Homework 14

\( \def\ZZ{\mathbb{Z}} \def\GG{\mathbb{G}} \def\HH{\mathbb{H}} \) Print this page and give the answers.


Name:______________________________     Alpha:________________________________

[18pts] We will review insecurity of the Plain RSA digital signature algorithm:
Let's work with a specific example. The public verification key \(pk = (N, e)\) is given as follows:
```
N = 1690334090971833824554846747206837515869129625105576902419675069024034246895604065945194508189044177278028981
e = 65537
```
[6pts] What should be the messages that will pass the verification algorithm? Fill out the blanks below.
```
msg1 = ______  
sig1 = 1629132894863156916614186635714460213173677771325305119944591810181897832329604864250007036675944890379346154
```
```
msg2 = ______
sig2 = 1204006904043146988764811123343045125247543322810270775436711304671813568788078424754145533529579376536620941
```
[6pts] You can figure out the valid signature on message 225. What is it? Fill the blank below.
```
msg = 225

sig = 1572449105534849782870079068822203588813052040209062272986931237364012995001101394789881978916666875
```
[6pts] How did you get the signature? Explain.
[10pts] Answer the following:
- CA stands for .
- TRUE/FALSE
  An expired certificate should be listed in CRL.
- Using , the client checks if the server certificate is revoked or not, by downloading the list of all certificates that CA has revoked and seeing if the server certificate is in the list.
- Using , the client checks if the server certificate is revoked or not, by directly contacting CA and ask about it?
- OSCP incurs a huge overhead to the client / CA (choose the right one).

[10pts] Consider the following X.590 certificate:

Certificate:
 Data:
  Version: 3 (0x2)
  Serial Number: 434 (0x1b2)
  Signature Algorithm: sha1WithRSAEncryption
  Issuer: C=US, O=U.S. Government, OU=DoD, OU=PKI, CN=DoD Root CA 2
  Validity
   Not Before: Sep  8 15:50:25 2011 GMT
   Not After : Sep  8 15:50:25 2017 GMT
  Subject: C=US, O=U.S. Government, OU=DoD, OU=PKI, CN=DOD CA-27
  Subject Public Key Info:
   Public Key Algorithm: rsaEncryption
    Public-Key: (2048 bit)
    Modulus:
     00:96:84:08:fd:7a:ba:b6:94:83:d0:9d:3b:19:0b:
     cf:04:df:88:2a:9e:b8:1a:58:eb:87:22:2a:63:3a:
     7f:39:c3:6b:6b:e7:bc:1a:a8:11:02:f5:61:cd:01:
     ...(omitted)...
     04:ba:a7:55:16:69:0e:93:d4:bc:8c:62:4d:4f:56:
     82:b6:c7:b4:78:2f:7d:d9:d3:43:ed:73:26:f1:53:
     ee:ff:b3:d5:b0:e4:6e:b6:be:2d:1b:68:0d:77:58:
     84:57:42:cf:40:70:8c:bc:ca:c0:39:75:4e:f7:19:
     88:7c:6b:ec:29:c6:64:1d:e8:53:50:bd:94:aa:e4:
     83:dd
    Exponent: 65537 (0x10001)
  X509v3 extensions:
   X509v3 Key Usage: critical
    Digital Signature, Certificate Sign, CRL Sign
   X509v3 Authority Key Identifier: 
    keyid:49:74:BB:0C:5E:BA:7A:FE:02:54:EF:7B:A0:C6:95:C6:09:80:70:96

   X509v3 Subject Key Identifier: 
    1B:04:04:40:45:5E:7D:2B:5E:0B:CC:99:65:4D:F3:A4:DE:90:77:17
   X509v3 Basic Constraints: critical
    CA:TRUE, pathlen:0
   X509v3 Policy Constraints: 
    Require Explicit Policy:0
   X509v3 Certificate Policies: 
    Policy: 2.16.840.1.101.2.1.11.5
    Policy: 2.16.840.1.101.2.1.11.9
    Policy: 2.16.840.1.101.2.1.11.17
    Policy: 2.16.840.1.101.2.1.11.18
    Policy: 2.16.840.1.101.2.1.11.19
    Policy: 2.16.840.1.101.3.2.1.3.26
    Policy: 2.16.840.1.101.3.2.1.3.27

   X509v3 CRL Distribution Points: 

    Full Name:
      URI:http://crl.disa.mil/crl/DODROOTCA2.crl

   Authority Information Access: 
    CA Issuers - URI:http://crl.disa.mil/issuedto/DODROOTCA2_IT.p7c
    OCSP - URI:http://ocsp.disa.mil
    CA Issuers - URI:ldap://crl.gds.disa.mil/cn%3dDoD%20Root%20CA%202%2cou
    %3dPKI%2cou%3dDoD%2co%3dU.S.%20Government%2cc%3dUS?crossCertificatePair;binary

 Signature Algorithm: sha1WithRSAEncryption
  40:c0:0c:4b:9f:8d:23:a6:31:d1:34:ae:9e:91:5c:5f:84:dd:
  9c:04:95:61:cd:80:14:1f:6e:de:88:97:7c:e9:af:a5:f5:f7:
  ...(omitted)...
  58:c8:c8:1e:dd:cb:75:10:b5:41:01:e6:16:5a:68:f7:37:39:
  d6:11:b6:30:25:fb:b4:7e:c8:12:c6:d8:9f:63:a9:d9:6d:86:
  d2:36:47:a1:73:29:22:fe:02:f4:63:2b:29:20:97:ae:b5:34:
  bc:58:e6:60:b6:11:d7:82:a6:e7:e2:37:7e:3b:7b:06:78:26:
  6f:6c:45:73

Who issued this certificate? In other words, what's the name of the CA that generated this certificate? Give its common name (CN).
How long had this certificate been valid?
Give the subject's identity. The common name (CN) is enough.
Circle the subject's public key in the left box.
Is the subject a certificate authority?
```
 Yes / No  (choose the right answer) 
```
If you said yes, draw rectangles around the relevant parts in the left box.