Paul Bouché wrote:
I would like to know what the bit length of the public and private keys
> for the test executed with openssl speed rsa
The keys are 512bit, 1024bit, 2048bit, 4096bit as stated in the output from the
program.
The actual keys are in the header file testrsa.h in the apps directory.
To write them out nicely you can compile the following in the 'apps' directory
with gcc -o x x.c and run and then use
openssl rsa -inform d -in rsa0.der -text -noout
(repeat with rsa1.der, rsa2.der, rsa3.der)
Alternatively the keys are all listed below.
Tim.
---8<---
#include <stdio.h>
#include "testrsa.h"
#define RSA_NUM 4
int main(int argc,char *argv[])
{
static unsigned char *rsa_data[RSA_NUM]=
{test512,test1024,test2048,test4096};
static int rsa_data_length[RSA_NUM]={
sizeof(test512),sizeof(test1024),
sizeof(test2048),sizeof(test4096)};
int i,l;
FILE *fp=NULL;
char buf[BUFSIZ];
for(i=0;i<RSA_NUM;i++) {
snprintf(buf,sizeof(buf),"rsa%d.der",i);
fp=fopen(buf,"wb");
if (fp==NULL) {
fprintf(stderr,"create %s failed\n",buf);
continue;
}
l=rsa_data_length[i];
if (fwrite(rsa_data[i],l,1,fp)!=1) {
fprintf(stderr,"write %s failed\n",buf);
}
fclose(fp);
}
}
[EMAIL PROTECTED] ~/work/openssl/apps> openssl rsa -text -noout -inform d -in
rsa0.der
Private-Key: (512 bit)
modulus:
00:d6:33:b9:c8:fb:4f:3c:7d:c0:01:86:d0:e7:a0:
55:f2:95:93:cc:4f:b7:5b:67:5b:94:68:c9:34:15:
de:a5:2e:1c:33:c2:6e:fc:34:5e:71:13:b7:d6:ee:
d8:a5:65:05:72:87:a8:b0:77:fe:57:f5:fc:5f:55:
83:87:dd:57:49
publicExponent: 65537 (0x10001)
privateExponent:
00:a7:f7:91:c5:0f:84:57:dc:07:f7:6a:7f:60:52:
b3:72:f1:66:1f:7d:97:3b:9e:b6:0a:8f:8c:cf:42:
23:00:04:d4:28:0e:1c:90:c4:11:25:25:a5:93:a5:
2f:70:02:df:81:9c:49:03:a0:f8:6d:54:2e:26:de:
aa:85:59:a8:31
prime1:
00:eb:47:d7:3b:f6:c3:dd:5a:46:c5:b9:2b:9a:a0:
09:8f:a6:fb:f3:78:7a:33:70:9d:0f:42:6b:13:68:
24:d3:15
prime2:
00:e9:10:b0:b3:0d:e2:82:68:77:8a:6e:7c:da:bc:
3e:53:83:fb:d6:22:e7:b5:ae:6e:80:da:00:55:97:
c1:d0:65
exponent1:
4c:f8:73:b1:6a:49:29:61:1f:46:10:0d:f3:c7:e7:
58:d7:88:15:5e:94:9b:bf:7b:a2:42:58:45:41:0c:
cb:01
exponent2:
12:11:ba:31:57:9d:3d:11:0e:5b:8c:2f:5f:e2:02:
4f:05:47:8c:15:8e:b3:56:3f:b8:fb:ad:d4:f4:fc:
10:c5
coefficient:
18:a1:29:99:5b:d9:c8:d4:fc:49:7a:2a:21:2c:49:
e4:4f:eb:ef:51:f1:ab:6d:fb:4b:14:e9:4b:52:b5:
82:2c
[EMAIL PROTECTED] ~/work/openssl/apps> openssl rsa -text -noout -inform d -in
rsa1.der
Private-Key: (1024 bit)
modulus:
00:dc:98:43:e8:3d:43:5b:e4:05:cd:d0:a9:3e:cb:
83:75:f6:b5:a5:9f:6b:e9:34:41:29:18:fa:6a:55:
4d:70:fc:ec:ae:87:38:0a:20:a9:c0:45:77:6e:57:
60:57:f4:ed:96:22:cb:8f:e1:33:3a:17:1f:ed:37:
a5:6f:eb:a6:bc:12:80:1d:53:bd:70:eb:21:76:3e:
c9:2f:1a:45:24:82:ff:cd:59:32:06:2e:12:3b:23:
78:ed:12:3d:e0:8d:f9:67:4f:37:4e:47:02:4c:2d:
c0:4f:1f:b3:94:e1:41:2e:2d:90:10:fc:82:91:8b:
0f:22:d4:f2:fc:2c:ab:53:55
publicExponent: 65537 (0x10001)
privateExponent:
2b:cc:3f:8f:58:ba:8b:00:16:f6:ea:3a:f0:30:d0:
05:17:da:b0:eb:9a:2d:4f:26:b0:d6:38:c1:eb:f5:
d8:3d:1f:70:f7:7f:f4:e2:cf:51:51:79:88:fa:e8:
32:0e:7b:2d:97:f2:fa:ba:27:c5:9c:d9:c5:eb:8a:
79:52:3c:64:34:7d:c2:cf:28:c7:4e:d5:43:0b:d1:
a6:ca:6d:03:2d:72:23:bc:6d:05:fa:16:09:2f:2e:
5c:b6:ee:74:dd:d2:48:8e:36:0c:06:3d:4d:e5:10:
82:eb:6a:f3:4b:9f:d6:ed:11:b1:6e:ec:f4:fe:8e:
75:94:20:2f:cb:ac:46:f1
prime1:
00:f9:8c:a3:85:b1:dd:29:af:65:c1:33:f3:95:c5:
52:68:0b:d4:f1:e5:0e:02:9f:4f:fa:77:dc:46:9e:
c7:a6:e4:16:29:da:b0:07:cf:5b:a9:12:8a:dd:63:
0a:de:2e:8c:66:8b:8c:dc:19:a3:7e:f4:3b:d0:1a:
8c:a4:c2:e1:d3
prime2:
00:e2:4c:05:f2:04:86:4e:61:43:db:b0:b9:96:86:
52:2c:ca:8d:7b:ab:0b:13:0d:7e:38:5b:e2:2e:7b:
0e:e7:19:99:38:e7:f2:21:bd:85:85:e3:fd:28:77:
20:31:71:2c:d0:ff:fb:2e:af:85:b4:86:ca:f3:bb:
ca:aa:0f:95:37
exponent1:
0e:41:9a:95:e8:b3:59:ce:4b:61:de:35:ec:38:79:
9c:b8:10:52:41:63:ab:82:ae:6f:00:a9:f4:de:dd:
49:0b:7e:b8:a5:65:a9:0c:8f:8f:f9:1f:35:c6:92:
b8:5e:b0:66:ab:52:40:c0:b6:36:6a:7d:80:46:04:
02:e5:9f:41
exponent2:
00:c0:ad:cc:4e:21:ee:1d:24:91:fb:a7:80:8d:9a:
b6:b3:2e:8f:c2:e1:82:df:69:18:b4:71:ff:a6:65:
de:ed:84:8d:42:b7:b3:21:69:56:1c:07:60:51:29:
04:ff:34:06:dd:b9:67:2c:7c:04:93:0e:46:15:bb:
2a:b7:1b:e7:87
coefficient:
78:da:5d:07:51:0c:16:7a:9f:29:20:84:0d:42:fa:
d7:00:d8:77:7e:b0:b0:6b:d6:5b:53:b8:9b:7a:cd:
c7:2b:b8:6a:63:a9:fb:6f:a4:72:bf:4c:5d:00:14:
ba:fa:59:88:ed:e4:e0:8c:a2:ec:14:7e:2d:e2:f0:
46:49:95:45
[EMAIL PROTECTED] ~/work/openssl/apps> openssl rsa -text -noout -inform d -in
rsa2.der
Private-Key: (2048 bit)
modulus:
00:c0:c0:ce:3e:3c:53:67:3f:4f:c5:2f:a4:c2:5a:
2f:58:fd:27:52:6a:e8:cf:4a:73:47:8d:25:0f:5f:
03:26:78:ef:f0:22:12:d3:de:47:b2:1c:0b:38:63:
1a:6c:85:7a:80:c6:8f:a0:41:af:62:c4:67:32:88:
f8:a6:9c:f5:23:1d:e4:ac:3f:29:f9:ec:e1:8b:26:
03:2c:b2:ab:f3:7d:b5:ca:49:c0:8f:1c:df:33:3a:
60:da:3c:b0:16:f8:a9:12:8f:64:ac:23:0c:69:64:
97:5d:99:d4:09:83:9b:61:d3:ac:f0:de:dd:5e:9f:
44:94:db:3a:4d:97:e8:52:29:f7:db:94:07:45:90:
78:1e:31:0b:80:f7:57:ad:1c:79:c5:cb:32:b0:ce:
cd:74:b3:e2:94:c5:78:2f:34:1a:45:f7:8c:52:a5:
bc:8d:ec:d1:2f:31:3b:f0:49:59:5e:88:9d:15:92:
35:32:c1:e7:61:ec:50:48:7c:ba:05:f9:f8:f8:a7:
8c:83:e8:66:5b:eb:fe:d8:4f:dd:6d:36:c0:b2:90:
0f:b8:52:f9:04:9b:40:2c:27:d6:36:8e:c2:1b:44:
f3:92:d5:15:9e:9a:bc:f3:7d:03:d7:02:14:20:e9:
10:92:fd:f9:fc:8f:e5:18:e1:95:cc:9e:60:a6:fa:
38:4d
publicExponent: 65537 (0x10001)
privateExponent:
00:c3:c3:0d:b4:27:90:8d:4b:bf:b8:84:aa:d0:b8:
c7:5d:99:be:55:f6:3e:7c:49:20:cb:8a:8e:19:0e:
66:24:ac:af:03:33:97:eb:95:d5:3b:0f:40:56:04:
50:d1:e6:be:84:0b:25:d3:9c:e2:83:6c:f5:62:5d:
ba:2b:7d:3d:7a:6c:e1:d2:0e:54:93:80:01:91:51:
09:e8:5b:8e:47:bd:64:e4:0e:03:83:55:cf:5a:37:
f0:25:b5:7d:21:d7:69:df:6f:c2:cf:10:c9:8a:40:
9f:7a:70:c0:e8:e8:c0:e6:9a:15:0a:8d:4e:46:cb:
7a:db:b3:cb:83:02:c4:f0:ab:eb:02:01:0e:23:fc:
1d:c4:bd:d4:aa:5d:31:46:99:ce:9e:f8:04:75:10:
67:c4:53:47:44:fa:c2:25:73:7e:d0:8e:59:d1:b2:
5a:f4:c7:18:92:2f:39:ab:cd:a3:b5:c2:b9:c7:b9:
1b:9f:48:fa:13:c6:98:4d:ca:84:9c:06:ca:e7:89:
01:04:c4:6c:fd:29:59:35:e7:f3:dd:ce:64:59:bf:
21:13:a9:9f:0e:c5:ff:bd:33:00:ec:ac:6b:11:ef:
51:5e:ad:07:15:de:b8:5f:c6:b9:a3:22:65:46:83:
14:df:d0:f1:44:8a:e1:9c:23:33:b4:97:33:e6:6b:
81
prime1:
00:ec:12:a7:59:74:6a:de:3e:ad:d8:36:80:50:a2:
d5:21:81:07:f1:d0:91:f2:6c:12:2f:9d:1a:26:f8:
30:65:df:e8:c0:9b:6a:30:98:82:87:ec:a2:56:87:
62:6f:e7:9f:f6:56:e6:71:8f:49:86:93:5a:4d:34:
58:fe:d9:04:13:af:79:b7:ad:11:d1:30:9a:14:06:
a0:fa:b7:55:dc:6c:5a:4c:2c:59:56:f6:e8:9d:af:
0a:78:99:06:06:9e:e7:9c:51:55:43:fc:3b:6c:0b:
bf:2d:41:a7:af:b7:e0:e8:28:18:b4:13:d1:e6:97:
d0:9f:6a:80:ca:dd:1a:7e:15
prime2:
00:d1:06:0c:1f:e3:d0:ab:d6:ca:7c:bc:7d:13:35:
ce:27:cd:d8:49:51:63:64:0f:ca:06:12:fc:07:3e:
af:61:6d:e2:53:39:27:ae:c3:11:9e:94:01:4f:e3:
f3:67:f9:77:f9:e7:95:3a:6f:e2:20:73:3e:a4:7a:
28:d4:61:97:f6:17:a0:23:10:2b:ce:84:57:7e:25:
1f:f4:a8:54:d2:65:94:cc:95:0a:ab:30:c1:59:1f:
61:8e:b9:6b:d7:4e:b9:83:43:79:85:11:bc:0f:ae:
25:20:05:bc:d2:48:a1:68:09:84:f6:12:9a:66:b9:
2b:bb:76:03:17:46:4e:97:59
exponent1:
09:4c:fa:d6:e5:65:48:78:43:b5:1f:00:93:2c:b7:
24:e8:c6:7d:5a:70:45:92:c8:6c:a3:cd:e1:f7:29:
40:fa:3f:5b:47:44:39:c1:e8:72:9e:7a:0e:da:aa:
a0:2a:09:fd:54:93:23:aa:37:85:5b:cc:d4:f9:d8:
ff:c1:61:0d:bd:7e:18:24:73:6d:40:72:f1:93:09:
48:97:6c:84:90:a8:46:14:01:39:11:e5:3c:41:27:
32:75:24:ed:a1:d9:12:29:8a:28:71:89:8d:ca:30:
b0:01:c4:2f:82:19:14:4c:70:1c:b8:23:2e:e8:90:
49:97:92:97:6b:7a:9d:b9
exponent2:
0f:0e:a1:76:f6:a1:44:8f:af:7c:76:d3:87:bb:bb:
83:10:88:01:18:14:d1:d3:75:59:24:aa:f5:16:a5:
e9:9d:d1:cc:ee:f4:15:d9:c5:7e:27:e9:44:49:06:
72:b9:fc:d3:8a:c4:2c:36:7d:12:9b:5a:aa:dc:85:
ee:6e:ad:54:b3:f4:fc:31:a1:06:3a:70:57:0c:f3:
95:5b:3e:e8:fd:1a:4f:f6:78:93:46:6a:d7:31:b4:
84:64:85:09:38:89:92:94:1c:bf:e2:3c:2a:e0:ff:
99:a3:f0:2b:31:c2:36:cd:60:bf:9d:2d:74:32:e8:
9c:93:6e:bb:91:7b:fd:d9
coefficient:
00:a2:71:25:38:eb:2a:e9:37:cd:fe:44:ce:90:3f:
52:87:84:52:1b:ae:8d:22:94:ce:38:e6:04:88:76:
85:9a:d3:14:09:e5:69:9a:ff:58:92:02:6a:7d:7c:
1e:2c:fd:a8:ca:32:14:4f:0d:84:0d:37:43:bf:e4:
5d:12:c8:24:91:27:8d:46:d9:54:53:e7:62:71:a8:
2b:71:41:8d:75:f8:3a:a0:61:29:46:a6:e5:82:fa:
3a:d9:08:fa:fc:63:fd:6b:30:bc:f4:4e:9e:8c:25:
0c:b6:55:e7:3c:d4:4e:0b:fd:8b:c3:0e:1d:9c:44:
57:8f:1f:86:f7:d5:1b:e4:95
[EMAIL PROTECTED] ~/work/openssl/apps> openssl rsa -text -noout -inform d -in
rsa3.der
Private-Key: (4096 bit)
modulus:
00:c0:71:ac:1a:13:88:82:43:3b:51:57:71:8d:b6:
2b:82:65:21:53:5f:28:29:4f:8d:7c:8a:b9:44:b3:
28:41:4f:d3:fa:6a:f8:b9:28:50:39:67:53:2c:3c:
d7:cb:96:41:40:32:bb:eb:70:ae:1f:b0:65:f7:3a:
d9:22:fd:10:ae:bd:02:e2:dd:f3:c2:79:3c:c6:fc:
75:bb:af:4e:3a:36:c2:4f:ea:25:df:13:16:4b:20:
fe:4b:69:16:c4:7f:1a:43:a6:17:1b:b9:0a:f3:09:
86:28:89:cf:2c:d0:d4:81:af:c6:6d:e6:21:8d:ee:
ef:ea:dc:b7:c6:3b:63:9f:0e:ad:89:78:23:18:bf:
70:7e:84:e0:37:ec:db:8e:9c:3e:6a:19:cc:99:72:
e6:b5:7d:6d:fa:e5:d3:e4:90:b5:b2:b2:12:70:4e:
ca:f8:10:f8:a3:14:c2:48:19:eb:60:99:bb:2a:1f:
b1:7a:b1:3d:24:fb:a0:29:da:bd:1b:d7:a4:bf:ef:
60:2d:22:ca:65:98:f1:c4:e1:c9:02:6b:16:28:2f:
a1:aa:79:00:da:dc:7c:43:f7:42:3c:a0:ef:68:f7:
df:b9:69:fb:8e:01:ed:01:42:b5:4e:57:a6:26:b8:
d0:7b:56:6d:03:c6:40:8c:8c:2a:55:d7:9c:35:00:
94:93:ec:03:eb:22:ef:77:bb:79:13:3f:15:a1:8f:
ca:df:fd:d3:b8:e1:d4:cc:09:3f:3c:2c:db:d1:49:
7f:38:07:83:6d:eb:08:66:e9:06:44:12:ac:95:22:
90:23:67:d4:08:cc:f4:b7:dc:cc:87:d4:ac:69:35:
4c:b5:39:36:cd:a4:d2:95:ca:0d:c5:da:c2:c5:22:
32:28:08:e3:d2:8b:38:30:dc:8c:75:4f:6a:ec:7a:
ac:16:3e:a8:d4:6a:45:e1:a8:4f:2e:80:34:aa:54:
1b:02:95:7d:8a:6d:cc:79:ca:f2:a4:2e:8d:fb:fe:
15:51:10:0e:4d:88:b1:c7:f4:79:db:f0:b4:56:44:
37:ca:5a:c1:8c:48:ac:ae:48:80:83:01:3f:de:d9:
d3:2c:51:46:b1:41:b6:c6:91:72:f9:83:55:1b:8c:
ba:f3:73:e5:2c:74:50:3a:be:c5:2f:a7:b2:6d:8c:
9e:13:77:a3:13:cd:6d:8c:45:e1:fc:0b:b7:69:e9:
27:bc:65:c3:fa:9b:d0:ef:fe:e8:1f:b3:5e:34:f4:
8c:ea:fc:d3:81:bf:3d:30:b2:b4:01:e8:43:0f:ba:
02:23:42:76:82:31:73:91:ed:07:46:61:0d:39:83:
40:ce:7a:d4:db:80:2c:1f:0d:d1:34:d4:92:e3:d4:
f1:c2:01
publicExponent: 65537 (0x10001)
privateExponent:
00:97:6c:da:6e:ea:4f:cf:af:f7:4c:d9:f1:90:00:
77:db:f2:97:76:72:b9:b7:47:d1:9c:dd:cb:4a:33:
6e:c9:75:76:e6:e4:a5:31:8c:77:13:b4:29:cd:f5:
52:17:ef:f3:08:00:e3:bd:2e:bc:d4:52:88:e9:30:
75:0b:02:f5:cd:89:0c:6c:57:19:27:3d:1e:85:b4:
c1:2f:1d:92:00:5c:76:29:4b:a4:e1:12:b3:c8:09:
fe:0e:78:72:61:cb:61:6f:39:91:95:4e:d5:3e:c7:
8f:b8:f6:36:fe:9c:93:9a:38:25:7a:f4:4a:12:d4:
a0:13:bd:f9:1d:12:3e:21:39:fb:72:e0:05:3d:c3:
e5:50:a8:5d:85:a3:ea:5f:1c:b2:3f:ea:6d:03:91:
55:d8:19:0a:21:12:16:d9:12:c4:e6:07:18:5b:26:
a4:ae:ed:2b:b7:a6:ed:f8:ad:ec:77:e6:7f:4f:76:
00:c0:fa:15:92:b4:2c:22:c2:eb:6a:ad:14:05:b2:
e5:8a:9e:85:83:cc:04:f1:56:78:44:5e:de:e0:60:
1a:65:79:31:23:05:bb:01:ff:dd:2e:b7:b3:aa:74:
e0:a5:94:af:4b:de:58:0f:55:de:33:f6:e3:d6:34:
36:57:d6:79:91:2e:be:3b:d9:4e:b6:9d:21:5c:d3:
48:14:7f:4a:c4:60:a9:29:f8:53:7f:88:11:2d:b5:
c5:2d:6f:ee:85:0b:f7:8d:9a:be:b0:42:f2:2e:71:
af:19:31:6d:ec:cd:6f:2b:23:df:b4:40:af:2c:0a:
c3:1b:7d:7d:03:1d:4b:f3:b5:e0:85:d8:df:91:6b:
0a:69:f7:f2:69:66:5b:f1:cf:46:7d:e9:70:fa:6d:
7e:75:4e:a9:77:e6:8c:02:f7:14:4d:a5:41:8f:3f:
c1:62:1e:71:5e:38:b4:d6:e6:e1:4b:c2:2c:30:83:
81:6f:49:2e:96:e6:c9:9a:f7:5d:09:a0:55:02:a5:
3a:25:23:d0:92:c3:a3:e3:0e:12:2f:4d:ef:f3:55:
5a:be:e6:19:86:31:ab:75:9a:d3:f0:2c:c5:41:92:
d9:1f:5f:11:8c:75:1c:63:d0:02:80:2c:68:cb:93:
fb:51:73:49:b4:60:da:e2:26:af:a9:46:12:b8:ec:
50:dd:12:06:5f:ce:59:e6:f6:1c:e0:54:10:ad:f6:
cd:98:cc:0f:fb:cb:41:14:9d:ed:e4:b4:74:5f:09:
60:c7:12:f6:7b:3c:8f:a7:20:bc:e4:b1:ef:eb:a4:
93:c5:06:ca:9a:27:9d:87:f3:de:ca:e5:e7:f6:1c:
01:65:5b:fb:19:79:6e:08:26:c5:c8:28:0e:b6:3b:
07:08:c1
prime1:
00:e8:1c:73:a6:b8:e0:0e:6d:8d:1b:b9:53:ed:58:
94:e6:1d:60:14:5c:76:43:c4:58:19:c4:24:e8:bc:
1b:3b:0b:13:24:45:54:0e:cc:37:f0:e0:63:7d:c3:
f7:fb:81:74:81:c4:0f:1a:21:48:af:ce:c1:c4:94:
18:06:44:8d:d3:d2:22:2d:2d:3e:5a:31:dc:95:8e:
f4:41:fc:58:c9:40:92:17:5f:e3:da:ac:9e:3f:1c:
2a:6b:58:5f:48:78:20:b1:af:24:9b:3c:20:8b:93:
25:9e:e6:6b:bc:13:42:14:6c:36:31:ff:7a:d1:c1:
1a:26:14:7f:a9:76:a7:0c:f8:cc:ed:07:6a:d2:df:
62:ee:0a:7c:84:cb:49:90:b2:03:0d:a2:82:06:77:
f1:cd:67:f2:47:21:02:3f:43:21:f0:46:30:62:51:
72:b1:e7:48:c6:67:12:cd:9e:d6:15:e5:21:ed:fa:
8f:30:a6:41:fe:b6:fa:8f:34:14:19:e8:11:f7:a5:
77:3e:b7:f9:39:07:8c:67:2a:ab:7b:08:f8:b0:06:
a8:ea:2f:8f:fa:cc:cc:40:ce:f3:70:4f:3f:7f:e2:
0c:ea:76:4a:35:4e:47:ad:2b:a7:97:5d:74:43:97:
90:d2:fb:d9:f9:96:01:33:05:ed:7b:03:05:ad:f8:
49:03
prime2:
00:d4:40:17:66:10:92:95:c8:ec:62:a9:7a:cb:93:
8e:e6:53:d4:80:48:27:4b:41:ce:61:df:bf:94:a4:
3d:71:03:0b:ed:25:71:98:a4:d6:d5:4a:57:f5:6c:
1b:da:21:7d:35:45:b3:f3:6a:d9:d3:43:e8:5c:54:
1c:83:1b:b4:5f:f2:97:24:2e:dc:40:de:92:23:59:
8e:bc:d2:a1:f2:e0:4c:dd:0b:d1:e7:ae:65:bc:b5:
f5:5b:98:e9:d7:c2:b7:0e:55:71:0e:3c:0a:24:6b:
a6:e6:14:61:11:fd:33:42:99:2b:84:77:74:92:91:
f5:79:79:cf:ad:8e:04:ef:80:1e:57:f4:14:f5:35:
09:74:b2:13:71:58:6b:ea:32:5d:f3:d3:76:48:39:
10:23:84:9d:be:92:77:4a:ed:70:3e:1a:a2:6c:b3:
81:00:c3:c9:e4:52:c8:24:88:0c:41:ad:87:5a:ea:
a3:7a:85:1c:5e:31:7f:c3:35:c6:fa:10:c8:75:10:
c4:96:99:e7:fe:01:b4:74:db:b4:11:c3:c8:8c:f6:
f7:3b:66:50:fc:db:eb:ca:47:85:89:e1:65:d9:62:
34:3c:70:d8:2e:b4:2f:65:3c:4a:a6:2a:e7:c7:d8:
41:8f:8a:43:bf:42:f2:4d:bc:fc:9e:27:95:fb:75:
ff:ab
exponent1:
41:2f:44:57:6d:12:17:5b:32:c6:b7:6c:57:7a:8a:
0e:79:ef:72:a8:68:da:2d:38:e4:bb:8d:f6:02:65:
cf:56:13:e1:1a:cb:39:80:a6:b1:32:03:1e:dd:bb:
35:d9:ac:43:89:31:08:90:92:5e:35:3d:7b:9c:6f:
86:cb:17:dd:85:e4:ed:35:08:8e:c1:f4:05:d8:68:
c6:63:3c:f7:ff:f7:47:33:39:c5:3e:b7:0e:58:35:
9d:81:ea:f8:6a:2c:1c:5a:68:78:64:11:6b:c1:3e:
4e:7a:bd:84:cb:0f:c2:b6:85:1d:d3:76:c5:93:6a:
69:89:56:34:dc:4a:9b:bc:ff:a8:0d:6e:35:9c:60:
a7:23:30:c7:06:64:39:8b:94:89:ee:ba:7f:60:8d:
fa:b6:97:76:dc:51:4a:3c:eb:3a:14:2c:20:60:69:
4a:86:fe:8c:21:84:49:54:b3:20:e1:01:7f:58:df:
7f:b5:21:51:8c:47:9f:91:eb:97:3e:f2:54:cf:16:
46:f9:d9:b6:e7:64:c9:d0:54:ea:2f:a1:cf:a5:7f:
28:8d:84:ec:d5:39:03:76:5b:2d:8e:43:f2:01:24:
c9:6f:c0:f5:69:6f:7d:b5:85:d2:5f:7f:78:40:07:
7f:09:15:b5:1f:28:65:10:e4:19:a8:c6:9e:8d:dc:
cb
exponent2:
13:01:ee:56:80:93:70:00:7f:52:d2:94:a1:98:84:
4a:92:25:4c:9b:a9:91:2e:c2:79:b7:5c:e3:c5:d5:
8e:c2:54:16:17:ad:55:9b:25:76:12:63:50:22:2f:
58:58:79:6b:04:e3:f9:9f:8f:04:41:67:94:a5:1f:
ac:8a:15:9c:26:10:6c:f8:19:57:61:d7:3a:7d:31:
b0:2d:38:bd:94:62:ad:c4:fa:36:42:42:f0:24:67:
65:9d:8b:0b:7c:6f:82:44:1a:8c:c8:c9:ab:bb:4c:
45:fc:7b:38:ee:30:e1:fc:ef:8d:bc:58:df:2b:5d:
0d:54:e0:49:4d:97:99:8f:22:a8:83:be:40:bb:50:
2e:78:28:0f:95:78:8c:8f:98:24:56:c2:97:f3:2c:
43:d2:03:82:66:81:72:5f:53:16:ec:b1:b1:04:5e:
40:20:48:7b:3f:02:97:6a:eb:96:12:21:35:fe:1f:
47:c0:95:ea:c5:8a:08:84:4f:5e:63:94:60:0f:71:
5b:7f:4a:ec:4f:60:c6:ba:4a:24:f1:20:8b:a7:2e:
3a:ce:8d:e0:27:1d:b5:8e:b4:21:c5:e2:a6:16:0a:
51:83:55:88:d1:30:11:63:d5:d7:8d:ae:16:12:82:
c4:85:00:4e:27:83:a5:7c:90:2e:e5:a2:a3:d3:4c:
63
coefficient:
00:86:08:98:98:a5:00:05:39:77:d9:66:b3:cf:ca:
a0:71:b3:50:ce:3d:b1:93:95:35:c4:d4:2e:90:df:
0f:fc:60:c1:94:68:61:43:ca:9a:23:4a:1e:45:72:
99:b5:1e:61:8d:77:0f:a0:bb:d7:77:b4:2a:15:11:
88:2d:b3:56:61:5e:6a:ed:a4:46:4a:3f:50:11:d6:
ba:b6:d7:95:65:53:c3:a1:8f:e0:a3:f5:1c:fd:af:
6e:43:d7:17:a7:d3:81:1b:a4:df:e0:97:8a:46:03:
d3:46:0e:83:48:4e:d2:02:cb:c0:ad:79:95:8c:96:
ba:40:34:11:71:5e:e9:11:f9:c5:4a:5e:91:9d:f5:
92:4f:eb:c6:70:02:2d:3d:04:aa:e9:3a:8e:d5:a8:
ad:f7:ce:0d:16:b2:ec:0a:9c:f5:94:39:b9:8a:fc:
1e:f9:cc:f2:5f:21:31:74:72:6b:64:ae:35:61:8d:
0d:cb:e7:da:39:ca:f3:21:66:0b:95:d7:0a:7c:ca:
a1:a9:5a:e8:ac:e0:71:54:af:28:cf:d5:70:89:e0:
f3:9e:43:6c:8d:7b:99:01:68:4d:a1:45:46:0c:43:
bc:cc:2c:dd:c5:46:c8:4e:0e:be:ed:b9:26:ab:2e:
db:eb:8f:ff:db:b0:c6:55:af:f8:2a:91:9d:50:44:
21:17
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