func TestByteMatrix(t *testing.T) {
m := SBox
a := byte(0x63) // 0b01100011
if m.Mul(Row{byte(number.ByteFieldElem(0x53).Invert())})[0]^a != 0xED {
t.Fatalf("Substitution value was wrong! 0x53 -> 0xED")
}
if m.Mul(Row{byte(number.ByteFieldElem(0x10).Invert())})[0]^a != 0xCA {
t.Fatalf("Substitution value was wrong! 0x10 -> 0xCA")
}
}
func (tyi TyiTable) Get(i byte) (out [4]byte) {
// Calculate dot product of i and [0x02 0x01 0x01 0x03]
j := number.ByteFieldElem(i)
a := byte(number.ByteFieldElem(0x02).Mul(j))
b := byte(number.ByteFieldElem(0x01).Mul(j))
c := byte(number.ByteFieldElem(0x03).Mul(j))
// Merge into one output and rotate according to column.
res := [4]byte{a, b, b, c}
copy(out[:], append(res[(4-tyi):], res[0:(4-tyi)]...))
return
}
// FindPartialEncoding takes an affine encoded F and finds the values that strip its output encoding. It returns the
// parameters it finds and the input encoding of f up to a key byte.
func FindPartialEncoding(constr *chow.Construction, f table.Byte, L, AtildeInv matrix.Matrix) (number.ByteFieldElem, byte, encoding.ByteAffine) {
fInv := table.Invert(f)
id := encoding.ByteLinear(matrix.GenerateIdentity(8))
SInv := table.InvertibleTable(chow.InvTBox{saes.Construction{}, 0x00, 0x00})
S := table.Invert(SInv)
// Brute force the constant part of the output encoding and the beta in Atilde = A_i <- D(beta)
for c := 0; c < 256; c++ {
for d := 1; d < 256; d++ {
cand := encoding.ComposedBytes{
TableAsEncoding{f, fInv},
encoding.ByteAffine{id, byte(c)},
encoding.ByteLinear(AtildeInv),
encoding.ByteMultiplication(byte(d)), // D below
TableAsEncoding{SInv, S},
}
if isAffine(cand) {
a, b := DecomposeAffineEncoding(cand)
return number.ByteFieldElem(d), byte(c), encoding.ByteAffine{encoding.ByteLinear(a), byte(b)}
}
}
}
panic("Failed to strip output encodings!")
}
func UnMixColumns(i, j byte) [4]byte {
k, l := number.ByteFieldElem(i), number.ByteFieldElem(j)
var a, b, c, d number.ByteFieldElem
a = number.ByteFieldElem(0x0e).Mul(k)
b = number.ByteFieldElem(0x09).Mul(k)
c = number.ByteFieldElem(0x0d).Mul(k)
d = number.ByteFieldElem(0x0b).Mul(k)
a = number.ByteFieldElem(0x0b).Mul(l).Add(a)
b = number.ByteFieldElem(0x0e).Mul(l).Add(b)
c = number.ByteFieldElem(0x09).Mul(l).Add(c)
d = number.ByteFieldElem(0x0d).Mul(l).Add(d)
return [4]byte{byte(a), byte(b), byte(c), byte(d)}
}
func (constr *Construction) UnMixColumn(slice []byte) {
column := number.ArrayFieldElem{
number.ByteFieldElem(slice[0]), number.ByteFieldElem(slice[1]),
number.ByteFieldElem(slice[2]), number.ByteFieldElem(slice[3]),
}.Mul(number.ArrayFieldElem{
number.ByteFieldElem(0x0e), number.ByteFieldElem(0x09),
number.ByteFieldElem(0x0d), number.ByteFieldElem(0x0b),
})
for i := 0; i < 4; i++ {
if len(column) > i {
slice[i] = byte(column[i])
} else {
slice[i] = 0x00
}
}
}
func MixColumns(i, j byte) [4]byte {
k, l := number.ByteFieldElem(i), number.ByteFieldElem(j)
var a, b, c, d number.ByteFieldElem
a = number.ByteFieldElem(0x02).Mul(k)
b = number.ByteFieldElem(0x01).Mul(k)
d = number.ByteFieldElem(0x03).Mul(k)
a = number.ByteFieldElem(0x03).Mul(l).Add(a)
c = number.ByteFieldElem(0x01).Mul(l)
d = c.Add(d)
c = c.Add(b)
b = number.ByteFieldElem(0x02).Mul(l).Add(b)
return [4]byte{byte(a), byte(b), byte(c), byte(d)}
}
func (constr *Construction) SubByte(e byte) byte {
// AES S-Box
m := matrix.Matrix{ // Linear component.
matrix.Row{0xF1}, // 0b11110001
matrix.Row{0xE3}, // 0b11100011
matrix.Row{0xC7}, // 0b11000111
matrix.Row{0x8F}, // 0b10001111
matrix.Row{0x1F}, // 0b00011111
matrix.Row{0x3E}, // 0b00111110
matrix.Row{0x7C}, // 0b01111100
matrix.Row{0xF8}, // 0b11111000
}
a := byte(0x63) // 0b01100011 - Affine component.
return m.Mul(matrix.Row{byte(number.ByteFieldElem(e).Invert())})[0] ^ a
}
func (constr *Construction) UnSubByte(e byte) byte {
// AES Inverse S-Box
m := matrix.Matrix{
matrix.Row{0xA4},
matrix.Row{0x49},
matrix.Row{0x92},
matrix.Row{0x25},
matrix.Row{0x4a},
matrix.Row{0x94},
matrix.Row{0x29},
matrix.Row{0x52},
}
a := byte(0x63)
invVal := m.Mul(matrix.Row{e ^ a})[0]
return byte(number.ByteFieldElem(invVal).Invert())
}
func (bm ByteMultiplication) Encode(i byte) byte {
x, j := number.ByteFieldElem(bm), number.ByteFieldElem(i)
return byte(x.Mul(j))
}