DSA with LCG nonces

Even we don't know how to solve this one


Discuss The Problem

Hint has been tweeted. @id0rsa

Consider the following DSA parameters:

P:
        00:b9:26:6b:04:bf:72:64:38:0c:93:53:89:ef:a8:
        39:a9:05:89:44:d6:3f:fb:35:bf:49:3c:d9:b0:1d:
        c0:75:82:28:18:ac:3c:a1:6c:e4:64:2b:8e:89:86:
        cb:6e:01:f2:ad:cf:b2:28:72:9c:d9:e6:c6:67:68:
        1a:61:09:21:9f
Q:
        00:d5:f0:0a:9c:48:d1:45:92:07:84:bf:b1:a5:6b:
        1f:1f:95:e7:f7:47
G:
        17:03:ed:8e:7c:ad:59:d8:83:a0:d5:4c:e1:8f:03:
        af:02:30:2f:9d:38:f5:79:8d:0d:4b:65:2a:0b:89:
        05:1b:78:4a:19:81:b1:8c:fb:6f:cd:fb:7e:b9:c9:
        56:eb:b0:f3:bd:51:9a:c5:29:e0:20:97:b3:9c:45:
        f8:9b:2e:1f

Using these parameters I've signed a pair of messages (the messages are hashed via SHA1 in the signing algorithm):

m1, r1, s1 = (
    "message1",
    202861689990073510420857440842954393147681706677,
    316598684468735233298185340984928938581112602589
)
m2, r2, s2 = (
    "message2",
    43602034738807436825901197549075276008737747591,
    642028161610139974743754581527505118749777770326
)

The nonces used when signing these messages were generated via a LCG seeded with a secret value and with these parameters:

$a = 545094182407654161786276305190438612396347946877\\ c = 106527113109554186270186272440947601748633355206\\ m = 983310466739698185049446758331422281214830590642$

Recover the signing key. Submit your answer in lowercase hex, no leading 0x.