func TestFindBasisAndSort(t *testing.T) {
constr := fastTestConstruction()
S := GenerateS(constr, 0, 0, 0)
basis := FindBasisAndSort(S)
// Test that each vector is correct in place.
for i, perm := range S {
vect := [256]byte{}
copy(vect[:], table.SerializeByte(FunctionFromBasis(i, basis)))
if vect != perm {
t.Fatalf("FindBasisAndSort, position #%v is wrong!\n%v\n%v", i, vect, perm)
}
}
// Test composition of two functions.
x := table.SerializeByte(table.ComposedBytes{
table.ParsedByte(S[39][:]),
table.ParsedByte(S[120][:]),
})
y := [256]byte{}
copy(y[:], x)
if y != S[39^120] {
t.Fatalf("Function composition was wrong!\n%v\n%v", x, S[39^120])
}
}
// GenerateS creates the set of elements S, of the form fXX(f00^(-1)(x)) = Q(Q^(-1)(x) + b) for indeterminate x is
// isomorphic to the additive group (GF(2)^8, xor) under composition.
func GenerateS(constr *chow.Construction, round, inPos, outPos int) [][256]byte {
f00 := table.InvertibleTable(F{constr, round, inPos, outPos, 0x00})
f00Inv := table.Invert(f00)
S := make([][256]byte, 256)
for x := 0; x < 256; x++ {
copy(S[x][:], table.SerializeByte(table.ComposedBytes{
f00Inv,
F{constr, round, inPos, outPos, byte(x)},
}))
}
return S
}
// FindBasisAndSort finds 8 elements of S that act as a basis for S and build isomorphism psi.
func FindBasisAndSort(S [][256]byte) (basis []table.Byte) {
for len(basis) < 8 { // Until we have a full basis.
basis = append(basis, table.ParsedByte(S[1<<uint(len(basis))][:])) // Add the first independent vector to the basis.
// Move all (now) dependent vectors from S into their correct position.
for i := 1 << uint(len(basis)-1); i < 1<<uint(len(basis)); i++ {
vect := [256]byte{}
copy(vect[:], table.SerializeByte(FunctionFromBasis(i, basis)))
// Move it to the correct position in S.
for j := i; j < len(S); j++ {
if vect == S[j] {
S[i], S[j] = S[j], S[i]
break
}
}
}
}
return
}
