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


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

lambda = 128
q = 31
l = 3
v = 165
m = 60
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 = 11111111111111111111111111111126
y_input = 010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101

#####################################################
### KeyGen
#####################################################
seed_pk = c172f9b5360282a13ca1855c6c05fd9e
S' = 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### Sign
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L = 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
u = 1e110011091c1c180815191b1e0c0d1a0118171c05071c1c0511021e030c000007141c101d160117051a12190b0f09180a0c070a1202130c010c050b
t = 0f110e051a140d0b1a06131c090403110102180a10081b1402040e01111613090d030812161819050919141e051b0d1e1b0e13111d031d130201081b
y_solution = 110b141b1e1e081411161b1312011516110c0111121e0a181a031c07151a151e151a0b12131b1c1a1c0118091904020d160e091b141d1e120a070101
s = 031902110915030f1a10030d08161a1309130f1d18051e1e1b0c0d030f14110b1e07130a04100505020e051b180f120c010007081613061c13110f14181a1710181e131d060813071d19121e18031001031e040f1611160418060b0c0916020e18191b0d0104050f16080d0e0511180e061b121c0c010508001207170e180d1205050d19151a06160f090d1418150805031212150816151e0b1a1d1103190305120c18120b110b141b1e1e081411161b1312011516110c0111121e0a181a031c07151a151e151a0b12131b1c1a1c0118091904020d160e091b141d1e120a070101

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### Verify
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t' = 0f110e051a140d0b1a06131c090403110102180a10081b1402040e01111613090d030812161819050919141e051b0d1e1b0e13111d031d130201081b
