Thanks! but more functions didnt work like TropicalPolynomial[x,y]. It would be nice if you try your own code like I did to get a numeric key but with no result, surelly you have a functional workinq notebook to share. Thx.
PUBLIC PARAMETERS GENERATION
A = {{1, 5}, {-2, 7}}
B = {{5, 0}, {-3, 4}}
ALICE
p1[A] = TropicalPolynomial[p1, A]
p2[B] = TropicalPolynomial[p2, B]
p = TropicalMatrixTimes[p1[A], p2[B]
BOB
q1[A] = TropicalPolynomial[q1, A]
q2[B] = TropicalPolynomial[q2, B]
q = TropicalMatrixTimes[q1[A], q2[B]]
KEYS
keyA = TropicalMatrixTimes[TropicalMatrixTimes[p1A, q], p2B]
keyB = TropicalMatrixTimes[TropicalMatrixTimes[q1A, p], q2B]
Best
Peter