openssl x509 -text -in verisign-class3.cer
Certificate:
Data:
Version: 1 (0x0)
Serial Number:
70:ba:e4:1d:10:d9:29:34:b6:38:ca:7b:03:cc:ba:bf
Signature Algorithm: md2WithRSAEncryption
Issuer: C=US, O=VeriSign, Inc., OU=Class 3 Public Primary Certification Authority
Validity
Not Before: Jan 29 00:00:00 1996 GMT
Not After : Aug 1 23:59:59 2028 GMT
Subject: C=US, O=VeriSign, Inc., OU=Class 3 Public Primary Certification Authority
Subject Public Key Info:
Public Key Algorithm: rsaEncryption
RSA Public Key: (1024 bit)
Modulus (1024 bit):
00:c9:5c:59:9e:f2:1b:8a:01:14:b4:10:df:04:40:
db:e3:57:af:6a:45:40:8f:84:0c:0b:d1:33:d9:d9:
11:cf:ee:02:58:1f:25:f7:2a:a8:44:05:aa:ec:03:
1f:78:7f:9e:93:b9:9a:00:aa:23:7d:d6:ac:85:a2:
63:45:c7:72:27:cc:f4:4c:c6:75:71:d2:39:ef:4f:
42:f0:75:df:0a:90:c6:8e:20:6f:98:0f:f8:ac:23:
5f:70:29:36:a4:c9:86:e7:b1:9a:20:cb:53:a5:85:
e7:3d:be:7d:9a:fe:24:45:33:dc:76:15:ed:0f:a2:
71:64:4c:65:2e:81:68:45:a7
Exponent: 65537 (0x10001)
Signature Algorithm: md2WithRSAEncryption
bb:4c:12:2b:cf:2c:26:00:4f:14:13:dd:a6:fb:fc:0a:11:84:
8c:f3:28:1c:67:92:2f:7c:b6:c5:fa:df:f0:e8:95:bc:1d:8f:
6c:2c:a8:51:cc:73:d8:a4:c0:53:f0:4e:d6:26:c0:76:01:57:
81:92:5e:21:f1:d1:b1:ff:e7:d0:21:58:cd:69:17:e3:44:1c:
9c:19:44:39:89:5c:dc:9c:00:0f:56:8d:02:99:ed:a2:90:45:
4c:e4:bb:10:a4:3d:f0:32:03:0e:f1:ce:f8:e8:c9:51:8c:e6:
62:9f:e6:9f:c0:7d:b7:72:9c:c9:36:3a:6b:9f:4e:a8:ff:64:
0d:64
-----BEGIN CERTIFICATE-----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-----END CERTIFICATE-----
In decimal, the modulus is 141400322044550516865173371773024584879899609644618927642375342633349057300960400037232334924701046781298765077061770383151646234219179990772047200045837817821582483532549791304588064624083040538534190301571832597441704620988055765289140138246856927863523873759538652326729606982847841094220861282830980236711
Much havoc could be wrought by factoring this number. As expected, gp repeats ellfact for a long time. Let's try to find a smooth factorization of a number in the neighborhood, or vicinity of a multiple.
? nextprime(m)-m %6 = 1032 ? precprime(m)-m %7 = -398 ? for(i=m-100,m+100,print(i-m," ",factorint(i,15)))
7 comments :
m-322=
[3, 1; 11, 1; 83, 1; 419, 1; 619, 1; 6899, 1; 322940119, 1; 422696671, 1; 26602810850701, 1; 903605064852877, 1; 8792462764873702974871749624609593774378713494350497136003292015630608857347999664025266450227155345167298302429649219614225919729692955976908289787143862810363798749528530236746114297110884456430667100896237655525404955249232457337412793667578949133, 1]
Files
Oops, only needed to do odd numbers around 2m.
small*small*modulus +/- 1
Two small because the first range might have already been searched.
for(i=1, 10000000, p=random+1;q=random+1; print("CTX ",p," ",q); print(factorint(p*q*m+1,15)); print(factorint(p*q*m-1,15)))
offset 4 factored
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