Digital Trust: The Magic of r and s

So, what does a digital signature look like? Well, it often has an r value and an s value: (r,s). So, let’s look at the DSA (Digital…

Digital Trust: The Magic of r and s

So, what does a digital signature look like? Well, it often has an r value and an s value: (r,s). So, let’s look at the DSA (Digital Signature Algorithm) signature. For this, Figure 1 shows an outline of the setup of the DSA signature, and where Bob uses his private key (sk) to sign a hash of a message, and Alice proves with his public key (pk,g,p,q). We also use a random nonce value (k) for the signature, and we must take care that we do not reuse the value.

The output of the signature is (r,s). We can create a keypair and signature for a file named test.txt. In this case, we create a 1,024 bit key pair and use the SHA-256 hash. The file contains “This is a test.” [here]:

openssl dsaparam -out dsaparam.pem 1024
openssl gendsa -out 1.pem dsaparam.pem
openssl dgst -sha256 -sign 1.pem -out 1.sig -hex test.txt
type 1.sig
type 1.sig | openssl enc -base64
openssl dsa -in 1.pem - text

and a sample test [here]:

SA-SHA2-256(test.txt)= 303c021c41f04a15af85a5215f181ccd1999931db8051cd6c77c71d9dfa9b079021c17be382511cd4313fb24bec6618390638a1b652600a68d633bf9b23e

RFNBLVNIQTItMjU2KHRlc3QudHh0KT0gMzAzYzAyMWM0MWYwNGExNWFmODVhNTIx
NWYxODFjY2QxOTk5OTMxZGI4MDUxY2Q2Yzc3YzcxZDlkZmE5YjA3OTAyMWMxN2Jl
MzgyNTExY2Q0MzEzZmIyNGJlYzY2MTgzOTA2MzhhMWI2NTI2MDBhNjhkNjMzYmY5
YjIzZQ0K

Private-Key: (1024 bit)
priv:
    76:44:c6:a7:37:71:ba:6d:b2:ac:73:b4:e1:14:4f:
    69:32:cf:d5:9f:e3:9b:cb:af:ef:fb:38:ac
pub: 
    00:c5:80:e0:ac:15:4c:17:63:7e:c1:52:50:19:54:
    6c:1f:3b:6b:00:a4:5f:9f:e6:82:51:59:d2:9d:fb:
    c1:53:cf:c7:03:60:ce:64:6b:b2:7d:31:3f:84:ae:
    bb:9e:54:25:cd:eb:19:aa:e3:69:82:e1:22:e4:25:
    0a:93:bf:7b:61:1a:22:50:2c:61:72:ce:9d:33:dc:
    77:b2:c7:e8:6e:b7:20:21:84:50:83:78:9a:6c:13:
    af:74:2c:41:c3:48:b7:a0:ec:07:99:36:4b:f3:c3:
    c8:22:e8:62:ff:ac:b8:fa:f5:bb:c5:31:57:f0:0f:
    45:3d:21:36:dd:2f:b7:5a:45
P:   
    00:f7:52:0b:82:62:03:34:97:82:ac:7f:91:07:cb:
    6c:bb:d1:5a:2c:a5:d5:b2:28:f3:05:ec:70:80:be:
    65:c3:40:dd:47:16:1b:31:21:c1:49:91:6d:50:b3:
    4d:4d:54:96:5e:9f:4e:1b:66:cc:fb:ee:df:f1:ba:
    86:58:66:fd:e0:16:2e:ad:d6:5e:7e:ea:ac:1d:60:
    2c:98:a8:ac:c6:75:5c:ab:d0:6a:f7:6a:e1:d8:20:
    86:68:aa:75:a0:bf:c3:43:9b:55:03:46:9b:0c:73:
    33:0c:5d:bf:db:0a:1d:a9:29:07:b4:e6:63:30:dc:
    5d:5d:0d:83:7c:86:b2:07:b5
Q:   
    00:aa:c1:56:61:8d:80:7c:b1:e5:7a:24:27:5e:40:
    67:88:88:47:cd:ac:fd:63:64:cc:8d:88:82:49
G:   
    00:a3:f8:a3:80:62:cf:a5:1a:0f:90:d3:41:26:ef:
    c2:09:ed:09:84:5c:87:ff:9e:7f:de:c6:2b:23:98:
    f2:0e:26:9b:59:99:43:0d:0c:61:a5:de:39:1e:16:
    6c:3d:dd:d1:02:11:57:da:c4:f5:e2:48:2c:91:5d:
    56:11:28:8b:5d:e2:fb:b5:94:e5:db:50:32:c5:f2:
    cd:8e:bb:eb:3a:40:e1:c1:0a:09:ef:40:84:48:d0:
    e6:24:11:13:5a:ff:74:f2:06:de:2a:df:14:a6:f2:
    0c:34:db:8b:ae:71:b2:a3:67:4a:fc:51:31:46:06:
    d2:27:29:c3:60:41:4c:82:dd

-----BEGIN DSA PRIVATE KEY-----
MIIBzAIBAAKBgQD3UguCYgM0l4Ksf5EHy2y70VospdWyKPMF7HCAvmXDQN1HFhsx
IcFJkW1Qs01NVJZen04bZsz77t/xuoZYZv3gFi6t1l5+6qwdYCyYqKzGdVyr0Gr3
auHYIIZoqnWgv8NDm1UDRpsMczMMXb/bCh2pKQe05mMw3F1dDYN8hrIHtQIdAKrB
VmGNgHyx5XokJ15AZ4iIR82s/WNkzI2IgkkCgYEAo/ijgGLPpRoPkNNBJu/CCe0J
hFyH/55/3sYrI5jyDiabWZlDDQxhpd45HhZsPd3RAhFX2sT14kgskV1WESiLXeL7
tZTl21AyxfLNjrvrOkDhwQoJ70CESNDmJBETWv908gbeKt8UpvIMNNuLrnGyo2dK
/FExRgbSJynDYEFMgt0CgYEAxYDgrBVMF2N+wVJQGVRsHztrAKRfn+aCUVnSnfvB
U8/HA2DOZGuyfTE/hK67nlQlzesZquNpguEi5CUKk797YRoiUCxhcs6dM9x3ssfo
brcgIYRQg3iabBOvdCxBw0i3oOwHmTZL88PIIuhi/6y4+vW7xTFX8A9FPSE23S+3
WkUCHHZExqc3cbptsqxztOEUT2kyz9Wf45vLr+/7OKw=
-----END DSA PRIVATE KEY-----

-----BEGIN DSA PARAMETERS-----
MIIBJwKBgQD3UguCYgM0l4Ksf5EHy2y70VospdWyKPMF7HCAvmXDQN1HFhsxIcFJ
kW1Qs01NVJZen04bZsz77t/xuoZYZv3gFi6t1l5+6qwdYCyYqKzGdVyr0Gr3auHY
IIZoqnWgv8NDm1UDRpsMczMMXb/bCh2pKQe05mMw3F1dDYN8hrIHtQIdAKrBVmGN
gHyx5XokJ15AZ4iIR82s/WNkzI2IgkkCgYEAo/ijgGLPpRoPkNNBJu/CCe0JhFyH
/55/3sYrI5jyDiabWZlDDQxhpd45HhZsPd3RAhFX2sT14kgskV1WESiLXeL7tZTl
21AyxfLNjrvrOkDhwQoJ70CESNDmJBETWv908gbeKt8UpvIMNNuLrnGyo2dK/FEx
RgbSJynDYEFMgt0=
-----END DSA PARAMETERS-----

The signature in this case is: “303c021c41f04a15af85a5215f181ccd1999931db8051cd6c77c71d9dfa9b079021c17be382511cd4313fb24bec6618390638a1b652600a68d633bf9b23e”.

This is in the DER format (and where we see it starting with a “30”. We can interpret with [here]:

DER string: 303c021c41f04a15af85a5215f181ccd1999931db8051cd6c77c71d9dfa9b079021c17be382511cd4313fb24bec6618390638a1b652600a68d633bf9b23e

==Sequence==
Integer (02):  0x41f04a15af85a5215f181ccd1999931db8051cd6c77c71d9dfa9b079
Integer (02):  0x17be382511cd4313fb24bec6618390638a1b652600a68d633bf9b23e

In this case, we have an r value of “0x41f04a15af85a5215f181ccd1999931db8051cd6c77c71d9dfa9b079”, and an s value of “0x17be382511cd4313fb24bec6618390638a1b652600a68d633bf9b23e”.

In case we also have a PEM format, and which is in the form of:

Conclusions

The DSA signature is generally being phased-out and replaced with ECDSA (as used with Bitcoin and Ethereum). Overall, though, the method has scaled from discrete logs to elliptic curve methods.