#####################################################
### 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 = AES

#####################################################
### 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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
Pi1 = 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### Sign
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L = 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
u = 4b44275126417b64197e63122606215c0c0f090c12582d196f0e65400516070f241428187d1f52653f7a5723512c405f4c307a3d49631a566b1e3905
t = 107d263c7e191942713f6564626d0f4711482e4f056a69104d5b7e5e7d0243032b2c471d6a79266674610c66257e416c00344644395e7d771107144d
y_solution = 461b732b402467370b02576d0e3a08633108055757621d6965160b5e69107e4916494d061a7b3f3409517a3b38283e7a296d1f7b077b7a41605c0153
s = 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

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