Argument Dimension = 4 Argument space has 16 elements. Image Dimension = 4 Image space has 16 elements. 1. Algebraic Normal Form: [Columns = Image components] 1 2 3 4 -------- 0000| 0 1 1 1 0001| 0 1 0 1 0010| 1 0 0 1 0011| 0 0 1 0 0100| 0 1 0 0 0101| 1 1 0 1 0110| 1 0 1 0 0111| 1 1 1 0 1000| 1 0 1 1 1001| 0 1 0 0 1010| 0 1 0 0 1011| 1 0 0 0 1100| 1 1 1 0 1101| 0 1 0 1 1110| 1 0 0 1 1111| 0 0 0 0 2. Truth Table: [Columns = Image components] 1 2 3 4 -------- 0000| 0 1 1 1 0001| 0 0 1 0 0010| 1 1 1 0 0011| 1 0 0 1 0100| 0 0 1 1 0101| 1 0 1 1 0110| 0 0 0 0 0111| 0 1 0 0 1000| 1 1 0 0 1001| 1 1 0 1 1010| 0 0 0 1 1011| 1 0 1 0 1100| 0 1 1 0 1101| 1 1 1 1 1110| 1 0 0 0 1111| 0 1 0 1 3. Characteristic Function: 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 -------------------------------------------------------------------------------- 0000| 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0001| 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0010| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0011| 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0100| 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0101| 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0110| 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0111| 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1000| 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1001| 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1010| 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1011| 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1100| 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1101| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1110| 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1111| 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 4. Walsh Spectrum: 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 -------------------------------------------------------------------------------- 0000| 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0001| 0 4 0 4 0 -4 8 4 4 -8 -4 0 4 0 4 0 0010| 0 -4 -8 4 -4 0 -4 0 0 4 -8 -4 4 0 4 0 0011| 0 0 0 0 -4 -4 -4 -4 4 -4 -4 4 -8 0 0 8 0100| 0 0 0 -8 0 0 0 -8 -4 -4 -4 4 4 4 4 -4 0101| 0 -4 0 4 -8 -4 0 -4 0 -4 8 -4 0 4 0 -4 0110| 0 4 8 4 -4 8 -4 0 4 0 -4 0 0 4 0 -4 0111| 0 0 0 8 4 4 4 -4 -8 0 0 0 -4 4 4 4 1000| 0 0 -4 4 4 -4 0 0 4 4 0 8 0 8 -4 -4 1001| 0 -4 -4 0 -4 8 0 4 0 -4 4 8 4 0 0 4 1010| 0 -4 -4 0 8 4 -4 0 4 -8 0 -4 -4 0 0 -4 1011| 0 -8 4 4 0 0 4 -4 0 0 -4 4 0 -8 -4 -4 1100| 0 0 -4 -4 -4 4 8 0 0 0 -4 -4 -4 4 -8 0 1101| 0 4 -4 0 -4 0 0 4 -4 0 0 4 -8 -4 4 -8 1110| 0 4 -4 0 0 4 4 -8 8 4 4 0 0 -4 4 0 1111| 0 -8 4 -4 0 0 4 4 4 4 0 0 -4 4 8 0 5. Linear Profile: [To normalize divide by 16] 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 -------------------------------------------------------------------------------- 0000| 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0001| 0 1 0 1 0 1 4 1 1 4 1 0 1 0 1 0 0010| 0 1 4 1 1 0 1 0 0 1 4 1 1 0 1 0 0011| 0 0 0 0 1 1 1 1 1 1 1 1 4 0 0 4 0100| 0 0 0 4 0 0 0 4 1 1 1 1 1 1 1 1 0101| 0 1 0 1 4 1 0 1 0 1 4 1 0 1 0 1 0110| 0 1 4 1 1 4 1 0 1 0 1 0 0 1 0 1 0111| 0 0 0 4 1 1 1 1 4 0 0 0 1 1 1 1 1000| 0 0 1 1 1 1 0 0 1 1 0 4 0 4 1 1 1001| 0 1 1 0 1 4 0 1 0 1 1 4 1 0 0 1 1010| 0 1 1 0 4 1 1 0 1 4 0 1 1 0 0 1 1011| 0 4 1 1 0 0 1 1 0 0 1 1 0 4 1 1 1100| 0 0 1 1 1 1 4 0 0 0 1 1 1 1 4 0 1101| 0 1 1 0 1 0 0 1 1 0 0 1 4 1 1 4 1110| 0 1 1 0 0 1 1 4 4 1 1 0 0 1 1 0 1111| 0 4 1 1 0 0 1 1 1 1 0 0 1 1 4 0 6. Differential Profile: [To normalize divide by 8] 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 -------------------------------------------------------------------------------- 0000| 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0001| 0 1 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0010| 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1 1 0011| 0 0 0 1 0 0 1 2 0 0 0 1 2 0 1 0 0100| 0 0 1 0 1 0 0 0 0 2 1 0 0 1 1 1 0101| 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0110| 0 0 1 0 1 1 1 2 1 0 0 0 0 1 0 0 0111| 0 0 1 1 0 2 0 0 0 1 1 0 1 0 1 0 1000| 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 2 1001| 0 0 0 0 1 1 0 0 1 0 1 0 2 1 1 0 1010| 0 0 1 0 1 0 2 0 1 0 0 2 0 0 1 0 1011| 0 0 1 3 0 1 1 0 0 0 0 0 0 1 0 1 1100| 0 2 0 0 0 0 2 0 0 0 0 0 1 1 1 1 1101| 0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 1110| 0 1 1 0 0 0 1 1 1 1 0 0 1 0 0 1 1111| 0 1 1 0 0 0 0 0 1 1 2 0 0 1 0 1 7. Linearity/nonlinearity measures: Linear potential: 4/16 [Higher values mean more linearity.] [Theoretical minimum = 1/16 | maximum = 1] Differential potential: 3/8 [Higher values mean more linearity.] [Theoretical minimum = 1/16 | maximum = 1] Nonlinearity: 4 [Lower values mean more linearity.] [Theoretical minimum = 0 | maximum = 6]