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


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

lambda = 128
q = 127
l = 10
v = 540
m = 60
f = x^10 - 2 x^3 - 1
W = 
[[0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
 [0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
 [0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
 [0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
 [0, 0, 0, 0, 0, 0, 1, 0, 0, 0],
 [0, 0, 0, 0, 0, 1, 0, 0, 0, 0],
 [0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
 [0, 0, 0, 1, 0, 0, 0, 0, 0, 0]]
PRG = SHAKE

#####################################################
### Fixed Test Inputs
### All values are expressed by hexstring
#####################################################
seed_sk = 1111111111111111111111111111111111111111111111111111111111111110
message = 68656c6c6f776f726c64
salt rho = 11111111111111111111111111111111
y_input = 010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101

#####################################################
### KeyGen
#####################################################
seed_pk = c172f9b5360282a13ca1855c6c05fd9e
S' = 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### Sign
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L = 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
u = 312e0437792b0245496123210b3a4e201c522f3c1d2a1e6a5e705746603d04542374335c027d55442e050477663854350c64100a42230b11355b1b6c
t = 107d263c7e191942713f6564626d0f4711482e4f056a69104d5b7e5e7d0243032b2c471d6a79266674610c66257e416c00344644395e7d771107144d
y_solution = 490c2d04030420475e49774b18443612686a17133f6e215b0c0565036462124737683d45060938780e03667d4b0624242a6e575d2e436f716161486d
s = 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

#####################################################
### Verify
#####################################################
t' = 107d263c7e191942713f6564626d0f4711482e4f056a69104d5b7e5e7d0243032b2c471d6a79266674610c66257e416c00344644395e7d771107144d
