Example #1
0
// cleanLeft gets the last affine layer back to a matrix with 16-by-16 blocks along the diagonal, times ShiftRows, times
// MixColumns and returns the matrix on the input encoding that it used to do this.
func (al *affineLayer) cleanLeft() encoding.Block {
	inverse := matrix.GenerateEmpty(128, 128)
	mixcols := matrix.GenerateEmpty(128, 128)

	// Combine individual blocks of the inverse matrix into the full inverse matrix. Also build the matrix corresponding
	// to the full-block MixColumns operation.
	for block := 0; block < 4; block++ {
		inv := al.findBlockOfInverse(block)

		for row := 0; row < 32; row++ {
			copy(inverse[32*block+row][4*block:], inv[row])
			copy(mixcols[32*block+row][4*block:], mixColumn[row])
		}
	}

	out := encoding.NewBlockLinear(inverse.Compose(mixcols))
	al.leftCompose(out)
	return encoding.InverseBlock{out}
}
Example #2
0
// RecoverKey returns the AES key used to generate the given white-box construction.
func RecoverKey(constr *xiao.Construction) []byte {
	round1 := round{
		construction: constr,
		round:        1,
	}

	// Decomposition Phase
	constr1 := aspn.DecomposeSPN(round1, cspn.ASA)

	var (
		first, last = affineLayer(constr1[0].(encoding.BlockAffine)), affineLayer(constr1[2].(encoding.BlockAffine))
		middle      = sboxLayer(constr1[1].(encoding.ConcatenatedBlock))
	)

	// Disambiguation Phase
	// The SPN decomposition naturally leaves the last affine layer without a constant part. We would push it into the
	// middle S-boxes if that wasn't the case.

	// Put the affine layers in diagonal form.
	perm := first.findPermutation()
	permEnc := encoding.NewBlockLinear(perm)

	first.rightCompose(encoding.InverseBlock{permEnc})
	middle.permuteBy(perm, false)
	last.leftCompose(permEnc)

	// Whiten the S-boxes so that they are linearly equivalent to Sbar.
	mask := middle.whiten()
	encoding.XOR(first.BlockAdditive[:], first.BlockAdditive[:], mask[:])

	// Fix the S-boxes so that they are equal to Sbar.
	in, out := middle.cleanLinear()

	first.rightCompose(in)
	last.leftCompose(out)

	// Add ShiftRows matrix to make search possible.
	last.rightCompose(encoding.NewBlockLinear(constr.ShiftRows[2]))

	// Clean off remaining noise from self-equivalences of Sbar.
	left := last.cleanLeft()
	right := encoding.ComposedBlocks{
		middle, left, encoding.InverseBlock{middle},
	}

	first.rightCompose(right)

	// Convert Sbar back to AES's "standard" S-box.
	for pos := 0; pos < 16; pos++ {
		first.BlockAdditive[pos] ^= 0x52
		middle[pos] = encoding.ComposedBytes{encoding.ByteAdditive(0x52), middle[pos]}
	}

	// fmt.Println(encoding.ProbablyEquivalentBlocks(
	//   encoding.ComposedBlocks{first, middle, last},
	//   encoding.ComposedBlocks{aspn.Encoding{round1}, encoding.NewBlockLinear(constr.ShiftRows[2])},
	// ))
	// fmt.Println(encoding.ProbablyEquivalentBlocks(
	//   aspn.Encoding{constr1},
	//   aspn.Encoding{round1},
	// ))
	//
	// Output:
	//   true
	//   true

	roundKey := shiftrows{}.Decode(first.BlockAdditive)
	return backOneRound(roundKey[:], 1)
}
Example #3
0
	round = encoding.NewBlockLinear(matrix.Matrix{
		matrix.Row{0xf8, 0x00, 0x00, 0x00, 0x00, 0x09, 0x00, 0x00, 0x00, 0x00, 0xf1, 0x00, 0x00, 0x00, 0x00, 0xf1},
		matrix.Row{0x09, 0x00, 0x00, 0x00, 0x00, 0xea, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x00, 0x00, 0x00, 0x00, 0xe3},
		matrix.Row{0xe3, 0x00, 0x00, 0x00, 0x00, 0x24, 0x00, 0x00, 0x00, 0x00, 0xc7, 0x00, 0x00, 0x00, 0x00, 0xc7},
		matrix.Row{0x3f, 0x00, 0x00, 0x00, 0x00, 0xb0, 0x00, 0x00, 0x00, 0x00, 0x8f, 0x00, 0x00, 0x00, 0x00, 0x8f},
		matrix.Row{0x77, 0x00, 0x00, 0x00, 0x00, 0x68, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x1f},
		matrix.Row{0x1f, 0x00, 0x00, 0x00, 0x00, 0x21, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x3e},
		matrix.Row{0x3e, 0x00, 0x00, 0x00, 0x00, 0x42, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x7c},
		matrix.Row{0x7c, 0x00, 0x00, 0x00, 0x00, 0x84, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x00, 0x00, 0x00, 0x00, 0xf8},
		matrix.Row{0xf1, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x00, 0x00, 0x00, 0x00, 0x09, 0x00, 0x00, 0x00, 0x00, 0xf1},
		matrix.Row{0xe3, 0x00, 0x00, 0x00, 0x00, 0x09, 0x00, 0x00, 0x00, 0x00, 0xea, 0x00, 0x00, 0x00, 0x00, 0xe3},
		matrix.Row{0xc7, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x00, 0x00, 0x00, 0x00, 0x24, 0x00, 0x00, 0x00, 0x00, 0xc7},
		matrix.Row{0x8f, 0x00, 0x00, 0x00, 0x00, 0x3f, 0x00, 0x00, 0x00, 0x00, 0xb0, 0x00, 0x00, 0x00, 0x00, 0x8f},
		matrix.Row{0x1f, 0x00, 0x00, 0x00, 0x00, 0x77, 0x00, 0x00, 0x00, 0x00, 0x68, 0x00, 0x00, 0x00, 0x00, 0x1f},
		matrix.Row{0x3e, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x21, 0x00, 0x00, 0x00, 0x00, 0x3e},
		matrix.Row{0x7c, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x42, 0x00, 0x00, 0x00, 0x00, 0x7c},
		matrix.Row{0xf8, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x84, 0x00, 0x00, 0x00, 0x00, 0xf8},
		matrix.Row{0xf1, 0x00, 0x00, 0x00, 0x00, 0xf1, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x00, 0x00, 0x00, 0x00, 0x09},
		matrix.Row{0xe3, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x00, 0x00, 0x00, 0x00, 0x09, 0x00, 0x00, 0x00, 0x00, 0xea},
		matrix.Row{0xc7, 0x00, 0x00, 0x00, 0x00, 0xc7, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x00, 0x00, 0x00, 0x00, 0x24},
		matrix.Row{0x8f, 0x00, 0x00, 0x00, 0x00, 0x8f, 0x00, 0x00, 0x00, 0x00, 0x3f, 0x00, 0x00, 0x00, 0x00, 0xb0},
		matrix.Row{0x1f, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x77, 0x00, 0x00, 0x00, 0x00, 0x68},
		matrix.Row{0x3e, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x21},
		matrix.Row{0x7c, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x42},
		matrix.Row{0xf8, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x84},
		matrix.Row{0x09, 0x00, 0x00, 0x00, 0x00, 0xf1, 0x00, 0x00, 0x00, 0x00, 0xf1, 0x00, 0x00, 0x00, 0x00, 0xf8},
		matrix.Row{0xea, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x00, 0x00, 0x00, 0x00, 0x09},
		matrix.Row{0x24, 0x00, 0x00, 0x00, 0x00, 0xc7, 0x00, 0x00, 0x00, 0x00, 0xc7, 0x00, 0x00, 0x00, 0x00, 0xe3},
		matrix.Row{0xb0, 0x00, 0x00, 0x00, 0x00, 0x8f, 0x00, 0x00, 0x00, 0x00, 0x8f, 0x00, 0x00, 0x00, 0x00, 0x3f},
		matrix.Row{0x68, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x77},
		matrix.Row{0x21, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x1f},
		matrix.Row{0x42, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x3e},
		matrix.Row{0x84, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x00, 0x00, 0x00, 0x00, 0x7c},
		matrix.Row{0x00, 0x00, 0x00, 0xf1, 0xf8, 0x00, 0x00, 0x00, 0x00, 0x09, 0x00, 0x00, 0x00, 0x00, 0xf1, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0xe3, 0x09, 0x00, 0x00, 0x00, 0x00, 0xea, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0xc7, 0xe3, 0x00, 0x00, 0x00, 0x00, 0x24, 0x00, 0x00, 0x00, 0x00, 0xc7, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x8f, 0x3f, 0x00, 0x00, 0x00, 0x00, 0xb0, 0x00, 0x00, 0x00, 0x00, 0x8f, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x1f, 0x77, 0x00, 0x00, 0x00, 0x00, 0x68, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x3e, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x21, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x7c, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x42, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0xf8, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x84, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0xf1, 0xf1, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x00, 0x00, 0x00, 0x00, 0x09, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0xe3, 0xe3, 0x00, 0x00, 0x00, 0x00, 0x09, 0x00, 0x00, 0x00, 0x00, 0xea, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0xc7, 0xc7, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x00, 0x00, 0x00, 0x00, 0x24, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x8f, 0x8f, 0x00, 0x00, 0x00, 0x00, 0x3f, 0x00, 0x00, 0x00, 0x00, 0xb0, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x1f, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x77, 0x00, 0x00, 0x00, 0x00, 0x68, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x3e, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x21, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x7c, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x42, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0xf8, 0xf8, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x84, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x09, 0xf1, 0x00, 0x00, 0x00, 0x00, 0xf1, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0xea, 0xe3, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x00, 0x00, 0x00, 0x00, 0x09, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x24, 0xc7, 0x00, 0x00, 0x00, 0x00, 0xc7, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0xb0, 0x8f, 0x00, 0x00, 0x00, 0x00, 0x8f, 0x00, 0x00, 0x00, 0x00, 0x3f, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x68, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x77, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x21, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x42, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x84, 0xf8, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0xf8, 0x09, 0x00, 0x00, 0x00, 0x00, 0xf1, 0x00, 0x00, 0x00, 0x00, 0xf1, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x09, 0xea, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0xe3, 0x24, 0x00, 0x00, 0x00, 0x00, 0xc7, 0x00, 0x00, 0x00, 0x00, 0xc7, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x3f, 0xb0, 0x00, 0x00, 0x00, 0x00, 0x8f, 0x00, 0x00, 0x00, 0x00, 0x8f, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x77, 0x68, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x1f, 0x21, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x3e, 0x42, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00},
		matrix.Row{0x00, 0x00, 0x00, 0x7c, 0x84, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x00},
		matrix.Row{0x00, 0x00, 0xf1, 0x00, 0x00, 0x00, 0x00, 0xf1, 0xf8, 0x00, 0x00, 0x00, 0x00, 0x09, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0xe3, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x09, 0x00, 0x00, 0x00, 0x00, 0xea, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0xc7, 0x00, 0x00, 0x00, 0x00, 0xc7, 0xe3, 0x00, 0x00, 0x00, 0x00, 0x24, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x8f, 0x00, 0x00, 0x00, 0x00, 0x8f, 0x3f, 0x00, 0x00, 0x00, 0x00, 0xb0, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x77, 0x00, 0x00, 0x00, 0x00, 0x68, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x21, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x42, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0xf8, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x84, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x09, 0x00, 0x00, 0x00, 0x00, 0xf1, 0xf1, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0xea, 0x00, 0x00, 0x00, 0x00, 0xe3, 0xe3, 0x00, 0x00, 0x00, 0x00, 0x09, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x24, 0x00, 0x00, 0x00, 0x00, 0xc7, 0xc7, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0xb0, 0x00, 0x00, 0x00, 0x00, 0x8f, 0x8f, 0x00, 0x00, 0x00, 0x00, 0x3f, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x68, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x77, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x21, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x42, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x84, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xf8, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0xf8, 0x00, 0x00, 0x00, 0x00, 0x09, 0xf1, 0x00, 0x00, 0x00, 0x00, 0xf1, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x09, 0x00, 0x00, 0x00, 0x00, 0xea, 0xe3, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0xe3, 0x00, 0x00, 0x00, 0x00, 0x24, 0xc7, 0x00, 0x00, 0x00, 0x00, 0xc7, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x3f, 0x00, 0x00, 0x00, 0x00, 0xb0, 0x8f, 0x00, 0x00, 0x00, 0x00, 0x8f, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x77, 0x00, 0x00, 0x00, 0x00, 0x68, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x21, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x42, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x84, 0xf8, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0xf1, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x09, 0x00, 0x00, 0x00, 0x00, 0xf1, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0xe3, 0x00, 0x00, 0x00, 0x00, 0x09, 0xea, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0xc7, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x24, 0x00, 0x00, 0x00, 0x00, 0xc7, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x8f, 0x00, 0x00, 0x00, 0x00, 0x3f, 0xb0, 0x00, 0x00, 0x00, 0x00, 0x8f, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x77, 0x68, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x21, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x42, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00, 0x00},
		matrix.Row{0x00, 0x00, 0xf8, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x84, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x00, 0x00},
		matrix.Row{0x00, 0x09, 0x00, 0x00, 0x00, 0x00, 0xf1, 0x00, 0x00, 0x00, 0x00, 0xf1, 0xf8, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0xea, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x09, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x24, 0x00, 0x00, 0x00, 0x00, 0xc7, 0x00, 0x00, 0x00, 0x00, 0xc7, 0xe3, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0xb0, 0x00, 0x00, 0x00, 0x00, 0x8f, 0x00, 0x00, 0x00, 0x00, 0x8f, 0x3f, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x68, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x77, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x21, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x1f, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x42, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x3e, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x84, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x7c, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0xf8, 0x00, 0x00, 0x00, 0x00, 0x09, 0x00, 0x00, 0x00, 0x00, 0xf1, 0xf1, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x09, 0x00, 0x00, 0x00, 0x00, 0xea, 0x00, 0x00, 0x00, 0x00, 0xe3, 0xe3, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0xe3, 0x00, 0x00, 0x00, 0x00, 0x24, 0x00, 0x00, 0x00, 0x00, 0xc7, 0xc7, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x3f, 0x00, 0x00, 0x00, 0x00, 0xb0, 0x00, 0x00, 0x00, 0x00, 0x8f, 0x8f, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x77, 0x00, 0x00, 0x00, 0x00, 0x68, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x1f, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x21, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x3e, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x42, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x7c, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x84, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xf8, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0xf1, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x00, 0x00, 0x00, 0x00, 0x09, 0xf1, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0xe3, 0x00, 0x00, 0x00, 0x00, 0x09, 0x00, 0x00, 0x00, 0x00, 0xea, 0xe3, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0xc7, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x00, 0x00, 0x00, 0x00, 0x24, 0xc7, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x8f, 0x00, 0x00, 0x00, 0x00, 0x3f, 0x00, 0x00, 0x00, 0x00, 0xb0, 0x8f, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x77, 0x00, 0x00, 0x00, 0x00, 0x68, 0x1f, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x21, 0x3e, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x42, 0x7c, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0xf8, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x84, 0xf8, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0xf1, 0x00, 0x00, 0x00, 0x00, 0xf1, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x09, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0xe3, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x00, 0x00, 0x00, 0x00, 0x09, 0xea, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0xc7, 0x00, 0x00, 0x00, 0x00, 0xc7, 0x00, 0x00, 0x00, 0x00, 0xe3, 0x24, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x8f, 0x00, 0x00, 0x00, 0x00, 0x8f, 0x00, 0x00, 0x00, 0x00, 0x3f, 0xb0, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x77, 0x68, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x1f, 0x21, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00, 0x00, 0x00, 0x00, 0x3e, 0x42, 0x00, 0x00, 0x00},
		matrix.Row{0x00, 0xf8, 0x00, 0x00, 0x00, 0x00, 0xf8, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x84, 0x00, 0x00, 0x00},
	})