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I came across a certificate that contains values $P,Q$, and $G$ besides the public key.

Obviously, $P$ and $Q$ here are primes, but not the two secret primes. I am curious are those values

Public Key Algorithm: dsaEncryption
                Public-Key: (1024 bit)
                pub:
                    56:3f:cd:3b:b0:ef:03:60:2e:43:4e:14:da:e0:db:
                    9c:77:15:f5:ad:78:e2:8a:1f:ff:62:b8:6c:19:60:
                    f0:64:8c:59:ec:88:df:e8:f0:29:e6:6d:d1:27:9e:
                    a9:e5:5a:8d:99:c2:53:27:5f:83:85:d8:b4:7a:93:
                    52:4c:e5:74:da:60:16:f5:95:1a:c9:42:c4:92:d2:
                    44:6b:73:45:dd:62:87:43:d4:00:02:81:4b:27:1f:
                    69:ac:c1:57:70:20:97:da:5f:01:c0:dc:7a:e7:93:
                    04:12:51:dd:e2:c5:be:37:13:a2:0c:12:98:64:1f:
                    e4:c6:0f:ec:a2:5a:9a:43
                P:
                    00:fd:7f:53:81:1d:75:12:29:52:df:4a:9c:2e:ec:
                    e4:e7:f6:11:b7:52:3c:ef:44:00:c3:1e:3f:80:b6:
                    51:26:69:45:5d:40:22:51:fb:59:3d:8d:58:fa:bf:
                    c5:f5:ba:30:f6:cb:9b:55:6c:d7:81:3b:80:1d:34:
                    6f:f2:66:60:b7:6b:99:50:a5:a4:9f:9f:e8:04:7b:
                    10:22:c2:4f:bb:a9:d7:fe:b7:c6:1b:f8:3b:57:e7:
                    c6:a8:a6:15:0f:04:fb:83:f6:d3:c5:1e:c3:02:35:
                    54:13:5a:16:91:32:f6:75:f3:ae:2b:61:d7:2a:ef:
                    f2:22:03:19:9d:d1:48:01:c7
                Q:
                    00:97:60:50:8f:15:23:0b:cc:b2:92:b9:82:a2:eb:
                    84:0b:f0:58:1c:f5
                G:
                    00:f7:e1:a0:85:d6:9b:3d:de:cb:bc:ab:5c:36:b8:
                    57:b9:79:94:af:bb:fa:3a:ea:82:f9:57:4c:0b:3d:
                    07:82:67:51:59:57:8e:ba:d4:59:4f:e6:71:07:10:
                    81:80:b4:49:16:71:23:e8:4c:28:16:13:b7:cf:09:
                    32:8c:c8:a6:e1:3c:16:7a:8b:54:7c:8d:28:e0:a3:
                    ae:1e:2b:b3:a6:75:91:6e:a3:7f:0b:fa:21:35:62:
                    f1:fb:62:7a:01:24:3b:cc:a4:f1:be:a8:51:90:89:
                    a8:83:df:e1:5a:e5:9f:06:92:8b:66:5e:80:7b:55:
                    25:64:01:4c:3b:fe:cf:49:2a
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2 Answers 2

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It is the DSA where $(p,q,g)$ are public values. It is defined in FIPS 186-4 but not defined in FIPS 186-5.

The $p$ and $q$ primes of lengths, respectively;

  • L = 1024, N = 160
  • L = 2048, N = 224
  • L = 2048, N = 256
  • L = 3072, N = 256

and

  • $p-1$ must be multiple of $q$

  • with a random $h \in \{2,\ldots,p-2 \}$ chose $g = h^{(p-1)/q} \bmod p$. if $g = 1$ then choose another random $h$.

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    $\begingroup$ The tuple, (p, q, g) are the finite field group parameters in DSA, which are equivalent to the elliptic curve parameters in ECDSA. $\endgroup$
    – DannyNiu
    Commented May 27 at 7:56
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If you look above you'll see DSA, which is a signature algorithm, meaning you get to sign using the private key, hence to verify the digest according to RFC 3279 you should be able to use a public modulus for that purpose in a X.509 CRls infrastructure, therefore you have the public keys displayed to allow you to do so.

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