// generateBarriers creates the encoding barriers between rounds that compute ShiftRows and re-encodes data.
func generateBarriers(rs *common.RandomSource, out *Construction, inputMask, outputMask, sr *matrix.Matrix) {
// Generate the ShiftRows and re-encoding matrices.
out.ShiftRows[0] = MaskSwap(rs, 16, 0).Compose(*sr).Compose(*inputMask)
for round := 1; round < 10; round++ {
out.ShiftRows[round] = MaskSwap(rs, 16, round).Compose(*sr).Compose(MaskSwap(rs, 32, round-1))
}
// We need to apply a final matrix transformation to convert the double-level encoding to a block-level one.
out.FinalMask = outputMask.Compose(MaskSwap(rs, 32, 9))
}
// FindAtilde calculates a non-trivial matrix Atilde s.t. L <- Atilde = Atilde <- D(beta), where
// L = A_i <- D(beta) <- A_i^(-1)
func FindAtilde(constr *chow.Construction, L matrix.Matrix) matrix.Matrix {
beta := CharToBeta[FindCharacteristic(L)]
D, _ := DecomposeAffineEncoding(encoding.ByteMultiplication(beta))
x := L.RightStretch().Add(D.LeftStretch()).NullSpace()
m := matrix.Matrix(make([]matrix.Row, len(x)))
for i, e := range x {
m[i] = matrix.Row{e}
}
return m
}
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 matrixMul(m *matrix.Matrix, dst, src []byte) {
res := m.Mul(matrix.Row(src[:]))
copy(dst, res)
}