// 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}
}
// 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)
}
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},
})
