crypto-slides-23-dc-ddt.1x1

crypto-slides-23-dc-ddt.1x1 - Appendix - The Difference...

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Unformatted text preview: Appendix - The Difference Distribution Tables c Eli Biham - August 18, 2010 687 Appendix - The Difference Distribution Tables (23) The Difference Distribution Table of S1 Input XOR 0x 1x 2x 3x 4x 5x 6x 7x 8x 9x Ax Bx Cx Dx Ex Fx 10x 11x 12x 13x 14x 15x 16x 17x 18x 19x 1Ax 1Bx 1Cx 1 Dx 1Ex 1Fx 0x 1 x 64 0 00 00 14 4 00 48 04 24 00 10 2 08 24 00 66 04 20 00 68 08 24 08 04 08 44 06 26 06 44 0 10 42 02 24 2x 3x 00 06 08 22 06 62 24 10 4 0 12 40 62 0 10 08 48 88 24 00 24 42 46 80 64 10 8 60 60 24 40 24 10 6 40 60 10 6 4x 5x 6x 000 024 044 10 6 4 0 10 10 244 826 048 088 246 286 224 066 482 664 464 002 648 664 204 10 0 4 224 022 10 6 0 842 084 466 10 6 6 600 800 14 2 0 222 Output XOR 7x 8x 9x Ax Bx Cx Dx Ex Fx 000 0 0 0 0 0 0 4 0 10 12 4 10 6 2 4 406 8 6 12 6 4 2 264 4 0 2 2 2 0 604 6 4 2 8 6 2 204 4 0 12 2 4 6 284 4 2 4 2 0 12 424 8 2 2 2 4 4 406 2 8 8 2 2 4 022 8 0 10 0 2 12 064 6 0 4 0 2 10 026 2 6 6 4 2 12 006 6 4 6 6 14 2 606 4 6 0 2 0 2 066 4 0 0 4 0 8 248 2 2 2 6 8 8 14 0 6 6 12 4 6 8 6 640 6 6 0 4 0 0 664 2 6 6 0 4 0 620 6 8 4 6 4 6 282 2 4 4 8 4 0 10 6 2 0 10 0 4 6 4 6 10 2 0 2 0 6 2 6 244 4 6 6 6 2 0 224 6 8 6 6 2 2 6 10 4 0 4 2 8 4 0 662 2 0 4 4 6 8 462 2 4 2 2 4 2 12 6 4 0 0 2 4 4 0 2 10 0 2 6 6 6 14 0 0 6 4 10 8 2 2 6 2 868 0 0 0 4 6 4 c Eli Biham - August 18, 2010 688 Appendix - The Difference Distribution Tables (23) The Difference Distribution Table of S1 (cont.) Input XOR 20x 21x 22x 23x 24x 25x 26x 27x 28x 29x 2Ax 2Bx 2Cx 2 Dx 2Ex 2Fx 30x 31x 32x 33x 34x 35x 36x 37x 38x 39x 3Ax 3Bx 3Cx 3 Dx 3Ex 3Fx 0x 1 x 2 x 000 042 10 4 6 044 12 0 0 644 004 10 4 2 12 2 2 422 424 12 2 2 422 626 662 222 046 482 426 446 0 8 16 224 262 2 2 12 062 622 646 264 0 10 4 086 482 484 3x 10 4 2 8 2 12 10 0 8 10 6 2 4 2 2 2 0 10 4 2 6 0 2 4 2 4 4 0 0 2 2 2 4x 5x 0 12 48 28 02 22 44 10 10 24 26 02 02 46 02 84 02 26 12 6 22 42 10 8 20 80 80 24 20 12 6 68 02 12 0 26 24 40 6x 8 10 2 6 2 4 2 2 12 4 8 6 10 4 4 8 2 2 2 4 0 0 2 4 2 4 0 4 4 0 4 2 Output XOR 7x 8x 9x Ax Bx Cx Dx Ex Fx 206 4 4 4 2 0 12 0 4 4 10 0 4 0 2 8 222 6 0 4 0 4 10 066 2 10 2 4 0 10 0 14 14 2 0 2 6 2 4 10 2 2 2 0 4 2 2 2 404 6 4 4 4 2 0 048 0 4 8 8 4 4 002 6 0 4 0 6 2 0 0 14 10 2 4 6 0 4 2 2 14 2 6 2 6 2 2 202 6 2 6 0 8 4 422 4 8 8 4 2 6 424 6 0 8 2 0 6 640 6 2 12 2 6 4 824 4 6 8 2 4 2 282 4 4 6 2 2 4 260 0 2 2 4 10 8 466 4 8 2 2 8 0 240 2 2 4 6 2 4 12 6 0 0 0 0 8 0 6 0 14 4 6 8 0 2 14 0 242 6 8 6 4 10 0 10 4 4 2 6 0 2 2 4 246 4 4 4 6 10 10 840 2 4 2 4 4 0 622 6 2 2 6 4 0 646 8 6 4 4 6 2 260 4 12 4 4 2 0 844 0 4 0 12 4 4 14 4 2 0 2 0 8 4 4 442 4 8 8 6 2 2 c Eli Biham - August 18, 2010 689 Appendix - The Difference Distribution Tables (23) The Difference Distribution Table of S2 Input XOR 0x 1x 2x 3x 0x 64 0 0 0 1x 0004 2x 0002 3x 4848 4x 0000 5x 2048 6x 0 12 6 4 7x 4664 8x 0004 9x 14 2 4 10 Ax 0662 Bx 6220 Cx 0004 Dx 6262 Ex 0 6 12 8 Fx 0820 10x 0008 11x 6646 12x 0626 13x 4040 14x 0664 15x 6820 16x 0864 17x 6486 18x 0646 19x 2464 1Ax 0684 1Bx 0644 1Cx 0466 1 Dx 0622 1Ex 0482 1Fx 4266 4x 5x 00 02 04 46 06 24 64 24 04 28 10 4 24 0 14 10 2 04 66 04 40 24 86 10 0 82 22 44 10 4 42 24 0 12 12 0 60 10 6 22 6x 0 6 6 4 0 6 6 4 0 2 10 6 0 0 2 8 10 6 12 6 2 0 4 0 0 4 2 6 4 4 6 2 Output XOR 7x 8x 9x 000 4 0 14 400 242 14 0 6 620 2 2 10 264 8 0 10 624 262 2 10 2 10 0 6 4 0 10 082 244 202 482 464 002 12 6 2 222 264 462 248 264 282 422 0 10 2 16 4 4 084 486 Ax Bx Cx Dx Ex Fx 0 0 0 0 0 0 8 6 8 4 6 2 4 6 10 10 12 6 2 4 6 2 0 4 10 4 10 6 4 4 8 4 2 4 10 2 2 8 2 0 0 0 2 4 4 6 0 6 16 6 6 0 6 4 0 0 2 2 2 4 2 4 2 2 4 2 0 6 6 4 4 8 2 4 4 8 6 6 4 2 8 2 2 4 4 4 6 2 0 6 4 6 8 0 4 2 8 10 0 10 6 4 10 2 2 4 0 0 0 4 4 6 2 2 0 6 4 8 2 14 2 2 4 4 2 2 2 2 2 14 10 2 6 2 6 0 6 6 4 4 4 2 4 2 0 0 4 8 2 6 6 8 0 6 4 2 2 6 2 4 4 8 2 4 4 2 10 2 6 2 0 0 10 2 2 0 0 4 6 8 0 2 4 4 0 6 10 6 4 0 0 2 c Eli Biham - August 18, 2010 690 Appendix - The Difference Distribution Tables (23) The Difference Distribution Table of S2 (cont.) Input XOR 20x 21x 22x 23x 24x 25x 26x 27x 28x 29x 2Ax 2Bx 2Cx 2 Dx 2Ex 2Fx 30x 31x 32x 33x 34x 35x 36x 37x 38x 39x 3Ax 3Bx 3Cx 3 Dx 3Ex 3Fx 0x 0 0 4 8 10 6 2 6 8 0 4 2 10 2 2 12 0 0 8 2 0 0 8 6 0 0 4 16 0 0 4 4 1x 2x 00 46 12 8 20 40 0 12 24 00 08 24 04 26 68 22 40 46 40 10 2 46 26 12 6 12 4 24 22 88 20 02 44 26 16 10 40 00 3x 4x 20 82 42 28 00 28 42 26 24 10 2 86 40 60 40 2 10 82 24 06 06 10 2 46 62 04 26 10 6 08 84 28 28 24 10 2 20 5x 12 10 2 4 4 6 2 4 12 8 2 2 6 0 4 6 4 2 4 0 0 4 0 6 2 0 2 2 4 2 4 8 Output XOR 6x 7x 8x 9x Ax Bx Cx Dx Ex Fx 10 4 0 0 0 2 14 2 8 10 4226 4 2 6 2 0 6 0028 8 6 0 6 0 2 2648 2 2 6 4 2 4 0268 6 10 8 0 2 4 10 0 0 8 2 6 0 0 2 2 10 14 2 0 4 2 2 4 6 4 2444 8 4 8 0 6 6 2026 2 0 6 2 0 10 6 4 0 10 0 2 10 0 2 4 4466 2 6 2 2 4 4 2628 8 4 4 4 8 2 4442 4 4 0 0 2 4 0284 4 6 10 2 14 4 2022 6 2 8 8 10 2 2804 0 2 0 8 2 0 8 6 10 6 2 12 0 0 0 6 10 2 6 0 2 0 6 6 4 8 4846 8 0 2 2 2 0 0 6 4 4 12 8 4 2 2 0 4440 4 6 4 2 4 4 4 0 10 0 0 8 0 8 0 6 4208 4 2 6 16 2 2 4822 6 2 2 2 4 8 2040 4 2 4 0 4 10 10 4 10 0 8 4 4 4 4 6 2248 2 0 4 10 10 2 2644 4 2 0 2 2 2 6 0 10 2 2 4 4 10 4 0 4280 0 8 0 6 2 0 2 14 4 2 6 6 0 0 6 0 2402 4 4 4 14 10 6 c Eli Biham - August 18, 2010 691 Appendix - The Difference Distribution Tables (23) The Difference Distribution Table of S3 Input XOR 0x 0x 64 1x 0 2x 0 3x 8 4x 0 5x 6 6x 0 7x 2 8x 0 9x 10 Ax 0 Bx 2 Cx 0 Dx 8 Ex 0 Fx 4 10x 0 11x 8 12x 0 13x 4 14x 0 15x 4 16x 0 17x 0 18x 0 19x 4 1Ax 0 1Bx 4 1Cx 0 1 Dx 0 1Ex 0 1Fx 0 1x 0 0 0 6 0 2 10 0 0 2 10 6 0 2 4 6 0 2 2 4 6 8 6 6 8 2 8 10 6 2 4 6 2x 3x 00 02 02 10 4 04 48 66 04 0 10 02 60 2 10 08 80 42 46 04 26 82 12 0 44 28 10 2 60 46 48 64 20 88 06 82 80 4x 0 0 0 8 0 6 10 4 0 10 14 2 0 0 4 2 0 4 4 2 6 2 8 6 6 4 4 2 4 2 4 10 5x 6x 00 42 20 60 24 10 6 04 44 44 46 64 24 12 12 42 24 24 12 4 02 80 22 46 48 42 24 06 2 10 06 42 28 84 60 64 Output XOR 7x 8x 9x 000 12 0 14 804 644 2 0 12 228 12 2 4 2 10 4 606 206 046 042 408 028 4 10 4 862 804 084 880 10 2 2 286 042 022 462 240 222 448 482 0 12 0 620 4 10 0 642 Ax Bx Cx Dx Ex Fx 0 0 0 0 0 0 0 4 8 2 6 10 12 10 4 6 8 8 0 0 0 4 2 2 8 4 6 8 10 4 2 0 2 0 4 2 0 0 6 4 0 0 4 8 4 4 4 6 6 6 6 0 8 8 0 4 6 2 4 6 6 0 4 0 2 2 6 0 2 8 14 0 0 4 2 10 2 2 14 2 6 2 4 2 4 4 4 4 2 8 6 2 0 6 2 4 2 6 2 14 0 8 12 2 10 0 2 2 2 2 4 2 14 0 2 2 4 4 4 8 6 2 2 0 0 8 2 2 2 6 8 2 2 8 4 6 4 4 2 10 6 8 2 0 4 2 10 0 6 6 6 8 2 6 0 2 0 10 2 2 2 4 2 8 4 2 8 2 10 0 4 0 2 0 4 2 4 10 0 14 2 6 4 8 4 2 2 10 4 0 0 2 c Eli Biham - August 18, 2010 692 Appendix - The Difference Distribution Tables (23) The Difference Distribution Table of S3 (cont.) Input XOR 20x 21x 22x 23x 24x 25x 26x 27x 28x 29x 2Ax 2Bx 2Cx 2 Dx 2Ex 2Fx 30x 31x 32x 33x 34x 35x 36x 37x 38x 39x 3Ax 3Bx 3Cx 3 Dx 3Ex 3Fx 0x 1 x 2 x 000 10 8 8 12 6 4 220 482 602 620 024 6 2 10 028 260 10 2 6 10 4 6 424 402 820 0 10 8 262 204 446 062 460 444 482 0 8 12 264 602 226 024 468 864 264 3x 4x 00 08 42 60 12 6 08 44 16 8 06 40 42 64 24 44 10 0 04 62 04 82 86 2 16 10 8 40 42 02 06 24 00 2 12 62 42 00 Output XOR 5x 6x 7x 8x 9x Ax Bx Cx Dx Ex Fx 44802 2 4 10 16 12 2 42406 6 6 0 0 2 0 4 10 2 0 4 4 2 4 4 0 2 2 4 0 4 12 4 2 6 4 8 8 4 2 10 2 2 2 4 2 0 4 0 20288 2 2 4 4 10 6 0 4 0 4 2 14 0 8 10 0 6 66602 4 4 0 2 2 2 40442 4 8 2 2 8 2 4 0 6 4 10 4 8 4 4 4 2 44648 4 4 4 2 4 6 48042 2 0 2 4 4 6 2 2 2 4 10 4 4 0 2 6 2 2 4 16 2 0 0 4 4 2 6 6 6 10 4 2 6 6 2 2 0 2 8 44264 6 2 4 8 4 6 0 4 2 10 4 4 6 2 0 6 0 28822 2 0 2 12 6 6 84484 2 8 6 2 0 2 60222 6 4 12 0 0 2 2 2 2 12 2 4 0 4 2 0 8 02260 0 6 2 10 2 6 66444 4 4 0 6 2 8 26024 8 4 10 0 6 2 2 6 6 2 10 2 2 0 8 0 4 46480 4 4 2 4 8 2 64442 2 6 12 2 6 2 10 4 8 4 2 4 8 4 4 0 6 20620 2 8 4 6 4 10 2 2 2 10 2 6 6 2 4 2 0 10 2 0 2 2 4 2 4 2 10 2 10 8 2 2 8 6 4 6 2 0 4 c Eli Biham - August 18, 2010 693 Appendix - The Difference Distribution Tables (23) The Difference Distribution Table of S4 Input XOR 0x 1x 2x 3x 4x 5x 0x 64 0 0 0 0 0 1x 0 0 0 0 0 16 2x 000804 3x 862024 4x 000800 5x 4 2 2 8 2 12 6x 088488 7x 426460 8x 000408 9x 844440 Ax 066064 Bx 0 12 0 8 0 0 Cx 000408 Dx 844440 Ex 066460 Fx 066464 10x 000008 11x 4 2 2 16 2 4 12x 000804 13x 826064 14x 088080 15x 844048 16x 088488 17x 462420 18x 088884 19x 444044 1Ax 066460 1Bx 066464 1Cx 088884 1 Dx 444044 1Ex 066064 1Fx 0 0 12 8 12 0 Output XOR 6x 7x 8x 9x Ax Bx Cx Dx Ex Fx 0000 0 0 0 0 0 0 16 0 0 16 16 0 0 0 0 0 4804 4 8 8 8 8 0 8260 4 6 0 6 2 8 12 4 0 12 0 4 8 4 4 8 0 2 2 0 12 2 8 2 2 4 0080 8 0 4 0 0 8 16 6 2 0 0 2 4 2 6 4 4804 8 8 4 8 8 0 8440 0 4 4 4 4 8 4664 4 6 0 6 6 0 0 0 12 0 0 12 8 12 0 0 4804 8 8 4 8 8 0 0448 0 4 4 4 4 8 4664 0 6 4 6 6 0 0660 4 6 4 6 6 0 12 4 0 12 8 4 0 4 4 8 0220 4 2 16 2 2 4 4804 4 8 8 8 8 0 0628 4 2 0 2 6 8 8088 0 0 0 0 0 16 0440 8 4 0 4 4 8 0080 8 0 4 0 0 8 0 2 6 16 0 6 4 6 2 4 0080 4 0 8 0 0 8 16 4 4 0 4 4 0 4 4 4 4664 0 6 4 6 6 0 0660 4 6 4 6 6 0 0080 4 0 8 0 0 8 0 4 4 16 4 4 0 4 4 4 4664 4 6 0 6 6 0 0 12 0 0 0 0 8 0 12 0 c Eli Biham - August 18, 2010 694 Appendix - The Difference Distribution Tables (23) The Difference Distribution Table of S4 (cont.) Input XOR 20x 21x 22x 23x 24x 25x 26x 27x 28x 29x 2Ax 2Bx 2Cx 2 Dx 2Ex 2Fx 30x 31x 32x 33x 34x 35x 36x 37x 38x 39x 3Ax 3Bx 3Cx 3 Dx 3Ex 3Fx Output XOR 0x 1x 2x 3x 4x 5x 6x 7x 8x 9x Ax Bx Cx Dx Ex Fx 0 0 0 8 0 0 0 12 0 0 0 12 8 12 12 0 0480848840 4 4 0 4 8 0 8220248628 4 6 0 6 6 0 4628240260 4 6 8 6 2 4 0664640660 4 6 4 6 6 0 0844400488 0 8 4 8 4 0 0660648268 4 2 0 2 2 8 4628240260 4 6 8 6 2 4 16 4 4 0 4 4 4 4 4 4 4 4 0 4 4 0 0628240268 4 6 8 6 2 0 0 2 2 16 2 4 4 2 2 4 4 2 16 2 2 0 8 0 4 0 4 8 16 4 0 0 8 0 0 0 4 8 8444408448 0 4 4 4 4 0 4264680620 8 2 4 2 6 4 16 0 0 0 0 16 0 0 0 0 16 0 0 0 0 16 16 0 0 0 0 0 16 0 0 16 0 0 0 0 0 16 0664640660 4 6 4 6 6 0 0844400488 0 8 4 8 4 0 16 6 6 4 6 0 4 2 6 4 0 2 4 2 2 0 0264688620 8 2 4 2 6 0 0 12 12 8 12 0 0 0 12 0 0 0 8 0 0 0 0480848840 4 4 0 4 8 0 0224204624 0 6 4 6 6 16 0264688620 8 2 4 2 6 0 0440444444 4 4 0 4 4 16 0628240268 4 6 8 6 2 0 0440488448 8 4 0 4 4 0 16 4 4 0 4 0 0 4 4 0 0 4 0 4 4 16 0444408448 0 4 4 4 4 8 4264680620 8 2 4 2 6 4 0 2 2 8 2 12 4 2 2 4 12 2 8 2 2 0 8 4 0 8 0 0 0 0 4 16 0 4 8 4 0 8 c Eli Biham - August 18, 2010 695 Appendix - The Difference Distribution Tables (23) The Difference Distribution Table of S5 Input XOR 0x 1x 2x 3x 4x 5x 6x 7x 8x 9x Ax Bx Cx Dx Ex Fx 10x 11x 12x 13x 14x 15x 16x 17x 18x 19x 1Ax 1Bx 1Cx 1 Dx 1Ex 1Fx 0x 64 0 0 8 0 12 0 2 0 8 0 4 0 10 0 4 0 6 0 0 0 4 0 0 0 0 0 2 0 4 0 0 1x 0 0 0 2 0 2 8 0 0 6 6 2 0 4 6 4 0 6 2 0 12 8 6 6 10 4 2 8 10 6 2 6 2x 3x 00 04 04 46 08 04 46 48 02 04 86 24 0 10 22 48 08 00 10 10 42 62 26 02 10 2 84 80 62 16 2 12 0 26 20 62 84 4x 0 0 0 4 0 0 4 4 0 0 0 8 0 0 4 0 0 4 10 8 4 8 14 8 6 4 12 0 6 8 4 8 5x 0 10 10 4 4 4 6 2 8 6 8 10 2 6 6 2 4 0 4 0 0 0 0 4 4 4 2 2 6 2 0 8 Output XOR 6x 7x 8x 9x 0000 8604 6406 2268 10 6 0 6 8240 2244 6628 10 4 0 4 6 2 2 10 0 0 8 10 6426 10 2 0 6 16 0 0 2 10 2 4 4 0282 4 12 0 2 2624 0 10 8 6 0446 4484 2422 2244 0284 0444 2642 0640 2684 6482 4660 0 2 12 2 0662 Ax Bx Cx Dx Ex Fx 0 0 0 0 0 0 2 2 12 10 2 4 4 2 4 8 10 6 6 4 4 0 2 2 6 4 8 6 0 6 16 2 0 2 0 8 6 0 6 0 2 10 6 2 2 0 6 6 10 4 8 4 4 6 2 8 6 2 0 2 4 2 8 0 0 4 2 2 6 2 2 2 10 6 6 6 2 4 10 2 2 4 0 4 4 2 4 0 2 4 4 2 8 4 4 12 8 10 4 6 12 2 0 6 2 4 2 0 0 6 0 6 6 0 2 8 2 8 10 4 4 4 6 2 4 0 4 2 4 8 8 6 0 6 0 4 6 4 0 2 2 8 6 2 6 4 4 4 0 6 2 4 12 2 10 0 0 4 0 4 4 8 0 6 0 0 8 6 0 4 4 4 2 0 8 6 2 4 2 4 2 6 2 10 10 4 0 6 0 6 2 2 c Eli Biham - August 18, 2010 696 Appendix - The Difference Distribution Tables (23) The Difference Distribution Table of S5 (cont.) Input XOR 20x 21x 22x 23x 24x 25x 26x 27x 28x 29x 2Ax 2Bx 2Cx 2 Dx 2Ex 2Fx 30x 31x 32x 33x 34x 35x 36x 37x 38x 39x 3Ax 3Bx 3Cx 3 Dx 3Ex 3Fx 0x 1 x 00 00 14 4 20 62 60 12 0 12 2 28 64 44 46 86 44 60 10 4 04 06 46 8 10 04 04 44 42 04 08 0 14 02 00 06 44 86 2x 3x 08 06 0 10 04 84 08 04 02 46 68 02 26 26 04 24 02 84 64 02 0 14 42 16 0 46 22 84 12 0 40 22 10 2 12 2 10 0 60 4x 5x 08 62 02 22 44 28 04 0 12 24 84 24 00 48 06 06 26 64 10 2 64 80 14 4 84 22 42 12 0 22 46 44 60 48 24 42 Output XOR 6x 7x 8x 9x 2604 6 4 6 10 12 2 2 2 10 4 0 8 6226 2664 4408 2244 6066 6200 6200 12 2 0 4 6044 4 2 4 12 6 4 2 10 10 2 0 2 0 6 10 4 0044 6060 0820 0868 0444 2 12 2 4 0822 0 8 10 2 2 2 12 4 0062 8682 0262 0882 8822 2442 Ax Bx Cx Dx Ex Fx 4 4 6 6 8 8 14 4 0 0 4 2 10 2 0 0 2 2 8 2 6 8 0 8 6 2 6 2 2 2 2 2 4 2 6 6 4 0 12 8 0 4 8 4 8 2 2 0 4 0 2 2 2 10 2 2 10 0 2 4 6 4 10 4 4 12 12 2 6 4 0 4 0 2 6 0 6 2 0 4 4 6 4 6 6 10 6 2 0 0 2 4 6 2 2 10 2 4 2 6 4 0 0 0 4 6 12 6 4 6 4 10 6 0 2 4 0 4 4 0 2 2 0 4 6 0 0 8 0 4 4 4 4 8 2 4 4 0 2 12 6 2 8 6 0 0 0 4 2 10 0 8 0 4 4 4 10 8 0 0 4 6 2 2 6 14 2 0 2 10 2 4 10 8 2 0 2 2 4 4 0 2 6 8 4 0 8 6 2 4 6 0 c Eli Biham - August 18, 2010 697 Appendix - The Difference Distribution Tables (23) The Difference Distribution Table of S6 Input XOR 0x 1x 2x 3x 4x 5x 6x 7x 8x 9x Ax Bx Cx Dx Ex Fx 10x 11x 12x 13x 14x 15x 16x 17x 18x 19x 1Ax 1Bx 1Cx 1 Dx 1Ex 1Fx 0x 1 x 64 0 00 00 08 00 10 2 08 66 00 10 4 0 14 46 00 12 0 06 22 00 62 08 66 04 22 04 26 04 26 06 04 00 24 0 10 06 2x 3x 4x 000 060 020 080 080 444 448 402 060 260 440 202 0 12 0 2 10 6 404 226 080 646 420 12 0 12 628 664 14 6 8 800 668 024 608 10 2 4 8 2 12 068 828 686 5x 0 2 10 6 0 8 4 10 2 2 2 2 10 4 4 2 8 2 4 2 6 4 4 2 4 4 2 4 2 6 2 4 Output XOR 6x 7x 8x 9x Ax Bx Cx Dx Ex Fx 0000 0 0 0 0 0 0 6204 2 4 6 16 14 2 6 10 0 2 4 8 6 6 8 2 4644 4 12 2 4 2 0 8006 8 10 2 4 10 8 8422 0 4 0 8 0 4 2 2 12 0 2 6 6 2 2 2 2222 6 6 8 0 6 2 16 4 0 2 6 2 4 12 6 4 6240 8 6 4 4 2 4 2 2 10 4 4 4 6 4 2 2 12 8 2 2 2 6 8 2 0 6 4608 4 4 2 12 2 0 4242 6 0 2 6 0 4 10 8 6 2 4 6 2 0 6 2 6 2 10 4 8 2 6 4 4 2 0 12 0 4 2 6 8 4 6 6 6466 4 2 4 0 6 0 2 0 4 10 6 2 8 6 4 4 0662 0 4 0 2 4 2 0 2 6 10 4 0 2 4 6 4 2626 8 4 4 0 4 4 2620 2 0 4 2 0 10 0226 0 8 8 2 12 6 2264 6 4 2 4 2 4 4648 6 4 2 2 6 4 4642 4 6 2 0 4 10 2666 2 2 6 6 2 2 6286 6 2 4 0 4 2 0268 6 0 2 4 0 10 0264 2 4 6 4 2 4 2442 2 0 2 4 2 12 c Eli Biham - August 18, 2010 698 Appendix - The Difference Distribution Tables (23) The Difference Distribution Table of S6 (cont.) Input XOR 20x 21x 22x 23x 24x 25x 26x 27x 28x 29x 2Ax 2Bx 2Cx 2 Dx 2Ex 2Fx 30x 31x 32x 33x 34x 35x 36x 37x 38x 39x 3Ax 3Bx 3Cx 3 Dx 3Ex 3Fx 0x 1 x 00 28 16 2 04 10 8 02 22 84 68 24 60 12 0 42 62 46 10 0 0 12 26 42 42 04 6 12 02 10 2 04 24 84 04 06 06 42 04 2x 3x 00 68 46 04 06 42 0 12 08 46 40 06 40 60 26 24 48 82 10 4 28 22 42 42 24 26 14 0 80 04 66 16 0 22 24 66 Output XOR 4x 5x 6x 7x 8x 9x 066404 446684 242064 4 6 10 4 2 2 12 6 10 4 8 0 044040 226244 242406 042248 886864 646824 042226 068642 644262 244242 066204 060066 222460 10 8 8 6 0 2 6 0 4 0 10 6 640462 422482 4 4 4 0 2 10 14 2 2 6 2 0 820444 620626 620468 2 2 2 14 0 12 222842 268242 4 0 6 10 4 2 484048 Ax Bx Cx Dx Ex Fx 8 8 4 6 10 8 0 4 0 2 2 0 8 2 0 2 2 4 6 2 4 6 6 4 0 0 0 0 0 0 10 10 4 10 6 4 8 0 6 6 8 0 2 4 4 8 2 6 2 6 4 2 2 4 0 4 4 4 2 0 0 2 2 4 6 8 10 6 10 2 4 0 2 8 4 6 4 2 4 8 4 2 4 2 4 6 4 10 4 2 4 2 6 2 2 8 0 2 8 2 6 6 2 6 0 2 4 12 2 4 4 2 2 0 6 4 0 4 8 6 6 4 2 8 0 12 2 0 6 4 4 2 12 4 0 10 4 2 4 6 2 0 4 2 2 0 8 2 4 8 4 2 8 6 2 6 6 0 6 0 4 6 0 4 2 2 8 0 0 12 6 2 2 0 6 2 6 2 4 10 4 6 6 2 6 2 4 0 4 8 2 2 c Eli Biham - August 18, 2010 699 Appendix - The Difference Distribution Tables (23) The Difference Distribution Table of S7 Input XOR 0x 0x 64 1x 0 2x 0 3x 8 4x 0 5x 6 6x 0 7x 4 8x 0 9x 10 Ax 0 Bx 0 Cx 0 Dx 6 Ex 0 Fx 2 10x 0 11x 6 12x 0 13x 4 14x 0 15x 4 16x 0 17x 8 18x 0 19x 0 1Ax 0 1Bx 0 1Cx 0 1 Dx 4 1Ex 0 1Fx 2 1x 0 0 0 2 0 0 2 6 0 8 10 2 0 6 12 0 0 10 0 4 8 4 6 2 16 8 2 6 8 4 0 2 2x 0 0 0 12 0 0 12 4 0 4 6 2 0 2 10 0 0 10 8 2 6 8 10 4 2 0 4 2 4 4 2 10 3x 0 2 0 2 8 2 0 12 8 8 2 2 4 4 10 0 4 4 8 2 2 2 2 2 2 2 8 6 4 0 2 14 4x 5x 6x 000 044 0 12 2 686 044 808 848 042 006 622 12 2 4 486 048 264 024 688 028 420 282 860 882 404 222 640 606 4 4 10 12 4 0 424 266 024 12 6 2 242 Output XOR 7x 8x 9x Ax Bx Cx Dx Ex Fx 000 0 0 0 0 0 0 14 0 12 4 6 2 6 6 4 204 0 4 8 12 6 14 064 4 2 2 0 0 2 808 8 12 2 6 2 2 402 6 0 10 6 6 6 244 4 2 6 0 6 2 0 0 14 2 6 4 0 0 6 10 0 4 12 4 6 6 0 8 026 8 2 0 6 0 0 044 6 4 4 0 0 6 440 4 2 6 4 2 14 402 6 0 14 12 8 2 664 8 8 0 2 0 0 286 4 2 0 0 2 2 062 4 6 8 0 6 8 606 4 10 8 4 8 4 440 2 8 4 2 2 2 864 2 8 0 0 8 0 222 0 4 6 8 14 0 642 0 2 8 6 0 2 10 8 2 4 4 4 2 0 4 4 10 8 2 2 0 4 10 0 644 2 2 0 4 8 8 062 8 0 6 0 2 8 480 6 4 2 6 2 4 644 0 2 0 6 4 8 464 8 4 2 0 10 2 664 6 8 0 2 0 2 242 2 4 10 10 8 4 0 12 2 2 4 2 6 8 4 446 0 2 4 8 0 0 c Eli Biham - August 18, 2010 700 Appendix - The Difference Distribution Tables (23) The Difference Distribution Table of S7 (cont.) Input XOR 20x 21x 22x 23x 24x 25x 26x 27x 28x 29x 2Ax 2Bx 2Cx 2 Dx 2Ex 2Fx 30x 31x 32x 33x 34x 35x 36x 37x 38x 39x 3Ax 3Bx 3Cx 3 Dx 3Ex 3Fx 0x 1 x 00 42 10 6 06 42 20 6 10 40 14 4 22 24 16 6 26 62 24 22 06 08 24 0 16 04 06 20 66 02 44 16 6 20 00 24 46 14 0 2x 0 6 0 2 0 2 0 2 6 0 0 2 6 4 8 2 8 4 0 6 14 0 2 6 2 16 4 0 8 12 6 0 3x 14 2 2 2 6 16 10 0 4 2 0 4 8 2 0 8 2 0 0 8 8 0 2 8 2 8 0 2 0 2 6 0 4x 5x 08 12 2 44 24 82 24 06 22 46 08 02 6 10 22 88 22 02 84 62 64 20 22 10 8 46 42 88 06 20 04 12 8 22 20 80 Output XOR 6x 7x 8x 9x Ax Bx Cx Dx Ex Fx 4204 2 8 2 6 0 14 4 0 6 4 10 2 4 2 2 2 10 0 4 0 12 2 8 0 0 2 6 10 0 4 8 2 2 6 0 10 6082 2 0 8 2 12 2 6468 2 4 0 6 0 2 4422 4 6 2 4 2 2 14 0 4 6 6 2 12 2 4 4 2066 2 2 4 0 2 2 4246 4 4 6 4 12 4 8 12 0 8 2 4 8 4 4 6 2222 2 2 4 2 2 0 0608 4 2 2 6 8 2 2824 4 0 2 0 8 4 2402 8 4 14 6 0 6 2646 8 8 6 2 0 6 4 0 10 4 4 6 0 0 2 6 2660 0 2 6 4 8 10 10 6 6 4 6 2 4 6 2 2 2242 8 4 0 4 6 0 2 4 16 2 2 2 0 2 0 4 2260 0 8 6 4 4 8 4422 4 2 4 16 10 0 4440 6 8 2 4 0 0 0222 0 6 6 4 10 10 4244 2 6 0 2 2 0 2604 8 10 0 0 4 2 4426 2 6 6 12 12 2 2664 0 2 2 4 6 4 0 4 6 10 2 6 4 2 0 6 4 8 2 10 4 6 0 4 2 0 6842 0 0 4 8 4 6 c Eli Biham - August 18, 2010 701 Appendix - The Difference Distribution Tables (23) The Difference Distribution Table of S8 Input XOR 0x 0x 64 1x 0 2x 0 3x 6 4x 0 5x 4 6x 0 7x 6 8x 0 9x 8 Ax 0 Bx 2 Cx 0 Dx 6 Ex 0 Fx 8 10x 0 11x 0 12x 0 13x 4 14x 0 15x 0 16x 0 17x 0 18x 0 19x 6 1Ax 0 1Bx 2 1Cx 0 1 Dx 8 1Ex 0 1Fx 4 1x 2x 3x 4x 0000 0060 0080 0282 0020 10 6 0 0 0 10 4 6 2828 0040 4060 0 16 4 6 8062 0020 0 4 10 2 0684 0422 0040 6462 4086 2268 16 4 2 6 10 6 0 6 12 6 4 6 6806 12 2 2 8 4808 4628 4 8 10 2 12 6 4 6 6 0 0 10 4868 2426 Output XOR 5x 6x 7x 8x 9x Ax Bx Cx Dx Ex Fx 00000 0 0 0 0 0 0 16 10 0 0 0 6 0 14 6 2 4 10 4 2 0 10 2 4 8 8 6 2 64066 6 2 2 0 8 6 4 6 12 0 6 8 4 10 4 8 0 2 6 0 4 10 4 6 8 2 0 2 44826 4 2 4 2 2 6 10 6 6 4 2 0 4 0 0 0 6 64208 6 10 8 2 2 12 44624 6 2 12 2 0 4 64046 4 2 2 0 0 10 6 0 4 4 10 0 2 10 2 6 2 10 10 6 0 6 6 6 2 6 10 0 08622 6 10 2 2 2 2 8 0 2 10 6 2 4 6 2 4 2 42226 4 6 0 2 14 6 0 8 12 0 0 8 8 2 10 6 6 26646 4 6 0 4 4 4 28424 4 6 2 4 10 0 6 2 2 14 2 2 4 2 2 2 4 02640 4 6 4 6 4 0 02822 0 8 2 6 6 6 00086 6 2 2 6 4 2 24660 2 6 4 4 2 8 0 8 0 10 4 4 2 4 2 0 6 0 4 2 0 0 12 2 4 6 2 6 80480 0 0 6 2 0 16 42824 8 2 0 2 4 2 42260 4 4 2 10 2 0 0 0 8 10 4 2 2 2 8 4 0 2 4 4 10 2 2 4 2 0 6 2 24026 2 2 2 16 8 2 c Eli Biham - August 18, 2010 702 Appendix - The Difference Distribution Tables (23) The Difference Distribution Table of S8 (cont.) Input XOR 0x 1x 2x 20x 000 21x 002 22x 806 23x 480 24x 404 25x 046 26x 260 27x 660 28x 10 2 6 29x 400 2Ax 880 2Bx 220 2Cx 266 2 Dx 804 2Ex 622 2Fx 8 12 4 30x 046 31x 468 32x 666 33x 664 34x 0 2 12 35x 644 36x 462 37x 228 38x 048 39x 444 3Ax 880 3Bx 826 3Cx 066 3 Dx 228 3Ex 640 3Fx 066 3x 16 10 0 6 8 8 6 0 2 14 2 0 2 4 4 6 2 0 2 2 4 0 2 2 4 8 4 4 6 0 0 0 4x 5x 04 28 64 04 46 28 44 22 4 12 2 10 02 42 46 62 22 64 10 2 46 46 40 10 4 10 0 22 44 26 06 20 44 60 10 0 44 44 6x 0 10 10 8 2 8 4 6 12 4 4 10 2 0 6 2 2 0 0 0 0 0 6 4 6 0 10 4 0 2 0 6 Output XOR 7x 8x 9x Ax Bx Cx Dx Ex Fx 0 0 14 6 4 2 0 4 14 006 6 0 10 2 2 6 206 8 0 4 4 2 4 6 2 2 10 4 8 0 0 2 486 2 0 0 4 4 8 042 4 4 2 2 6 4 660 4 4 10 4 2 2 244 6 10 2 6 2 6 022 4 0 0 0 2 6 286 4 0 4 2 2 2 026 8 14 2 8 0 0 462 4 0 6 4 8 10 026 4 0 6 4 10 4 068 2 4 6 4 4 6 12 4 0 4 2 8 8 0 2 222 4 2 2 4 0 4 248 0 0 8 4 6 6 4 4 6 10 2 2 4 4 0 206 8 2 2 6 6 2 10 2 2 0 6 8 4 0 10 4 12 0 2 4 2 2 2 4 4 10 0 0 4 2 8 8 4 864 2 6 0 4 10 0 262 0 10 6 10 2 0 242 2 4 6 4 4 6 648 2 2 2 4 8 2 400 0 4 8 6 8 2 064 4 6 4 4 4 0 882 4 8 4 2 4 0 12 0 4 0 8 0 2 6 8 10 6 2 6 12 2 4 0 4 10 0 6 8 2 0 4 8 0 c Eli Biham - August 18, 2010 703 Appendix - The Difference Distribution Tables (23) ...
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