SAFER+ Invertible Linear Transformation

• Transformation Matrix M

2 2 1 1 16 8 2 1 4 2 4 2 1 1 4 4

1 1 1 1 8 4 2 1 2 1 4 2 1 1 2 2

1 1 4 4 2 1 4 2 4 2 16 8 2 2 1 1

1 1 2 2 2 1 2 1 4 2 8 4 1 1 1 1

4 4 2 1 4 2 4 2 16 8 1 1 1 1 2 2

2 2 2 1 2 1 4 2 8 4 1 1 1 1 1 1

1 1 4 2 4 2 16 8 2 1 2 2 4 4 1 1

1 1 2 1 4 2 8 4 2 1 1 1 2 2 1 1

2 1 16 8 1 1 2 2 1 1 4 4 4 2 4 2

2 1 8 4 1 1 1 1 1 1 2 2 4 2 2 1

4 2 4 2 4 4 1 1 2 2 1 1 16 8 2 1

2 1 4 2 2 2 1 1 1 1 1 1 8 4 2 1

4 2 2 2 1 1 4 4 1 1 4 2 2 1 16 8

4 2 1 1 1 1 2 2 1 1 2 1 2 1 8 4

16 8 1 1 2 2 1 1 4 4 2 1 4 2 4 2

8 4 1 1 1 1 1 1 2 2 2 1 2 1 4 2

• The matrix M is based on the Pseudo-Hadamard Transform (PHT) in the original SAFER family of ciphers.

• The matrix M can be realized as a series of 2-PHT butterflies and Armenian Shuffles ( a kind of permutation).

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