"
-	"\x02\x01\x00" /* prime1 - integer of 1 byte */
-	"\x02\x01\x00" /* prime2 - integer of 1 byte */
-	"\x02\x01\x00" /* exponent1 - integer of 1 byte */
-	"\x02\x01\x00" /* exponent2 - integer of 1 byte */
-	"\x02\x01\x00", /* coefficient - integer of 1 byte */
+	"\x02\x21" /* prime1 - integer of 33 bytes */
+	"\x00\xD8\x40\xB4\x16\x66\xB4\x2E\x92\xEA\x0D\xA3\xB4\x32\x04\xB5"
+    "\xCF\xCE\x33\x52\x52\x4D\x04\x16\xA5\xA4\x41\xE7\x00\xAF\x46\x12"
+    "\x0D"
+	"\x02\x21" /* prime2 - integer of 33 bytes */
+	"\x00\xC9\x7F\xB1\xF0\x27\xF4\x53\xF6\x34\x12\x33\xEA\xAA\xD1\xD9"
+    "\x35\x3F\x6C\x42\xD0\x88\x66\xB1\xD0\x5A\x0F\x20\x35\x02\x8B\x9D"
+    "\x89"
+	"\x02\x20" /* exponent1 - integer of 32 bytes */
+	"\x59\x0B\x95\x72\xA2\xC2\xA9\xC4\x06\x05\x9D\xC2\xAB\x2F\x1D\xAF"
+    "\xEB\x7E\x8B\x4F\x10\xA7\x54\x9E\x8E\xED\xF5\xB4\xFC\xE0\x9E\x05"
+	"\x02\x21" /* exponent2 - integer of 33 bytes */
+	"\x00\x8E\x3C\x05\x21\xFE\x15\xE0\xEA\x06\xA3\x6F\xF0\xF1\x0C\x99"
+    "\x52\xC3\x5B\x7A\x75\x14\xFD\x32\x38\xB8\x0A\xAD\x52\x98\x62\x8D"
+    "\x51"
+	"\x02\x20" /* coefficient - integer of 32 bytes */
+	"\x36\x3F\xF7\x18\x9D\xA8\xE9\x0B\x1D\x34\x1F\x71\xD0\x9B\x76\xA8"
+    "\xA9\x43\xE1\x1D\x10\xB2\x4D\x24\x9F\x2D\xEA\xFE\xF8\x0C\x18\x26",
 	.m = "\x54\x85\x9b\x34\x2c\x49\xea\x2a",
 	.c =
 	"\x63\x1c\xcd\x7b\xe1\x7e\xe4\xde\xc9\xa8\x89\xa1\x74\xcb\x3c\x63"
 	"\x7d\x24\xec\x83\xc3\x15\xe4\x7f\x73\x05\x34\xd1\xec\x22\xbb\x8a"
 	"\x5e\x32\x39\x6d\xc1\x1d\x7d\x50\x3b\x9f\x7a\xad\xf0\x2e\x25\x53"
 	"\x9f\x6e\xbd\x4c\x55\x84\x0c\x9b\xcf\x1a\x4b\x51\x1e\x9e\x0c\x06",
-	.key_len = 157,
+	.key_len = 316,
 	.m_size = 8,
 	.c_size = 64,
 	}, {
 	.key =
-	"\x30\x82\x01\x1D" /* sequence of 285 bytes */
+	"\x30\x82\x02\x5B" /* sequence of 603 bytes */
 	"\x02\x01\x00" /* version - integer of 1 byte */
 	"\x02\x81\x81" /* modulus - integer of 129 bytes */
 	"\x00\xBB\xF8\x2F\x09\x06\x82\xCE\x9C\x23\x38\xAC\x2B\x9D\xA8\x71"
@@ -238,12 +251,35 @@  static const struct akcipher_testvec rsa_tv_template[] = {
 	"\x93\x99\x26\xED\x4F\x74\xA1\x3E\xDD\xFB\xE1\xA1\xCE\xCC\x48\x94"
 	"\xAF\x94\x28\xC2\xB7\xB8\x88\x3F\xE4\x46\x3A\x4B\xC8\x5B\x1C\xB3"
 	"\xC1"
-	"\x02\x01\x00" /* prime1 - integer of 1 byte */
-	"\x02\x01\x00" /* prime2 - integer of 1 byte */
-	"\x02\x01\x00" /* exponent1 - integer of 1 byte */
-	"\x02\x01\x00" /* exponent2 - integer of 1 byte */
-	"\x02\x01\x00", /* coefficient - integer of 1 byte */
-	.key_len = 289,
+	"\x02\x41" /* prime1 - integer of 65 bytes */
+	"\x00\xEE\xCF\xAE\x81\xB1\xB9\xB3\xC9\x08\x81\x0B\x10\xA1\xB5\x60"
+    "\x01\x99\xEB\x9F\x44\xAE\xF4\xFD\xA4\x93\xB8\x1A\x9E\x3D\x84\xF6"
+    "\x32\x12\x4E\xF0\x23\x6E\x5D\x1E\x3B\x7E\x28\xFA\xE7\xAA\x04\x0A"
+    "\x2D\x5B\x25\x21\x76\x45\x9D\x1F\x39\x75\x41\xBA\x2A\x58\xFB\x65"
+    "\x99"
+	"\x02\x41" /* prime2 - integer of 65 bytes */
+	"\x00\xC9\x7F\xB1\xF0\x27\xF4\x53\xF6\x34\x12\x33\xEA\xAA\xD1\xD9"
+    "\x35\x3F\x6C\x42\xD0\x88\x66\xB1\xD0\x5A\x0F\x20\x35\x02\x8B\x9D"
+    "\x86\x98\x40\xB4\x16\x66\xB4\x2E\x92\xEA\x0D\xA3\xB4\x32\x04\xB5"
+    "\xCF\xCE\x33\x52\x52\x4D\x04\x16\xA5\xA4\x41\xE7\x00\xAF\x46\x15"
+    "\x03"
+	"\x02\x40" /* exponent1 - integer of 64 bytes */
+	"\x54\x49\x4C\xA6\x3E\xBA\x03\x37\xE4\xE2\x40\x23\xFC\xD6\x9A\x5A"
+    "\xEB\x07\xDD\xDC\x01\x83\xA4\xD0\xAC\x9B\x54\xB0\x51\xF2\xB1\x3E"
+    "\xD9\x49\x09\x75\xEA\xB7\x74\x14\xFF\x59\xC1\xF7\x69\x2E\x9A\x2E"
+    "\x20\x2B\x38\xFC\x91\x0A\x47\x41\x74\xAD\xC9\x3C\x1F\x67\xC9\x81"
+	"\x02\x40" /* exponent2 - integer of 64 bytes */
+	"\x47\x1E\x02\x90\xFF\x0A\xF0\x75\x03\x51\xB7\xF8\x78\x86\x4C\xA9"
+    "\x61\xAD\xBD\x3A\x8A\x7E\x99\x1C\x5C\x05\x56\xA9\x4C\x31\x46\xA7"
+    "\xF9\x80\x3F\x8F\x6F\x8A\xE3\x42\xE9\x31\xFD\x8A\xE4\x7A\x22\x0D"
+    "\x1B\x99\xA4\x95\x84\x98\x07\xFE\x39\xF9\x24\x5A\x98\x36\xDA\x3D"
+	"\x02\x41", /* coefficient - integer of 65 bytes */
+	"\x00\xB0\x6C\x4F\xDA\xBB\x63\x01\x19\x8D\x26\x5B\xDB\xAE\x94\x23"
+    "\xB3\x80\xF2\x71\xF7\x34\x53\x88\x50\x93\x07\x7F\xCD\x39\xE2\x11"
+    "\x9F\xC9\x86\x32\x15\x4F\x58\x83\xB1\x67\xA9\x67\xBF\x40\x2B\x4E"
+    "\x9E\x2E\x0F\x96\x56\xE6\x98\xEA\x36\x66\xED\xFB\x25\x79\x80\x39"
+    "\xF7",
+	.key_len = 607,
 	.m = "\x54\x85\x9b\x34\x2c\x49\xea\x2a",
 	.c =
 	"\x74\x1b\x55\xac\x47\xb5\x08\x0a\x6e\x2b\x2d\xf7\x94\xb8\x8a\x95"
@@ -259,7 +295,7 @@  static const struct akcipher_testvec rsa_tv_template[] = {
 	}, {
 #endif
 	.key =
-	"\x30\x82\x02\x20" /* sequence of 544 bytes */
+	"\x30\x82\x04\xA3" /* sequence of 1187 bytes */
 	"\x02\x01\x00" /* version - integer of 1 byte */
 	"\x02\x82\x01\x01\x00" /* modulus - integer of 256 bytes */
 	"\xDB\x10\x1A\xC2\xA3\xF1\xDC\xFF\x13\x6B\xED\x44\xDF\xF0\x02\x6D"
@@ -296,12 +332,55 @@  static const struct akcipher_testvec rsa_tv_template[] = {
 	"\x62\xFF\xE9\x46\xB8\xD8\x44\xDB\xA5\xCC\x31\x54\x34\xCE\x3E\x82"
 	"\xD6\xBF\x7A\x0B\x64\x21\x6D\x88\x7E\x5B\x45\x12\x1E\x63\x8D\x49"
 	"\xA7\x1D\xD9\x1E\x06\xCD\xE8\xBA\x2C\x8C\x69\x32\xEA\xBE\x60\x71"
-	"\x02\x01\x00" /* prime1 - integer of 1 byte */
-	"\x02\x01\x00" /* prime2 - integer of 1 byte */
-	"\x02\x01\x00" /* exponent1 - integer of 1 byte */
-	"\x02\x01\x00" /* exponent2 - integer of 1 byte */
-	"\x02\x01\x00", /* coefficient - integer of 1 byte */
-	.key_len = 548,
+	"\x02\x81\x81" /* prime1 - integer of 129 bytes */
+	"\x00\xFA\xAC\xE1\x37\x5E\x32\x11\x34\xC6\x72\x58\x2D\x91\x06\x3E"
+	"\x77\xE7\x11\x21\xCD\x4A\xF8\xA4\x3F\x0F\xEF\x31\xE3\xF3\x55\xA0"
+	"\xB9\xAC\xB6\xCB\xBB\x41\xD0\x32\x81\x9A\x8F\x7A\x99\x30\x77\x6C"
+	"\x68\x27\xE2\x96\xB5\x72\xC9\xC3\xD4\x42\xAA\xAA\xCA\x95\x8F\xFF"
+	"\xC9\x9B\x52\x34\x30\x1D\xCF\xFE\xCF\x3C\x56\x68\x6E\xEF\xE7\x6C"
+	"\xD7\xFB\x99\xF5\x4A\xA5\x21\x1F\x2B\xEA\x93\xE8\x98\x26\xC4\x6E"
+	"\x42\x21\x5E\xA0\xA1\x2A\x58\x35\xBB\x10\xE7\xBA\x27\x0A\x3B\xB3"
+	"\xAF\xE2\x75\x36\x04\xAC\x56\xA0\xAB\x52\xDE\xCE\xDD\x2C\x28\x77"
+	"\x03"
+	"\x02\x81\x81" /* prime2 - integer of 129 bytes */
+	"\x00\xDF\xB7\x52\xB6\xD7\xC0\xE2\x96\xE7\xC9\xFE\x5D\x71\x5A\xC4"
+	"\x40\x96\x2F\xE5\x87\xEA\xF3\xA5\x77\x11\x67\x3C\x8D\x56\x08\xA7"
+	"\xB5\x67\xFA\x37\xA8\xB8\xCF\x61\xE8\x63\xD8\x38\x06\x21\x2B\x92"
+	"\x09\xA6\x39\x3A\xEA\xA8\xB4\x45\x4B\x36\x10\x4C\xE4\x00\x66\x71"
+	"\x65\xF8\x0B\x94\x59\x4F\x8C\xFD\xD5\x34\xA2\xE7\x62\x84\x0A\xA7"
+	"\xBB\xDB\xD9\x8A\xCD\x05\xE1\xCC\x57\x7B\xF1\xF1\x1F\x11\x9D\xBA"
+	"\x3E\x45\x18\x99\x1B\x41\x64\x43\xEE\x97\x5D\x77\x13\x5B\x74\x69"
+	"\x73\x87\x95\x05\x07\xBE\x45\x07\x17\x7E\x4A\x69\x22\xF3\xDB\x05"
+	"\x39"
+	"\x02\x81\x80" /* exponent1 - integer of 128 bytes */
+	"\x5E\xD8\xDC\xDA\x53\x44\xC4\x67\xE0\x92\x51\x34\xE4\x83\xA5\x4D"
+	"\x3E\xDB\xA7\x9B\x82\xBB\x73\x81\xFC\xE8\x77\x4B\x15\xBE\x17\x73"
+	"\x49\x9B\x5C\x98\xBC\xBD\x26\xEF\x0C\xE9\x2E\xED\x19\x7E\x86\x41"
+	"\x1E\x9E\x48\x81\xDD\x2D\xE4\x6F\xC2\xCD\xCA\x93\x9E\x65\x7E\xD5"
+	"\xEC\x73\xFD\x15\x1B\xA2\xA0\x7A\x0F\x0D\x6E\xB4\x53\x07\x90\x92"
+	"\x64\x3B\x8B\xA9\x33\xB3\xC5\x94\x9B\x4C\x5D\x9C\x7C\x46\xA4\xA5"
+	"\x56\xF4\xF3\xF8\x27\x0A\x7B\x42\x0D\x92\x70\x47\xE7\x42\x51\xA9"
+	"\xC2\x18\xB1\x58\xB1\x50\x91\xB8\x61\x41\xB6\xA9\xCE\xD4\x7C\xBB"
+	"\x02\x81\x80" /* exponent2 - integer of 128 bytes */
+	"\x54\x09\x1F\x0F\x03\xD8\xB6\xC5\x0C\xE8\xB9\x9E\x0C\x38\x96\x43"
+	"\xD4\xA6\xC5\x47\xDB\x20\x0E\xE5\xBD\x29\xD4\x7B\x1A\xF8\x41\x57"
+	"\x49\x69\x9A\x82\xCC\x79\x4A\x43\xEB\x4D\x8B\x2D\xF2\x43\xD5\xA5"
+	"\xBE\x44\xFD\x36\xAC\x8C\x9B\x02\xF7\x9A\x03\xE8\x19\xA6\x61\xAE"
+	"\x76\x10\x93\x77\x41\x04\xAB\x4C\xED\x6A\xCC\x14\x1B\x99\x8D\x0C"
+	"\x6A\x37\x3B\x86\x6C\x51\x37\x5B\x1D\x79\xF2\xA3\x43\x10\xC6\xA7"
+	"\x21\x79\x6D\xF9\xE9\x04\x6A\xE8\x32\xFF\xAE\xFD\x1C\x7B\x8C\x29"
+	"\x13\xA3\x0C\xB2\xAD\xEC\x6C\x0F\x8D\x27\x12\x7B\x48\xB2\xDB\x31"
+	"\x02\x81\x81", /* coefficient - integer of 129 bytes */
+	"\x00\x8D\x1B\x05\xCA\x24\x1F\x0C\x53\x19\x52\x74\x63\x21\xFA\x78"
+	"\x46\x79\xAF\x5C\xDE\x30\xA4\x6C\x20\x38\xE6\x97\x39\xB8\x7A\x70"
+	"\x0D\x8B\x6C\x6D\x13\x74\xD5\x1C\xDE\xA9\xF4\x60\x37\xFE\x68\x77"
+	"\x5E\x0B\x4E\x5E\x03\x31\x30\xDF\xD6\xAE\x85\xD0\x81\xBB\x61\xC7"
+	"\xB1\x04\x5A\xC4\x6D\x56\x1C\xD9\x64\xE7\x85\x7F\x88\x91\xC9\x60"
+	"\x28\x05\xE2\xC6\x24\x8F\xDD\x61\x64\xD8\x09\xDE\x7E\xD3\x4A\x61"
+	"\x1A\xD3\x73\x58\x4B\xD8\xA0\x54\x25\x48\x83\x6F\x82\x6C\xAF\x36"
+	"\x51\x2A\x5D\x14\x2F\x41\x25\x00\xDD\xF8\xF3\x95\xFE\x31\x25\x50"
+	"\x12",
+	.key_len = 1191,
 	.m = "\x54\x85\x9b\x34\x2c\x49\xea\x2a",
 	.c =
 	"\xb2\x97\x76\xb4\xae\x3e\x38\x3c\x7e\x64\x1f\xcc\xa2\x7f\xf6\xbe"