#####################################################
### QR-UOV intermediate values
#####################################################


#####################################################
### Parameters
### All values are expressed by integer
#####################################################

lambda = 128
q = 127
l = 3
v = 156
m = 54
f = x^3 -   x   - 1
W = 
[[1, 0, 0],
 [0, 0, 1],
 [0, 1, 0]]
PRG = SHAKE

#####################################################
### Fixed Test Inputs
### All values are expressed by hexstring
#####################################################
seed_sk = 1111111111111111111111111111111111111111111111111111111111111110
message = 68656c6c6f776f726c64
salt rho = 11111111111111111111111111111111
y_input = 010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101

#####################################################
### KeyGen
#####################################################
seed_pk = c172f9b5360282a13ca1855c6c05fd9e
S' = 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
Pi1 = 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### Sign
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L = 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
u = 7c641b051724321f411d5e4f777e22003e3173223a5e00422d7a7a0d627311567c4576710226021a221f4e764f7c791d7d3120071b0b
t = 107d263c7e19197d713f6564626d0f4711482e4f056a69104d5b7e5e7d0243032b2c771d6a79266674610c66257e416c00344644395e
y_solution = 30797167582f0679245873050345765f437b2375470f25271953215e281b7b2b05204911247c76336935390c5d1e4a4c4f6b602d3852
s = 0327350e50381f02686a50290c7a547337776d6028043203020d320c0204392a31581568222200031824534b486d13591f180d444914457c59002d41077044014442110d64643970112878571a665f2475180e093909323d7d20754f534b04686a677a402b63482a604d7c732131660a44583d2f68015818734c413e55170f4b1437281a316e54210a041635144857230a56196e294068604023510a4f060e18275079065b270c7a7c3a09203c045c0a38705a58662c5e21576404547a5f366e5b03094c164a46732261353330141f52472d

#####################################################
### Verify
#####################################################
t' = 107d263c7e19197d713f6564626d0f4711482e4f056a69104d5b7e5e7d0243032b2c771d6a79266674610c66257e416c00344644395e
